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I thought this article was super cool! “Torus-Earth” was published on 04 February 2014 by Anders Sandberg in his blog, “Andart.”

00 - torusdonut2
One question at Io9 that came up when they published my Double Earth analysis was “What about a toroidal Earth?” This is by no means a new question, and there has been some lengthy discussions online and earlier modelling. But being a do-it-yourself person I decided to try to analyze it on my own.

Can toroid planets exist?

It is not obvious that a toroid planet is stable.

For all practical purposes planets are liquid blobs with no surface tension: the strength of rock is nothing compared to the weight of a planet. Their surfaces will be equipotential surfaces of gravity plus centrifugal potential. If they were not, there would be some spots that could reduce their energy by flowing to a lower potential. Another obvious fact is that there exists an upper rotation rate beyond which the planet falls apart: the centrifugal force at the equator becomes larger than gravity and material starts to flow into space.

The equilibrium shapes of self-gravitating rotating ellipsoidal planets have been extensively analyzed. Newton started it (leading to some early heroic expeditions to ascertain the true shape of Earth), Maclaurin refined it, Jacobi discovered that for high rotation rates ellipsoids with unequal axes were more stable than the oblate ellipsoids of Maclaurin. Chandrasekar has a nice history of the field. Since then computers have become available, and analytical and numerical calculations of more complex or the relativistic case have been done.

Similarly, equilibrium states of self-gravitating toroid shapes have been examined by Poincare, Kowalewsky and Dyson (Dyson 1893, Dyson 1893b). Indeed, one can at least in theory spin up an ellipsoidal planet into a ring, although there is plenty of potential for complex wobbles that destabilizes the whole system and it looks like there is a “jump” to the ring state. The ring may itself be unstable, in particular to a “bead” instability where more and more mass accumulates at some meridians than others, leading to breakup into two or more orbiting blobs. Dyson analysed this case and found it relevant when the major radius / minor radius > 3 – thin hoops are unstable. There is also a lower rotation rate where the ring become unstable to tidal forces and implodes into a “hamburger” or ellipsoid. So the total mass and angular momentum needs to be in the right region from the start.

It looks like a toroid planet is not forbidden by the laws of physics. It is just darn unlikely to ever form naturally, and likely will go unstable over geological timescales because of outside disturbances. So if we decide to assume it just is there, perhaps due to an advanced civilization with more aesthetics than sanity, what are its properties?

Directions

I will call the two circles along the plane of rotation the equators (the inner and outer). When it does not matter which one I talk about I will just call it “the equator”. As for the poles, they are the circles furthest away from the equatorial plane.

Hubward is towards the rotation axis, rimward is away from it. Planewards is towards the equatorial plane. North is towards the closest part of the North Pole circle, south towards the closest part of the South Pole circle.

Toroid gravity

How does gravity work on a toroid planet?

The case of a very large main radius torus is essentially a cylindrical planet. In this case the gravitational force falls off as 1/r, where r is the distance from the axis. The total force on any section will be proportional to the total mass (proportional to R, the major radius) and the gravitational force (proportional to 1/R), so the overall force will be constant as we increase R. Adding some rotation will balance it. The surface gravity is 2G rho/r, where rho is the mass per unit length. So as long as the surface gravity is big enough (by having a small r) this will overcome the centrifugal acceleration and stuff will indeed stay down. But things are much harder to guess for small radius torii.

I decided to use a Monte Carlo method to estimate the equilibrium shape. Given the total planetary mass and angular momentum, I start out by distributing a number of massive but infinitely thin rings (with the potential borrowed from this physics exercise – it is a good thing electric and gravitational potentials look the same in classical physics). I calculate their joint potential and added a centrifugal potential. This allows me to approximate equipotential surfaces and “fill” the potential near the center of the torus with more and more rings until their mass correspond to the planetary mass. I recalculate the angular speed based on the new mass distribution. Then I repeat the process until the planet either flies apart, implodes into a ball or enough iterations go by. This is not the most elegant way of doing it (the literature uses series expansions in toridal harmonics), but it works for me.

The main result is that toroid planets look feasible for sufficiently large enough angular momentum and mass. The cross-section is neither circular nor elliptic but rather egg-shaped, with a slightly sharper inside curvature than on the outside.

[ Why doesn’t the planet get squashed into a plane disk? The rotational pull tries to flatten the planet, but it must act against the local gravity field which tries to turn it into a ball (or cylinder).]

While these planets are stable in my simulation, the range of feasible values is not huge: most combinations of mass and angular momentum are unstable. And I have not examined the tricky issue of bead instability.

I will look at a chubby toroid of one Earth mass and a small central hole (“Donut”), and a wider hoop-like toroid with 6 Earth masses but more earth-like gravity (“Hoop”).

Donut

Figure 1: Local gravitational acceleration (m/s2) around Donut, as experienced by a co-rotating object.

Figure 1: Local gravitational acceleration (m/s2) around Donut, as experienced by a co-rotating object.

Donut has a hubward/interior equator 1,305 km from the center, and a rimward/exterior equator 10,633 km away. The equatorial diameter is 9,328 km.

The planet extends 1,953 km from the equatorial plane, with a north-south diameter of 3,906 km. The ratio of the diameters is 2.4.

The north-south circumference is 21,587 km (0.54 times Earth), while the east-west circumference is 66,809 km (1.7 of Earth).

The total area 8.2*108 km2, 1.6 times Earth. The total volume is 1.1*1012 km3, within 1% of Earth (after all, Donut was selected as a roughly one Earth mass world). The Volume/area = 1300, 61% of Earth: there is more surface per unit of volume.

One day is 2.84 hours long.

Hoop

Figure 2: Local gravitational acceleration around Hoop, as experienced by a co-rotating object.

Figure 2: Local gravitational acceleration around Hoop, as experienced by a co-rotating object.

Hoop has a hubward/interior equator 8,633 km from the center, and a rimward/exterior equator 19,937 km away. The equatorial diameter is 11,304 km.

The planet extends 4,070 km from the equatorial plane, with a north-south diameter of 8,141 km. The cross-section has roughly the 4:3 ratio of an old monitor. The center of mass circle is 14,294 km from the center.

The north-south circumference is 30,794 km (0.77 of Earth) while the east-west circumference is 125,270 km (3.1 times Earth). The total area is 2.5*109 km2, 4.9 times Earth, and the total volume 6.5*1012 km3, 6 times Earth. The volume/area = 1500, 70% of Earth.

The day is 3.53 hours.

Environment

So, what is life on these torus-Earths?

Gravity

The surface gravity depends on location. It is weakest along the interior and exterior equator, while strongest slightly hubward from the “poles”. This can be a fairly major difference.

Donut

Figure 3: Surface gravity (m/s2) of Donut.

Figure 3: Surface gravity (m/s2) of Donut.

