well i just did the math
. (should have warned ya... its a bit long
)
Ok here is the intial tangental velocity an vehicle would have at the equator
Vlaunch site = R * angular velocityof earth
Where R is the radius from the spin axis (radius to the center of the earth)
Vlaunch site = 6378.137 (km)* .0000729212 (rad/s)
Vlaunch site = .4651 (km/s)
ok now for the tangental velocity at the geo sync orbit
Vcircular orbit = Sqrt(mu/R)
Where mu is earths gravitational constant, 3.986*10^5 and R is the radius of the orbit to the center of the earth (altitude (km) + 6378.137(km)
Vcircular orbit = Sqrt(3.986*105(km3/sec2)/42158(km))
Vcircular orbit = Sqrt(9.4549(km2/sec2)
Vcircular orbit = 3.074 km/sec
so as you can see you would not be able to maintain a circular orbit.
ok now to prove that it will burn up ![Wink ;)](http://www.dynaverse.net/forum/Smileys/NewSmilies/wink.gif)
first we must find the specfic mechanical energy which is always negative for elliptacl orbits, 0 for parabolic, and positive for hyperbolic (which makes sense as it takes more energy than what it take sto just take a parabolic orbit)
SME=V2/2 - mu/R
where R is the radius of the orbit, and v is the velocity at that orbit
SME=.4651(km/s)2/2-3.986*105(km3/sec2/42158(km)
SME = -9.23855 (km2/s2)
from here we can calculate the semi major axis
a = - mu/(2*SME)
a = - 3.986*105(km3/(2*-9.23855)
a = 21572.76 km
and now to determine the radius at perogee (closet to earth)
a=(Ra + Rp)/2
we know the Ra (radius at apogee) is 42158 as this is the furthest distance from earth
21572.76(km)=(42158 (km)+ Rp)/2
Rp = 987 (km) < 6378.137(km) and thus will make contact w/ earth.
to prove it has a highly elliptical orbit we must check it eccentricity (e). when e=0 the orbit is circular, 0<e<1, the orbit is elliptical with values closer to one becoming more elliptical, e=1 the orbit is prabolic (leaving earth), e>1 the orbit is hyperbolic (leaving earth, used for interplanatary travel)
e = (Ra - Rp) / (Ra + Rp)
e = (42158(km) - 987(km)) / (42158(km) + 987(km))
e = .95 (unitless)
i would tell you the time it would take but that takes shyt load of time ![Wink ;)](http://www.dynaverse.net/forum/Smileys/NewSmilies/wink.gif)
hope that helps (that took alot of time to type arg lol)
I'll need to go through this later on when I'm more awake, but I can see what Ken Mattingly meant when he said "I don't know how to do 90% of this mission."
I would hate to be the poor sod who has to translate this into roll and pitch angles and burn durations...
Anyway, thanks for taking the time out for that, I appreciate it and will go through it step by step when I'm fully awake in a couple of hours...
![Smiley :)](http://www.dynaverse.net/forum/Smileys/NewSmilies/smiley.gif)