[amsat-bb] BY70-1

[Phil Karn]

On 2/23/17 21:47, Scott wrote:
> Very interesting stuff, Phil.
> 
> Brings to mind a couple of questions on the subject of a decaying orbit...
> 
> #1, is there some more-or-less constant altitude where an object is
> considered to have stopped orbiting and started re-entering the
> atmosphere, or does it vary with mass of the object, speed, etc.

Well, atmospheric density decays exponentially with altitude, so there's
no well-defined upper edge. There's the Karman Line that many people
consider the traditional "edge of space", set quite arbitrarily to a
nice round 100 km. But even a satellite at, say, 500 km will come down
in a number of years because it's already re-entered the atmosphere and
losing energy to air drag. (Strictly speaking, you could say that it
never "re-enters" the atmosphere because it never left it in the first
place.)

Karman reportedly chose 100 km as about where an aircraft moving at
orbital velocity would be just barely able to generate enough lift to
support its own weight. I.e., that would be the highest altitude
conceivably reachable with a winged aircraft. I'm not sure how he got
that result since it would depend on the size and shape of the wings,
the aircraft weight, etc. And of course no real aircraft can get
*anywhere* near 100 km with lift, to say nothing of achieving orbital
velocity with current aircraft propulsion. (Even with a rocket engine
Space Ship One could only briefly visit space; it had only about 4% of
the energy needed to attain a minimal orbit.)

>From memory, most meteors and decaying spacecraft break up below the
Karman line, in the mesosphere at maybe 70-80 km. The mesosphere is the
hardest region of the atmosphere to study since it's too high for
balloons and too low for satellites. It can only be briefly visited with
sounding rockets (or well protected re-entering spacecraft.)

So I can't give you an exact altitude, but I could say that an object
"stops orbiting" when its vacuum perigee (i.e., its projected trajectory
if you ignore the atmosphere) goes negative. As long as the vacuum
perigee is positive you could say that the satellite is still in orbit,
if not for long given the rate at which it's losing energy to drag (and
causing the instantaneous vacuum perigee to decrease). And that assumes
the spacecraft remains in one piece.

Just before re-entry, Apollo 11 was in a highly elliptical earth orbit
with a vacuum perigee of 38.5 km. But it lost so much energy to drag
that its vacuum perigee went negative well before it could reach that
original 38.5 km point. Had the vacuum perigee been too high, then when
it got to perigee it would have retained enough energy to fly back out
into space. Mike Collins wrote in his book that he carefully monitored
total spacecraft energy during entry, and he breathed a huge sigh of
relief when it fell below that required to maintain an orbit.


> #2, in the case of a spacecraft with radio TX capability, should we
> expect it to stop transmitting at some point prior to actual re-entry
> (for some electrical or RF reason) or do objects normally keep
> transmitting until they fail structurally due to heat & mechanical
> break-up?

Well, that depends on how much of the drag heat gets into the
electronics and whether they get too hot to function before structural
failure. The air is so thin in the upper mesosphere and the velocity is
still so high that heating effects probably overwhelm aerodynamic
forces, so initial structural failure probably comes from melting, not
mechanical pressure.

--Phil