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If an object enters Earth's atmosphere, what determines whether it burns up or not?

Example

A feather is released from a space-ship 30,000 km away from Earth and falls under the influence of Earth's gravity.

Will it burn up on re-entry or will it float down to the surface unharmed. If it would be unharmed, where is the cutoff point for which objects survive?

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    $\begingroup$ Why was this question downvoted? +1 from me. $\endgroup$
    – pela
    Commented Aug 21, 2015 at 22:41
  • $\begingroup$ Two related articles if interested. Curiously, the tiny meteors will often hit the ground it's just that it goes largely unnoticed as they slow down significantly before they do, more here: science.howstuffworks.com/question486.htm and I thought this was interesting too: earthsky.org/space/… $\endgroup$
    – userLTK
    Commented Aug 22, 2015 at 0:41

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I can give a partial answer to this. In general, larger objects are more likely to break up than smaller ones, and comets are more likely to break up than meteors. A feather would likely burn up too, here's why:

30,000 KM above the surface, or roughly 4.7 earth radii, the escape velocity at that height would be the square root of that or roughly 2.17 times less or 46% of the escape velocity from the surface, so a feather dropped from that height would be traveling at nearly 54% of earth's escape velocity when it hit the atmosphere, or about 6 KM per second. That's about 7 times as fast as a bullet and I'd wager, that would burn up a feather pretty quick.

Speed of space collisions is faster than free-fall velocity can reach cause anything that hits the earth from space is also in free fall and you can add to that any relative velocity between the objects. The slowest meteors hit the earth at about 11 KM per second, not surprisingly, the Earth's escape velocity.

http://www.amsmeteors.org/fireballs/faqf/#12

Now, if you drop a feather from the highest hot air balloon, then it probably would float down to the earth, accelerating faster at first in the thinner atmosphere, then more slowly as the air got thicker.

Small point to add, angle of approach matters too. A glancing blow and the object can effectively bounce off the atmosphere, not burn up in it.

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  • $\begingroup$ Downvote. Speed of collisions has nothing to do with burnup. Shock velocity due to high mach number, however has. $\endgroup$
    – AtmosphericPrisonEscape
    Commented Aug 21, 2015 at 22:23
  • $\begingroup$ I wasn't talking about speed of collision, I was talking about speed when the object hits the atmosphere. I'm open to being corrected, but I think you should provide a bit more info than you did. I have a hard time seeing why expressing hitting the atmosphere at dozens of times the speed of sound makes much difference expressed in KPS vs mach number - which varies due to atmospheric thickness anyway. $\endgroup$
    – userLTK
    Commented Aug 21, 2015 at 23:29

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