[amsat-bb] Re: Since We Are Off Topic Somewhat.... And drifting slightly

[Tony Langdon]

At 03:55 PM 2/16/2008, Greg D. wrote:

>To go from a low circular orbit to a higher one, you fire your 
>rocket behind you to pick up more speed.  The "point" of the burn 
>becomes the perigee of the new elliptical orbit, and half-way around 
>is the new apogee.   Ok, so far, so good.  Now, if at the instant of 
>apogee you

Yep. :)

>did nothing, you'd fall back down to perigee, and back again to 
>apogee on the next orbit.  But since you fired your rocket to speed 
>you up in the first place, to circularize the orbit you fire your 
>rocket at the point of apogee to slow you down, and in fact to a 
>slower speed than you started.  I would think that would make you 
>drop more steeply down on the next orbit, probably to a lower 
>perigee than you started.

Nope.  You fire the rocket to speed you up, which raises the perigee.

>  Instead, I'd think you should fire in the same direction as the 
> first burn, to make things round, but that would make you go even 
> faster, which Mr. Kepler said was wrong.

You're forgetting that the speed of a satellite in a non circular 
orbit varies as the satellite moves.  In fact, Kepler's Laws state 
that in you were able to attach a string (with a very high elasticity 
and low tension!) between the satellite and the point around which it 
is orbiting, this string would sweep out an equal area every second.


>My head is spinning (no pun intended)...  Where did I go wrong?

Time for a thought experiment.  I'll enlist the aid of Q of Star Trek 
(Next Generation) fame to shrink the Earth to a point, and the 
satellite to a very small size (maybe the size of a grain of 
salt).  We'll put the satellite into a highly elliptical orbit, with 
a perigee of 1 metre above this "Earth singularity", and an apogee of 
around 7000km (equal to 800km above the Earth's real surface).  As 
our satellite orbits this imaginary shrunken Earth, it picks up speed 
until it's travelling at some incredible speed at perigee (any 
mathematicians want to work it out, might even be relativistic, but 
let's assume Newtonian physics apply at all times and velocities - Q 
can make anything happen ;) ).  What happens at apogee is more 
interesting.  We're now approximately 7000 km above the singularity, 
and at the instant of apogee, there is no vertical motion, the 
velocity is horizontal, and only a few metres per _hour_ (since the 
orbit is very narrow).  Now, at the moment of apogee, we accelerate 
our tiny satellite to around 27000 km/h horizontally in the forward 
direction (Thanks Q for the push ;) ).  Hey presto, it's now in a 
circular orbit, approximately 7000km above the Earth singularity.  I 
can now get Q to put the Earth and Relativity back to normal, and we 
have the satellite in a nice 800km circular orbit. :)

Hope that extreme, imaginary example helps illustrate what's going on. :)

Metric was used, because that's the direction NASA and space science 
is headed.  I can work in either system myself... ;)

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