1. Two suns with identical masses M=5. 1030 kg and separated by a distance 2r=3.
ID: 1463953 • Letter: 1
Question
1. Two suns with identical masses M=5. 1030 kg and separated by a distance 2r=3. 1012 m. orbit about each other
(a) Determine the period of the orbit
2. A space station is in a circular orbit around earth at a height h=400 km above its surface.
(a) Calculate the period of this orbit. (RE=6.37. 106 m, ME=5.98. 1024 kg, G=6.67. 10-11 Nm2 /kg2 )
(b) Determine how much energy is required to lift a communication satellite with a mass of 1200 kg into a geostationary orbit starting from the space station.
Explanation / Answer
1)
a) using circular motion concept,
mv^2 / r = GMm / r^2
v^2 = (6.67 x 10^-11 x 5 x 10^30 ) / (3 x 10^12 /2 )
v = 14910.85 m/s
Period T = 2pi r / v = ( pi x 3 x 10^12 ) / ( 14910.85)
T= 6.32 x 10^8 sec
2) using circular motion concept,
mv^2 / r = GMm / r^2
v^2 = (6.67 x 10^-11 x 5.98 x 10^24 ) / (6.37x10^6 + 400x10^3 )
v = 7675.72 m/s
T = 2pi r / v
T = (2 x pi x (6.37x10^6 + 400x10^3 ) ) / 7675.72
T = 5541.78 sec
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