Donut has just below 0.3 G gravitation along the equators and 0.65 G along the poles. The escape velocity is not too different from Earth, 11.4 km/s.

The geosynchronous orbit of Donut is very close to the outer equator, less than 2,000 km up. A satellite orbiting there will stay over one spot, but unlike on Earth it will not be able to cover a hemisphere with transmissions, just a smaller region.

On the other hand, the circumferential velocity at the equator is 6.5 km/s, making launches easier. Launching east a rocket needs just 4.9 km/s velocity to escape.

There is a central unstable Lagrange point at the middle of the hole. A satellite will be attracted to the equatorial plane, but any deviation outwards will be amplified.

Hoop

Figure 4: Surface gravity (m/s2) of Hoop.

Figure 4: Surface gravity (m/s2) of Hoop.

Hoop has 1.1 G gravity along the poles but just 0.75 G along the rimward equator. The hubward equator has slightly higher gravity, 0.81 G.

Escape velocity is 19 km/s (remember, the planet weighs in at 6 earth masses). Rimward equator velocity is 9.9 km/s – a rocket will need to provide 10 km/s to escape if it launches eastward.

Note again that having a low gravity equator and high gravity poles does not mean stuff will roll or drift towards the poles: as mentioned before, the surface is an equipotential surface, so gravity (plus the centrifugal correction) is always perpendicular to it.

But an air mass flowing towards the pole will be squeezed together. In fact, the different gravities will create horizontal pressure differences that are going to interact with temperature differences to set up jet streams in nontrivial ways.

Light

First, the nights and days of these worlds are very short. There is not much time for the environment to cool down or heat up during the diurnal cycle. What really matters is how much light they get over longer periods like seasons. Assuming these worlds orbit at an Earth-like distance from a Sun-like star, these are long enough to matter.

[If the torus-worlds orbited closer, tidal forces would really start to bite and before long the planets would become unstable. Since luminosity grows roughly as the fourth power of star mass and the life zone radius scales as the square root of luminosity, in the life zone the experienced tidal forces scale as M/(√(M4))3=1/M5. That is, bright stars have far less tidal effect on habitable planets: maybe Donut and Hoop better orbit some blue-white F star rather than a G star like the sun to be really safe. ]

Torus-shaped worlds have an outer rim that is not too different from a normal ellipsoidal planet. Days occur with a sunrise at the eastern horizon and a sunset at the western horizon. The sun moves along a great circle that slowly shifts north and south over the year, giving seasons. However, on the interior side things are different. Here other parts of the planet can shadow the sun: to a first approximation we should expect far less solar energy.

We can look at three different cases: zero axial tilt, 23 degrees (like Earth) and 45 degrees.

Zero tilt

For zero tilt the hubward side will never get any sunlight: the sun is always hidden below the horizon or by the arc of the world. At the poles the sun is moving just along the horizon, and slightly inwards there will be a perennial dawn/dusk. The temperature difference will be big, with the interior at subarctic temperatures: this is not entirely different from a tidally locked world, and we should expect water (and maybe carbon dioxide) to condense permanently here. The end result would be an arid (but perhaps not super-hot) outer equator, possibly habitable twilight polar regions, and an iced-over interior.

23 degree tilt

Figure 5: Seasons on Donut during spring, summer, autumn and winter.

Figure 5: Seasons on Donut during spring, summer, autumn and winter.

For a terrestrial 23 degree tilt spring and autumn will be like the zero tilt case: light along the equator, dark inside the hole. But during summer and winter the sun has a chance to shine past the rim and onto the opposite side of the hole. Also, there will be large regions with midnight sun or perpetual night in summer and winter, respectively. On Earth the Polar Regions are small, but here they are at the very least long contiguous circles.

The spring dawns and autumn twilights on the hubward side would have some amazing deep colors, since the sun would be rising past the atmosphere of the other side (already pre-dawned or pre-twilighted, you could say). This would be added to the local atmospheric optics, producing some very deep reds and color gradients. Just before or after sunrise/sunset parts of the corona would also be visible.

These sights would be more impressive if they weren’t so brief. On Earth, the sun moves close to 15° per hour: at its fastest, the sun moves one diameter in 2.1 minutes. On Donut solar motion is 127° and on Hoop 102°: a sunrise takes 15 or 19 seconds, respectively. Coming in at a slanted angle and the delaying effects of atmospheric refraction would prolong things a bit, but to an Earthling it would still look very brief.

Standing on the hubward surface looking up, the other side will be about 20 degrees across on Hoop and 30 degrees on Donut – an enormous arc across the sky.

[Why is Donut not much wider? Donut is very flat, so the world is seen very foreshortened in the sky. Incidentally, this means that when sunlight refracts through the atmosphere on the other side to hit the hubward side during a dawn or twilight it will be far deeper red than on Hoop.]

On the inside, having lit parts of the other side would light things up like moonlight. But the total area could potentially be much larger, making for some very bright (if still nightly) nights. For Hoop, this is potentially 16,000 times stronger than Earth moonlight (8000 lux) when the entire opposite side is lit (assuming an Earthlike albedo), making a night as bright as an overcast day. On Donut this reaches low daylight levels (12000 lux). However, this is the “full opposing side” situation: near the equinoxes only a thin sliver is visible.

Figure 6: Averaged insolation over a day on Donut during spring, summer, autumn and winter for the 23 degree case.

Figure 6: Averaged insolation over a day on Donut during spring, summer, autumn and winter for the 23 degree case.

In the case of Donut, the rather flat surface means that the northern or southern hemisphere will also catch a lot of sunlight: the total heating on the planet is larger during these seasons than in spring and autumn, unlike on Earth where it is constant since the receiving area stays constant. There are also slightly nontrivial effects due to the angle between the surface and the sunlight, making the temperate zones get slightly less energy than the Polar Regions and tropics.

The rimward tropics have a fairly constant inflow of solar energy. As we go towards the poles seasonality becomes stronger: at the tropics there is more energy coming in during summer than ever happens at the equator. But the winters are of course equally darker. At the poles and beyond on the peak-gravity hubward side there is sun for half a year followed by polar night. Here the climate truly swings: the rimward tropics at least have brief 1.5 hour nights, but here they last 6 months. Finally, close to the hubward equator in the hole day and night return even in winter (plus extra light reflected from the other side), making it a bit more temperate

Figure 7: Averaged insolation during different seasons on Donut, as a function of latitude in the 23 degree case. 0 denotes the rimwards equator, 90 the north pole, 180 the hubward equator in the hole, 270 the south pole.

Figure 7: Averaged insolation during different seasons on Donut, as a function of latitude in the 23 degree case. 0 denotes the rimwards equator, 90 the north pole, 180 the hubward equator in the hole, 270 the south pole.

