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I know that capsules typically require heat shields to survive reentry from orbit. I'm wondering how an object's size, density and aerodynamic profile affects this.

For more specificity:

  • The feather would be the tail feather of an adult pigeon
  • The orbit would be that of the ISS at +-7.6 km/s
  • By "drop", I mean throw downwards toward earth at 5 m/s so that it de-orbits in a reasonable timeframe
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    $\begingroup$ An African or a European pigeon? $\endgroup$
    – Mark Adler
    Commented Jun 15, 2015 at 13:34
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    $\begingroup$ A wooden pigeon would certainly burn up. $\endgroup$
    – LocalFluff
    Commented Jun 15, 2015 at 13:48
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    $\begingroup$ Your premise that throwing it downward at 5 m/s is flawed. In fact, it would be rather difficult to make it re-enter in a reasonable time., although it would happen eventually... $\endgroup$
    – PearsonArtPhoto ♦
    Commented Jun 15, 2015 at 13:48
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    $\begingroup$ @MarkAdler The reference is actually to an African or a European swallow, which i had to say just to nerd it up. $\endgroup$
    – kim holder
    Commented Jun 15, 2015 at 14:15
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    $\begingroup$ See also: en.wikipedia.org/wiki/Paper_plane_launched_from_space $\endgroup$
    – szulat
    Commented Jun 15, 2015 at 14:31

1 Answer 1

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Throwing it down at 5 m/s will do basically nothing. That will simply cause it to advance in its orbit a bit. To deorbit, you need to throw it backwards, not down. However in this case, since the feather has a such a low ballistic coefficient, it will promptly deorbit from ISS altitude on its own, without you having to do anything at all. Just wait a bit.

Given a 10 cm feather with a mass of 0.05 g, I looked at two cases intended to bound the possibilities. The first case is that the feather trims to a face-on attitude, with the lowest possible ballistic coefficient. It reenters from the ISS altitude in less than three hours. The maximum deceleration is about 10 G's at 100 km altitude. My heating estimate is highly suspect (I am applying a blunt body formula with a nose radius based on feather feature sizes), but my rough estimate is $30\,\mathrm{W/cm^2}$, which is rather a lot for organic material. The feather would not look like a feather anymore.

However it is not clear how it would maintain that attitude. More likely would be a trim with the heavier part of the root of the feather forward. For that I used about 1/40th of the previous $C_D A$, measured from a Vulture feather. (Albeit at completely the wrong Reynolds numbers, but hey, this is just for fun.) Then I get that it decays from the ISS orbit in less than four days, with a maximum deceleration of 8 G's at about 80 km altitude. The heating is much worse, at $200\,\mathrm{W/cm^2}$. That is a typical Mars entry heat rate. The feather would be gone.

If anything, I suspect that my choice of approach and parameters underestimates the heating. So my conclusion is that, alas, the feather will burn up. And I had such high hopes for the feather.

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    $\begingroup$ Related question What is the mass of a pigeon tail feather? $\endgroup$
    – James Jenkins
    Commented Jun 15, 2015 at 16:33
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    $\begingroup$ Note the related question now provides an answer with a mass. $\endgroup$
    – James Jenkins
    Commented Jun 15, 2015 at 17:59
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    $\begingroup$ Why would the feather undergo extreme deceleration? The feather would initially encounter very thin air, presumably producing only a mild deceleration; as it descends, would the force not build only gradually? But... regardless of the deceleration force over the entire feather, molecules of the atmosphere would be striking the feather at orbital velocity. Would that not correspond to very high temperatures? $\endgroup$
    – Anthony X
    Commented Jun 16, 2015 at 1:16
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    $\begingroup$ @AnthonyX: very rough intuition, the high deceleration is because at orbital velocity it doesn't take long to travel from a region of the atmosphere with high terminal velocity, to a region of the atmosphere with much lower terminal velocity ;-) $\endgroup$
    – Steve Jessop
    Commented Jun 16, 2015 at 10:02
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    $\begingroup$ Would recent LightSail decay be a good approximation of how a feather behaves in low orbit, decay-wise? It seems to me they (feather and a 90-95% deployed LightSail's solar sail) should have rather similar $C_D$ and $A/m$, if an altogether different geometry and materials property. $\endgroup$
    – TildalWave
    Commented Jun 19, 2015 at 11:16

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