Lets say you are on a mission planning team to devise anappropriate orbit for a
ID: 1465835 • Letter: L
Question
Lets say you are on a mission planning team to devise anappropriate orbit for a spy satellite. The linear velocity ofa satellite decides the radius of its circular orbit. Theheight of a satellite is called its altitude (this is the distancebetween the satellite and the surface of theEarth). Let’s say a General wants you to put up a spysatellite high enough so that it will move at the same speed as theEarth rotates. This will result in the satellite staying overone spot of interest on the surface of the Earth and is called ageostationary orbit. Calculate the altitude of a geostationaryorbit. Now let’s say good imaging must take place at analtitude under 2000 km. Tell the General why a geostationaryspy satellite is a bad idea. What would you have to do to keepan eye on one spot on the Earth then?
Explanation / Answer
radius of the earth, re = 6.37*10^6 m
mass of the earth, Me = 5.98*10^24 kg
radius of orbit , r = Re + h
Time peridoe of geostationary satellite,
T = 24 hours
= 24*60*60
= 86400 s
Apply, T = 2*pi*r^(3/2)/sqrt(G*Me)
T^2 = 4*pi^2*r^3/(G*Me)
r^3 = G*Me*T^2/(4*pi^2)
r = (G*Me*T^2/(4*pi^2))^(1/3)
= (6.67*10^-11*5.98*10^24*86400^2/(4*pi^2))^(1/3)
= 4.225*10^7 m
so, h = r - Re
= 4.225*10^7 - 6.37*10^6
= 3.588*10^7 m
= 35880 km
this very large comared to 2000 km
from this height we do not get good images.
so, if the satellite is placed at altitude 2000km
r = 6.37*10^6 + 2000*10^3
= 6.57*10^6 m
T = 2*pi*r^(3.2)/sqrt(G*Me)
= 2*pi*(6.57*10^6)^1.5/sqrt(6.67*10^-11*5.98*10^24)
= 5298 s
= 1.47 hours
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