The rather big difference in energy deposited at the sunlit summer side of the hole and the dark winter side of the hole will tend to drive some strong weather – but as we will see, due to the other peculiarities of these worlds evening out the energy differences is harder than on Earth.

Overall, the total energy deposited is 2.5 times higher in the rimward equatorial area than in the temperate and polar areas, and the inside of the hole has about a fourth less energy than the surroundings.

Figure 8: Energy received across a year for different latitudes on Donut.

Figure 8: Energy received across a year for different latitudes on Donut.

Hoop has less self-shadowing. More importantly, it is not as flattened as Donut.

Figure 9: Average insolation during a day on Hoop, 23 degree case.

Figure 9: Average insolation during a day on Hoop, 23 degree case.

Figure 10: Averaged insolation during different seasons on Hoop, as a function of latitude in the 23 degree case. 0 denotes the rimwards equator, 90 the north pole, 180 the hubward equator in the hole, 270 the south pole.

Figure 10: Averaged insolation during different seasons on Hoop, as a function of latitude in the 23 degree case. 0 denotes the rimwards equator, 90 the north pole, 180 the hubward equator in the hole, 270 the south pole.

The seasons at first look like what one would expect. A spring and autumn where the hubward regions are in shadow, summers and winters where one polar circle gets a lot of sunlight and the other far less while the hubward regions get light. Note that this produces a seasonal cycle in the hubward area that is at double frequency of the rimward regions (this is true for Donut too): the warm weather happens in “July” and “January”.

Figure 11: Energy received across a year for different latitudes on Hoop.

Figure 11: Energy received across a year for different latitudes on Hoop.

Somewhat non-intuitively compared to Donut, here the hubward equator does get more sunlight across the year than the Polar Regions . We can hence expect the climate to be a bit like on Earth, with colder Polar Regions and warmer equatorial regions. The rimward equator still gets 60% more energy, though.

45 degree tilt

Perhaps the most surprising thing is that for high enough axial tilt we get four cold zones and four warm!

The easiest way of understanding this is to consider a spherical planet with 90 degree axial tilt like Uranus. For half of the year the North Pole is turned towards the sun and most of the hemisphere has constant daylight. As equinox approaches the axis points sideways, so the planet gets evenly irradiated. The end result is that the poles get more energy than the equator. On a torus world the same dynamics holds true, but now the Polar Regions are circular too.

Figure 12: Energy received across a year for different latitudes on Hoop in the 45 degree case.

Figure 12: Energy received across a year for different latitudes on Hoop in the 45 degree case.

For Hoop the difference is not enormous, about 10% in total insolation. The rimward equator is mildly hotter than the Polar Regions and the hubward equator.

Donut slightly larger differences but in practice most of the surface is dominated by the mildly warm polar regions. The rimward equator is only slightly warmer than the cooler rimward temperate areas.

Geosphere

The surface area is larger than on Earth, and the volume/area ratio is smaller (For Donut the ratio is 1,300 km, for Hoop 1,500 km, for Earth 2,124 km). One might hence suspect that more thermal energy is leaking out, reducing volcanism and plate tectonics. However, even a small amount of tidal heating due to influences from the sun might release plenty of energy stored in angular momentum. In the case of Hoop there are also 6 times more radioisotopes inside the planet than on Earth but only 5 times more surface area.

Continental drift would be affected by the different inner and outer radii. A circle r km inwards from a circle of radius R will be just 2*pi*r km shorter, and the relative change will be r/R. So for Hoop a continental plate drifting from the outer equator across a pole to the inner equator will have to shrink to 43% of its original width to fit. On Donut the effect is much bigger: it becomes 12% of its original width! Hence continental plates moving hubwards on the inside will tend to experience folding, while plates moving rimwards on the inside will experience rifting. Expect some rugged landscape and archipelagoes near the hubward equator.

Gravity affects the height of mountains. On Hoop the difference is not enormous compared to Earth, but on Donut mountains at the poles can be 1.5 times higher (maximum around 12 km) and near the equators 3 times higher (24 km). Combined with the ruggedness near the hole this might make for some dramatic landscapes.

The fast rotation will likely produce a strong magnetic field; unlike on Earth the polar regions will not have auroras since the field lines will not intersect the surface… I think – figuring out dynamo currents in a toroid iron core sounds fun but is beyond me.

Atmosphere

We have seen that the light levels change a lot, and that would make us suspect plenty of wind transporting heat from hot sunlit areas to cool shadowed areas. However, the high rate of rotation means that the Coriolis Effect will influence air and water flows to a large degree.

The Coriolis Effect makes air moving towards or away from the rotational axis bend away, since it has more or less velocity than the ground. A parcel of air “at rest” near the equator has a lot of actual momentum since the equator is moving fast around the rotation axis: if that air were to flow pole-wards it would now have a noticeable velocity eastwards or westwards. This is why the global airflow is not just simple convection cells from the equator towards the poles: as heat is transferred using air polewards the air flow gets twisted around, producing trade winds.

On torus worlds the rotation rate is 8 times faster than on Earth and the velocity differences are larger. Air hence tends to be twisted around far more, producing a more banded zonal climate than on Earth. Exactly how banded is hard to tell without detailed atmospheric calculations, but it is likely more like on Jupiter than on Earth. This in turn means that heat transfer is less effective: the temperature differences between the hot and cold regions will be bigger.

It is likely that there will be inter-tropical convergence zone (ITCZ, alias the doldrums or equatorial lows) around the rimward equator, where winds approaching from north and south will blow westwards (trade winds) while warm air rises, moves away from the equator, cools and descends at a higher or lower latitude (where we should expect major deserts). The big seasonality changes especially on Donut will make the ITCZ shift north and south, triggering monsoons in some regions. However, the rapid rotation will make the Hadley cell thinner than Earth’s 30 degree size (exactly how much thinner is slightly tricky to estimate, since it also depends on the latitude-varying gravity).

Big temperature differences over short distances are going to power plenty of weather, even if it is hard to predict exactly how it is going to look. Especially near the hole on Donut seasonal weather will be wild: warm air from the sunlit side will flow through it in a big vortex, balanced by cool winds from the dark side circulating in the opposite direction.

The scale height, how quickly pressure drops off with altitude, is proportional to gravity. Hence clouds will be 3 to 1.5 times taller on Donut, while Hoop clouds will be more Earth-like.

Like on Earth cyclones can form at the mid-latitudes. Stronger Coriolis forces would make tighter hurricanes, about four times smaller. However, they would tend to last longer on Donut (since the high scale height gives them far more air to play with). Wind speeds depend on the temperature difference between the top of the atmosphere and the ocean, which could vary a great deal across the year.

Hydrosphere

The amount of water on either world is not vastly different from Earth, although Hoop’s 6 times greater mass with merely 5 times greater area would provide it with 20% more water volume from the initial accretion (so for the same coverage the oceans would be 20% deeper). The higher mass might also accumulate more cometary infall, but it is hard to judge how much this would be.

