# If I drop a feather from orbit, would it burn up or “hit” the ground?

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
• An African or a European pigeon? – Mark Adler Jun 15 '15 at 13:34
• A wooden pigeon would certainly burn up. – LocalFluff Jun 15 '15 at 13:48
• 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... – PearsonArtPhoto Jun 15 '15 at 13:48
• @MarkAdler The reference is actually to an African or a European swallow, which i had to say just to nerd it up. – kim holder Jun 15 '15 at 14:15
• – szulat Jun 15 '15 at 14:31

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.

• Related question What is the mass of a pigeon tail feather? – James Jenkins Jun 15 '15 at 16:33
• Note the related question now provides an answer with a mass. – James Jenkins Jun 15 '15 at 17:59
• For reference, the answer quotes 0.05 g for a 10 cm feather. – Mark Adler Jun 15 '15 at 18:33
• According to this PDF an "aerodynamic study on eight bird wings and one single feather in a wind tunnel." is documented here: Withers, P., An Aerodynamic Analysis of Bird Wings as Fixed Airfoils, Journal of Experimental Biology, 90, 143 - 162 (1981) not sure if that will get you the drag or not, but it is a place to start. – James Jenkins Jun 15 '15 at 18:45
• @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 ;-) – Steve Jessop Jun 16 '15 at 10:02