The big seasonal temperature swings will be more pronounced far from the moderating influence of oceans: continents near the poles will be more extreme than equatorial ones. Whether they can maintain ice caps throughout polar summer depends on their layout and the background temperature; since ice reflects away sunlight effectively and the Coriolis Effect can keep air from warming them it is likely. The same for sea ice, although here there is potential for warming sea currents from hubwards or rimwards. Since the flow of water in oceans is constrained by the shape of the basins, the Coriolis Effect will merely drive gyres rather than prevent north-south flow; large oceans like the Pacific will be more east-westerly than narrow north-south oceans like the Atlantic.

The low gravity near the equator will make some tall waves on Donut: they can be expected to be three times taller than on Earth. Waves at Donut’s poles are still 150% of the ones on Earth. Hoop is closer to normal (133% taller at the equator, 90% height at the poles). The wild hubward summer-winter weather on Donut will likely drive some amazing storm waves.

Biosphere

From these considerations, it seems likely that one could have a fairly Earth-like biosphere on Donut and Hoop. Storms, severe weather and long winters are things species on Earth have adapted to fine. There might be interesting differences in ecosystems based on latitude, since there are more variation between different bands than on Earth (gravity, seasonality, temperatures etc.). Also, at least on Hoop each band has a much larger surface area: there is more room for species diversity within each eco-zone.

Moons

Would these worlds be able to keep moons?

A moon orbiting exactly in the equatorial plane in a circular orbit it would just feel a potential looking like it came from a spherical planet of some intermediate density. However, if it orbited in slightly eccentric orbit things would change. The potential field close to the planet falls of more slowly than 1/r (the answer for normal spherical planets): the Kepler ellipse is no longer the right solution. And as soon as the orbit becomes slightly tilted things turn even more complicated – now the moon will feel the flatness.

In many ways this is the problem facing satellite designers already: Earth is oblate enough that orbits are affected. This problem was dealt with in the earliest days of spaceflight (see Wikipedia, (Tremaine & Yavetz 2013) or (Nielsen, Goodwin,& Mersman 1958)).

Basically, the main effect is that an elliptic orbit precesses – it slowly changes direction in space, for Earth largely depending on the inclination. Eccentricity can also drift, which is a bigger deal. In any case, for a toroid world these effects are far larger: the multipole moments (measures of just how non-spherical the field is) are of course enormous. In fact, they are so big that the standard methods no longer work and we need to do computer simulations.

However, I feel confident that moons in sufficiently remote and circular orbits will be pretty stable. Most likely they will precess so that their orbit is more of a rosette than an ellipse, but they will not go crazy. Of course, moons in close orbits are another matter…

Running a simulation (where I did not use the full torus potential, but rather a ring of 30 masses) demonstrate some of the possibilities. Indeed, an equatorial elliptic orbit looks nice and stable but precesses into a rosette.

13 - equatorial

A nearly polar orbit has even more precession, not just making it rosette around in a plane but also slowly precessing the plane. The moon could appear in the sky in any constellation.

14 - polar a and b

What about orbits through the hole? As mentioned earlier, the exact center is an unstable Lagrange point. Place a moon there, and any kick will make it fall out. But there are orbits through the center that look stable (or rather, give them a kick and they turn into another similar-looking orbit rather than fall down). The simplest is just a moon bobbing up and down through the hole:

15 - linear

In fact, one can have a moon bobbing up and down over a particular longitude in a bent rectangular region.

16 - wobblelong

And given some longitudinal velocity, it will move around the hole, filling out a wobbly hyperboloid of one sheet (a “vase orbit”?).

17 - waseorbit

What about orbits that actually go through the hole in just one direction? It turns out that there are plenty of “figure 8”-like orbits that go through, precessing to form a larger torus-shaped tangle.

18 - figure8 a and b

Note that the orbit is a bit “elliptic”, with a lopsided figure 8. From “apogee” above the rimward equator it will go through the hole and turn over the opposite side, where it will have a “perigee” near the antipode of its starting point. Then it will go through the hole, coming out near where it started – but precession will make it wind along the torus. Hence the two-sheet appearance of the entire orbit.

These simulations should be taken as first sketches, since the real case requires quite a bit of computational care. My numerical precision is not good enough to tell what the long term stability truly is. Hoop and Donut have even messier gravity fields since they are flattened, and there will of course be perturbations due to the sun and other planets.

Tidal forces

Tidal forces are an issue. Imagine a moon orbiting equatorially outside a torus world. It causes a bulge of water and rock beneath it. The rapid rotation will tend to push the bulge ahead of the moon (assuming the moon orbits in the same direction the planet turns and is above geostationary orbit). The gravity of the bulge will hence drag the moon forward, imparting a slightly faster motion – which in space means the moon moves outward to a slightly higher orbit.

This is how Luna has absorbed a fair deal of Earths angular momentum, slowing Earth’s rotation and drifting further away. In the case of wild rotation like on a torus-world this effect is bigger: moons will tend to be pushed away and possibly lost.
What happens to close moons, orbiting below the geostationary orbit? They actually move faster than the bulge, and now it slows them. That means a lower orbit. Soon they spiral inwards and become giant meteors. The same happens for retrograde moons when they are too close. Of course, if the moon is big enough it might break up due to tidal forces into a ring.

The wilder orbits through the hole are likely to be destabilized by tidal forces. The bobbing orbits will tend to acquire angular momentum from the bulge, and turn faster and faster – until they crash into the planet or are lost. Some figure-8 orbits might be in the right resonance to gain and lose energy equally, but I suspect they generally have the same problem. So sadly, I suspect torus-worlds will lack the truly exotic moons. However, artificial satellites with a bit of station-keeping are still possible. Those bobbing orbits might be good for communications satellites for the hubward surface.

Summary

Torus-worlds are unlikely to exist naturally. But if they did, they would make awesome places for adventure. A large surface area. Regions with very different climate, seasons, gravity and ecosystems. Awesome skies on the interior surface. Dramatic weather. Moons in strange orbits.
We better learn how to make them outside of simulations.

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Columbia Space Shuttle Disaster Explained (Infographic)

by Karl Tate, SPACE.com Infographics Artist | February 01, 2013 09:14am ET

030201-F-9999G-001

On Feb. 1, 2003, the shuttle Columbia was returning to Earth after a successful 16-day trip to orbit, where the crew conducted more than 80 science experiments ranging from biology to fluid physics. However, the seemingly healthy orbiter had suffered critical damage during its launch, when foam from the fuel tank’s insulation fell off and hit Columbia’s left wing, tearing a hole in it that later analysis suggested might have been as large as a dinner plate.

The damage occurred just after Columbia’s liftoff on Jan. 16, but went undetected. During re-entry, the hole in a heat-resistant reinforced carbon carbon panel on Columbia’s left wing leading edge allowed super-hot atmospheric gases into the orbiter’s wing, leading to its destruction.

Killed in the Columbia shuttle disaster were STS-107 mission commander Rick Husband and included pilot Willie McCool, mission specialists Kalpana Chawla, Laurel Clark and David Brown, payload commander Michael Anderson and payload specialist Ilan Ramon, Israel’s first astronaut.

columbia-space-shuttle-disaster-2003-130129a-02

 

A subsequent inquiry by the Columbia Accident Investigation Board (CAIB) faulted NASA’s internal culture as much as the foam strike as causes of the shuttle disaster. The Columbia accident ultimately led then-President George W. Bush to announce plans to retire NASA’s space shuttle fleet (which was more than 20 years old at the time) once construction of the International Space Station was complete. A capsule-based spacecraft was planned to replace the shuttles. [Photos: The Columbia Space Shuttle Tragedy]

NASA’s space shuttle fleet resumed launches in July 2005, after spending more than two years developing safety improvements and repair tools and techniques to avoid a repeat of the Columbia disaster. In 2011, NASA launched the final space shuttle mission, STS-135, to complete the shuttle fleet’s role in space station construction.

In 2012, NASA’s three remaining shuttles – Discovery, Atlantis and Endeavour – were delivered to museums in Washington, D.C., Florida and California, while the test shuttle Enterprise was delivered to New York City. Under President Barack Obama, NASA was directed to rely on private spacecraft to launch Americans to the International Space Station and return them to Earth. NASA, meanwhile, is developing a new giant rocket – the Space Launch System – and the Orion space capsule for future deep-space missions to an asteroid, the moon and Mars.

Video: Remembering Columbia’s Crew – ‘In Their Own Words’

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I came across the following graphic which made we wonder how fast are we really moving while standing still.

Tangential Speed of Earth's Surface Due to Rotational Motion

In my search, I came across this article.

How Fast Are You Moving When You Are Sitting Still?

By Andrew Fraknoi, Foothill College & the Astronomical Society of the Pacific

Introduction

When, after a long day of running around, you finally find the time to relax in your favorite armchair, nothing seems easier than just sitting still. But have you ever considered how fast you are really moving when it seems you are not moving at all?

Daily Motion

earthWhen we are on a smoothly riding train, we sometimes get the illusion that the train is standing still and the trees or buildings are moving backwards. In the same way, because we “ride” with the spinning Earth, it appears to us that the Sun and the stars are the ones doing the moving as day and night alternate. But actually, it is our planet that turns on its axis once a day — and all of us who live on the Earth’s surface are moving with it. How fast do we turn?

To make one complete rotation in 24 hours, a point near the equator of the Earth must move at close to 1000 miles per hour (1600 km/hr). The speed gets less as you move north, but it’s still a good clip throughout the United States. Because gravity holds us tight to the surface of our planet, we move with the Earth and don’t notice its rotation in everyday life.

The great circular streams of water in our oceans and of air in our atmosphere give dramatic testimony to the turning of the Earth. As the Earth turns, with faster motion at the equator and slower motion near the poles, great wheels of water and air circulate in the northern and southern hemisphere. For example, the Gulf Stream, which carries warm water from the Gulf of Mexico all the way to Great Britain, and makes England warmer and wetter than it otherwise would be, is part of the great wheel of water in the North Atlantic Ocean. The wheel (or gyre) that the Gulf Stream is part of contains more water than all the rivers of the world put together. It is circulated by the energy of our turning planet.

Yearly Motion

sunIn addition to spinning on its axis, the Earth also revolves around the Sun. We are approximately 93 million miles (150 million km) from the Sun, and at that distance, it takes us one year (365 days) to go around once. The full path of the Earth’s orbit is close to 600 million miles (970 million km). To go around this immense circle in one year takes a speed of 66,000 miles per hour (107,000 km/hr). At this speed, you could get from San Francisco to Washington DC in 3 minutes. As they say on TV, please don’t try going this fast without serious adult supervision.

The Sun’s Motion

galaxyOur Sun is just one star among several hundred billion others that together make up the Milky Way Galaxy. This is our immense “island of stars” and within it, each star is itself moving. Any planet orbiting a star will share its motion through the Galaxy with it. Stars, as we shall see, can be moving in a random way, just “milling about” in their neighborhoods, and also in organized ways, moving around the center of the Galaxy.

If we want to describe the motion of a star like our Sun among all the other stars, we run up against a problem. We usually define motion by comparing the moving object to something at rest. A car moves at 60 miles per hour relative to a reference post attached to the Earth, such as the highway sign, for example. But if all the stars in the Galaxy are moving, what could be the “reference post” to which we can compare its motion?

Astronomers define a local standard of rest in our section of the Galaxy by the average motion of all the stars in our neighborhood. (Note that in using everyday words, such as “local” and “neighborhood”, we do a disservice to the mind-boggling distances involved. Even the nearest star is over 25 thousand billion miles (40 thousand billion km) away. It’s only that the Galaxy is so immense, that compared to its total size, the stars we use to define our Sun’s motion do seem to be in the “neighborhood.”)

Relative to the local standard of rest, our Sun and the Earth are moving at about 43,000 miles per hour (70,000 km/hr) roughly in the direction of the bright star Vega in the constellation of Lyra. This speed is not unusual for the stars around us and is our “milling around” speed in our suburban part of the Galaxy.

Orbiting the Galaxy

In addition to the individual motions of the stars within it, the entire Galaxy is in spinning motion like an enormous pinwheel. Although the details of the Galaxy’s spin are complicated (stars at different distances move at different speeds), we can focus on the speed of the Sun around the center of the Milky Way Galaxy.

It takes our Sun approximately 225 million years to make the trip around our Galaxy. This is sometimes called our “galactic year”. Since the Sun and the Earth first formed, about 20 galactic years have passed; we have been around the Galaxy 20 times. On the other hand, in all of recorded human history, we have barely moved in our long path around the Milky Way.

How fast do we have to move to make it around the Milky Way in one galactic year? It’s a huge circle, and the speed with which the Sun has to move is an astounding 483,000 miles per hour (792,000 km/hr)! The Earth, anchored to the Sun by gravity, follows along at the same fantastic speed. (By the way, as fast as this speed is, it is still a long way from the speed limit of the universe—the speed of light. Light travels at the unimaginably fast pace of 670 million miles per hour or 1.09 billion km/hr.)

Moving through the Universe

NationalGeographicTheUniverseMapAs we discussed the different speeds of our planet so far, we always needed to ask, “Compared to what are you measuring this motion?” In your armchair, your motion compared to the walls of your room is zero. Your motion compared to the Moon or the Sun, on the other hand, is quite large. When we talk about your speed going around the Galaxy, we measure it relative to the center of the Milky Way.

Now we want to finish up by looking at the motion of the entire Milky Way Galaxy through space. What can we compare its motion to — what is the right frame of reference? For a long time, astronomers were not sure how to answer this question. We could measure the motion of the Milky Way relative to a neighbor galaxy, but this galaxy is also moving. The universe is filled with great islands of stars (just like the Milky Way) and each of them is moving in its own way. No galaxy is sitting still! But then, a surprising discovery in the 1960s showed us a new way to think of our galaxy’s motion.

The Flash of the Big Bang

the big bangTo understand this new development, we have to think a little bit about the Big Bang, the enormous explosion that was the beginning of space, time, and the whole universe. Right after the Big Bang, the universe was full of energy and very, very hot. In fact, for the first few minutes, the entire universe was hotter than the center of our Sun. It was an unimaginable maelstrom of energy and subatomic particles, slowly cooling and sorting itself out into the universe we know today.

At that early time, the energy in the universe was in the form of gamma rays, waves of energy like the visible light we see, but composed of much shorter waves with higher energy. Today on Earth, it takes a nuclear bomb to produce significant amounts of gamma rays. But then, the whole universe was filled with them. You can think of these gamma-rays as the “flash” of the Big Bang — just like fireworks or a bomb can produce a flash of light, the Big Bang resulted in a flash of gamma rays. But these gamma rays were everywhere in the universe. They filled all of space, and as the universe grew (expanded), the gamma rays expanded with it.

When people first think about the expansion of the universe, they naturally think of other expansions they have experience with: how the American colonies eventually expanded to become the 48 states of the U.S. or how an exploding bomb might throw shrapnel in every direction. In these situations, the space into which the colonies or the shrapnel is expanding already exists. But the expansion of the universe is not like any other expansion. When the universe expands, it is space itself that is stretching. The galaxies in the universe are moving apart because space stretches and creates more distance between them.

What does this mind-stretching idea of stretching space mean for our gamma rays? The gamma rays are waves of energy moving through space. As space stretches, the waves that are in space must stretch too. Stretched gamma rays are called x-rays. So as the universe expanded, the waves of energy filling space stretched out to become less energetic (cooler) x-rays. As the universe continued to expand, the same waves became ultra-violet light. Later they became visible light, but there were no eyes in the hot compressed universe to see them yet. (When we take the lid of a hot pressure cooker, the steam will expand into the room and cool down. In the same way, we can think of the waves of energy in the expanding universe as cooling down — getting less energetic.)

Today, some 12 to 15 billion years after the Big Bang, there has been a lot of stretching. Space has expanded quite a bit. The flash of the Big Bang has stretched until it is now much longer, lower energy waves — microwaves and other radio waves. But the waves have stretched with the space they occupy, and so they still fill the universe, just the way they did at the time of creation.

Astronomers call the collection of all these stretched waves the cosmic background radiation or CBR. Physicists back in the late 1940’s predicted that there should be such a background, but since no one had the equipment to find it, the prediction was forgotten. Then, in the mid 1960s, two scientists working for Bell Laboratories, Arno Penzias and Robert Wilson, accidentally discovered the CBR while helping to get communications satellite technology going for the phone company. After astronomers used other telescopes and rockets in orbit to confirm that the radio waves the two scientists had discovered were really coming from all over space, Penzias and Wilson received the Nobel Prize in physics for having found the most direct evidence for the Big Bang.

Moving through the CBR

IDL TIFF fileWhat, you might be asking yourself, does all this have to do with how fast we are moving? Well, astronomers can now measure how fast the Earth is moving compared to this radiation filling all of space. (Technically, our motion causes one kind of Doppler Shift in the radiation we observe in the direction that we are moving and another in the direction opposite.)

Put another way, the CBR provides a “frame of reference” for the universe at large, relative to which we can measure our motion. From the motion we measure compared to the CBR, we need to subtract out the motion of the Earth around the Sun and the Sun around the center of the Milky Way. The motion that’s left must be the particular motion of our Galaxy through the universe!

And how fast is the Milky Way Galaxy moving? The speed turns out to be an astounding 1.3 million miles per hour (2.1 million km/hr)! We are moving roughly in the direction on the sky that is defined by the constellations of Leo and Virgo. Although the reasons for this motion are not fully understood, astronomers believe that there is a huge concentration of matter in this direction. Some people call it The Great Attractor, although we now know that the pull is probably not due to one group of galaxies but many. Still the extra gravity in this direction pulls the Milky Way (and many neighbor galaxies) in that direction.

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Can you guess who said the following and where it’s from?

Whenever life gets you down, Mrs.Brown
And things seem hard or tough
And people are stupid, obnoxious or daft
And you feel that you’ve had quite enough

Just remember that you’re standing on a planet that’s evolving
And revolving at nine hundred miles an hour
That’s orbiting at nineteen miles a second, so it’s reckoned
A sun that is the source of all our power

The sun and you and me and all the stars that we can see
Are moving at a million miles a day
In an outer spiral arm, at forty thousand miles an hour
Of the galaxy we call the ‘milky way’

Our galaxy itself contains a hundred billion stars
It’s a hundred thousand light years side to side
It bulges in the middle, sixteen thousand light years thick
But out by us, it’s just three thousand light years wide

We’re thirty thousand light years from galactic central point
We go ’round every two hundred million years
And our galaxy is only one of millions of billions
In this amazing and expanding universe

The universe itself keeps on expanding and expanding
In all of the directions it can whizz
As fast as it can go, the speed of light, you know
Twelve million miles a minute and that’s the fastest speed there is

So remember, when you’re feeling very small and insecure
How amazingly unlikely is your birth
And pray that there’s intelligent life somewhere up in space
‘Cause there’s bugger all down here on Earth

How about this?

Do you know like we were sayin’? About the Earth revolving? It’s like when you’re a kid. The first time they tell you that the world’s turning and you just can’t quite believe it ’cause everything looks like it’s standin’ still. I can feel it. The turn of the Earth. The ground beneath our feet is spinnin’ at 1,000 miles an hour and the entire planet is hurtling around the sun at 67,000 miles an hour, and I can feel it. We’re fallin’ through space, you and me, clinging to the skin of this tiny little world, and if we let go… That’s who I am.

John Nelson of IDV Solutions created these awesome animated graphics which show our home as it really is.

A Breathing Earth - The Annual Pulse of Vegitation and Ice 01

A Breathing Earth - The Annual Pulse of Vegitation and Ice 02Source

HOW COOL IS THIS?

Substitute “Daddy” for “Mommy” when necessary.

7 Parenting Tips for Working from Home with Young Children

[By L.R.Knost, author of  Two Thousand Kisses a Day: Gentle Parenting Through the Ages and Stages now available on Amazon]

work at home momWith economies struggling all over the world, more and more moms are trying to juggle work and children. Working from home is one way to earn a living or supplement your household income while still parenting full-time, but it comes with its own unique set of challenges. Here are seven tips to help you parent your little ones gently while operating a home business:

1. Think ‘routine’ instead of ‘schedule.’ Gentle parenting is very much about being in-sync with your child’s needs. Being tied to an inflexible schedule will only cause stress and conflict as your child’s needs evolve from day to day, week to week, month to month, and year to year. Children do, however, enjoy the comfort and familiarity of a regular routine, and knowing what to expect helps them to make transitions throughout the day. So, instead of making a minute to minute schedule, try working with your child to establish a routine that’s flexible enough to adjust to meet their fluctuating needs, but builds into your day the time you need to devote to your work. For example, a routine could look something like this:

    • Morning cuddles, breakfast, playtime with mommy
    • Playtime while mommy works
    • Snack and storytime with mommy
    • Play while mommy works
    • Lunch and outside playtime with mommy
    • Naptime while mommy works
    • Playtime with mommy
    • Playtime while mommy works
    • Help mommy with dinner
    • Dinnertime
    • Help mommy clean up after dinner
    • Playtime while mommy works
    • Evening snack
    • Bathtime, bedtime story, cuddles, night-night time

Notice that there are no time limits, only a loose plan for the day that you can adjust if your little one is sick or teething or just needs some extra mommy time during the day. A younger baby will need more naps during the day and can be worn in a baby carrier for naps and/or in place of playtime, and some toddlers and preschoolers will outgrow their need for naps earlier than others, and some will need more outside time, etc. so you’ll want to come up with a routine that accommodates your child’s age, sleep needs, and temperament. Also, of course, if your spouse or a trusted family member or friend is available to help, be sure to include them in your routine.

2. Children love the novelty value of new toys, so get a box for each of your working days of the week. Label each box with one day of the week and place a set of toys in them that you only bring out on that day. Remember to think outside the box (lol) and don’t only choose store-bought toys. One box could be full of paper towel and toilet paper tubes and various sizes of bouncy balls and hot wheels, etc. so your little one can make tunnels and chutes and all sorts of inventions. Another box could have kitchen utensils and bowls and pots and pans. Don’t be afraid of a little mess, either! Children are washable, and messy play can keep them happily engaged for long stretches of time, so in one box you could have a plastic tablecloth from the dollar store or even a little blow-up wading pool, some paintbrushes, and shaving cream. Just put down the tablecloth or blow up the pool and add a touch of different colors of food coloring to a few small bowls of shaving cream let your little Picasso go to town! The trick is to be creative and choose things that are out of the ordinary that will engage your child’s imagination, not just keep them busy.

3. For older preschoolers or early elementary ages, an independent project is an excellent idea to help them stay happily engaged while you’re working. During your work periods, provide your child with an ongoing project that they’re interested in and can work on independently. It can be a paint-by-number project, a jigsaw puzzle, a simple model car, a jewelry making set, or any number of other things. Since time is a hard concept for young children, setting a timer for your work periods and having a little sticker chart on the fridge for you and your child to ‘clock in’ and ‘clock out’ of work might be a fun, helpful part of your routine, as well.

4. Meal planning is a huge, huge help in freeing up time and mental energy. Take the time to write out a list of every meal you know how to make that your family likes, then break each of those meals down into their ingredients. Save the list on your laptop, and then twice a month simply cut and paste two weeks of meals into a Word doc. Then print it out, cross off any ingredients you already have on hand, and ‘voila’ you have a shopping list and menu for two weeks done in one shot!

5. Simplify, simplify, simplify. Be realistic about your commitments and expectations for yourself. Have fruit and cheese for breakfast most mornings instead of eggs and pancakes and sausage. It’s healthier, faster, and there’s less to cleanup! Resign from any pre-working-at-home commitments you can such as directing your church’s Vacation Bible School or doing the book work for your local food pantry. No one expects you to be able to do everything, and someone else can take on those tasks while you’re doing double duty as a work-and-stay-at-home-mom. And, once you’ve cleared up your commitments, avoid the temptation to fill up your time with playgroups and playdates and mommy-and-me classes. Your little ones need you, not activities.

6. Don’t be afraid to go mobile. Find a local park that is suitable for your child’s age and temperament (i.e. Don’t go to a park with a lake if your little one is a runner, and don’t choose a playground with only big kid slides and jungle gyms if you’ve got a toddler.). Once you’ve found a park that’s a good fit, take your laptop or iPhone and answer emails or return phone calls or do other simple tasks that you can manage while swinging your little one in a baby swing or watching your toddler dig in the sand. Make sure you take the time to play with them while you’re there, too, and don’t worry if you get a few judgmental looks from other parents. They don’t know your life, but you know you’re doing the best you can to meet your child’s needs while doing what you need to do for work, so take comfort in that knowledge.

7. Don’t forget to take care of yourself! We can get so caught up in meeting our family’s needs at times that we forget to take care of our own needs. Make sure you include a bit of downtime in your routine each day to simply be still and have a cup of coffee or read the newspaper or simply stare out the window and daydream for a few minutes. Take the time on a regular basis to do your nails, go have your hair done, and make a lunch date with a friend. Even if you bring your little one with you, you’ll still be out and about in a non-working environment for a bit and actually get to feel like an adult. If you’ve got a teething baby or a sick child and aren’t getting much sleep at night, take a nap during the day when your little one’s asleep instead of working during their nap. You may get a bit less work done, but you’ll enjoy your life and your family more, and isn’t that really the point of it all anyway?

*reprinted with permission from The Natural Parent Magazine

Related posts:

 L.R.Knost is a best-selling parenting and children’s book author and founder and director of Little Hearts/Gentle Parenting Resources, an online resource for gentle parenting education, articles, and research. Books by L.R.Knost include Whispers Through Time: Communication Through the Ages and Stages of Childhood , Two Thousand Kisses a Day: Gentle Parenting Through the Ages and Stages , and The Gentle Parent: Positive, Practical, Effective Discipline the first three books in the Little Hearts Handbook gentle parenting series, as well as her children’s picture books Petey’s Listening Ears and the soon-to-be-released Grumpykins series available from Amazon and other major retailers.

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snide morons and the space pen

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I was made aware of this post by a friend via Facebook. I loved it and read it while looking up at my daughter multiple times while she slept soundly in her bed. I hope that you enjoy it as much as I have.

I was in tears as I read through this list, as I’m sure many grown daughters will be. Mothers – bookmark this list of rules and encourage your daughter’s daddy to read them, memorize them, and put them in to action. And, to all you Dads out there – be sure you pay close attention and heed these wise words.

About Michael 
Michael Mitchell is an (almost) thirty-something dad who blogs daily tips and life lessons for dads of daughters at lifetoheryears.com. He spends his days practicing the arts of fatherhood and husbandry, while attempting to be a man of God and a professional raiser of philanthropic funds. On the rare occasion he’s not tied up with the aforementioned and other pursuits of awesomeness, he enjoys fighting street gangs for local charities and drinking from a cup that’s half full. Bookmark Life To Her Years, follow Michael on Twitter, and “like” him on Facebook for more “rules”.


1. Love her mom. Treat her mother with respect, honor, and a big heaping spoonful of public displays of affection. When she grows up, the odds are good she’ll fall in love with and marry someone who treats her much like you treated her mother. Good or bad, that’s just the way it is. I’d prefer good.


2. Always be there. Quality time doesn’t happen without quantity time. Hang out together for no other reason than just to be in each other’s presence. Be genuinely interested in the things that interest her. She needs her dad to be involved in her life at every stage. Don’t just sit idly by while she add years to her… add life to her years.


3. Save the day. She’ll grow up looking for a hero. It might as well be you. She’ll need you to come through for her over and over again throughout her life. Rise to the occasion. Red cape and blue tights optional.


4. Savor every moment you have together. Today she’s crawling around the house in diapers, tomorrow you’re handing her the keys to the car, and before you know it, you’re walking her down the aisle. Some day soon, hanging out with her old man won’t be the bees knees anymore. Life happens pretty fast. You better cherish it while you can.


5. Pray for her. Regularly. Passionately. Continually.


6. Buy her a glove and teach her to throw a baseball. Make her proud to throw like a girl… a girl with a wicked slider.


7. She will fight with her mother. Choose sides wisely.


8. Go ahead. Buy her those pearls.


9. Of course you look silly playing peek-a-boo. You should play anyway.


10. Enjoy the wonder of bath time.


11. There will come a day when she asks for a puppy. Don’t over think it. At least one time in her life, just say, “Yes.”


12. It’s never too early to start teaching her about money. She will still probably suck you dry as a teenager… and on her wedding day.


13. Make pancakes in the shape of her age for breakfast on her birthday. In a pinch, donuts with pink sprinkles and a candle will suffice.


14. Buy her a pair of Chucks as soon as she starts walking. She won’t always want to wear matching shoes with her old man.



Photo Credit :: Danielle Rocke Toews

15. Dance with her. Start when she’s a little girl or even when she’s a baby. Don’t wait ‘til her wedding day.


16. Take her fishing. She will probably squirm more than the worm on your hook. That’s OK.


17. Learn to say no. She may pitch a fit today, but someday you’ll both be glad you stuck to your guns.


18. Tell her she’s beautiful. Say it over and over again. Someday an animated movie or “beauty” magazine will try to convince her otherwise.


19. Teach her to change a flat. A tire without air need not be a major panic inducing event in her life. She’ll still call you crying the first time it happens.


20. Take her camping. Immerse her in the great outdoors. Watch her eyes fill with wonder the first time she sees the beauty of wide open spaces. Leave the iPod at home.


21. Let her hold the wheel. She will always remember when daddy let her drive.


22. She’s as smart as any boy. Make sure she knows that.


23. When she learns to give kisses, she will want to plant them all over your face. Encourage this practice.


24. Knowing how to eat sunflower seeds correctly will not help her get into a good college. Teach her anyway.


25. Letting her ride on your shoulders is pure magic. Do it now while you have a strong back and she’s still tiny.


26. It is in her nature to make music. It’s up to you to introduce her to the joy of socks on a wooden floor.


27. If there’s a splash park near your home, take her there often. She will be drawn to the water like a duck to a puddle.


28. She will eagerly await your return home from work in the evenings. Don’t be late.


29. If her mom enrolls her in swim lessons, make sure you get in the pool too. Don’t be intimidated if there are no other dads there. It’s their loss.


30. Never miss her birthday. In ten years she won’t remember the present you gave her. She will remember if you weren’t there.


31. Teach her to roller skate. Watch her confidence soar.


32. Let her roll around in the grass. It’s good for her soul. It’s not bad for yours either.


33. Take her swimsuit shopping. Don’t be afraid to veto some of her choices, but resist the urge to buy her full-body beach pajamas.


34. Somewhere between the time she turns three and her sixth birthday, the odds are good that she will ask you to marry her. Let her down gently.


35. She’ll probably want to crawl in bed with you after a nightmare. This is a good thing.


36. Few things in life are more comforting to a crying little girl than her father’s hand. Never forget this.


37. Introduce her to the swings at your local park. She’ll squeal for you to push her higher and faster. Her definition of “higher and faster” is probably not the same as yours. Keep that in mind.


38. When she’s a bit older, your definition of higher and faster will be a lot closer to hers. When that day comes, go ahead… give it all you’ve got.


39. Holding her upside down by the legs while she giggles and screams uncontrollably is great for your biceps. WARNING: She has no concept of muscle fatigue.


40. She might ask you to buy her a pony on her birthday. Unless you live on a farm, do not buy her a pony on her birthday. It’s OK to rent one though.


41. Take it easy on the presents for her birthday and Christmas. Instead, give her the gift of experiences you can share together.


42. Let her know she can always come home. No matter what.


43. Remember, just like a butterfly, she too will spread her wings and fly some day. Enjoy her caterpillar years.


44. Write her a handwritten letter every year on her birthday. Give them to her when she goes off to college, becomes a mother herself, or when you think she needs them most.


45. Learn to trust her. Gradually give her more freedom as she gets older. She will rise to the expectations you set for her.


46. When in doubt, trust your heart. She already does.


47. When your teenage daughter is upset, learning when to engage and when to back off will add years to YOUR life. If you succeed in doing this, tell me how.


48. Ice cream covers over a multitude of sins. Know her favorite flavor.


49. This day is coming soon. There’s nothing you can do to be ready for it. The sooner you accept this fact, the easier it will be.


50. Today she’s walking down the driveway to get on the school bus. Tomorrow she’s going off to college. Don’t blink.


Photo Credits can be found at the bottom of Michael’s original post.

**9/15/11**This post has resonated so well with daughters and fathers, mothers and grandfathers, and has received many beautiful and heartfelt comments. As much as it pains me, I have had to disable the comment feature. If you have a comment you would like for the author to see, please contact him via his blog, or email me directly at christineATfromdatestodiapersDOTcom and I’ll be sure to pass it along to Michael.

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I thought that I knew exactly what I wanted my dissertation to be on:
“The Fourth World and the Right of Self-Determination in International Law”

Now after just a few weeks studying Diplomacy and Conflict Studies at the Interdisciplinary Center (IDC) Herzliya, I am beginning to find another subject matter appealing and it is really growing on me:
“The Psychology of Political Decision Making from a Neuroeconomic Perspective”

I wonder if I could do both? Now I know that I am out of my mind for even considering such a thing. Wacko!

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