Question

The International Space Station (ISS) orbits Earth at an altitude of 422 km. (a) What is its orbital speed? (b) What is the speed of a receiving antenna on Earth s equator? (c) Suppose the ISS is moving directly toward the antenna, and the antenna is moving directly away from the ISS. If the ISS transmits a radio signal at 145.8000 MHz, what frequency is received by the antenna?

Answer 1

a)

h = altitude = 422 km = 0.422 x 10⁶ m

R = radius of earth = 6.371 x 10⁶ m

r = orbital radius = R + h = 6.371 x 10⁶ + 0.422 x 10⁶ = 6.793 x 10⁶ m

M = mass of earth = 5.98 x 10²⁴ kg

orbital velocity is given as

v = sqrt(GM/r)

v = sqrt((6.67 x 10^-11) (5.98 x 10²⁴)/(6.793 x 10⁶))

v = 7.7 x 10³ m/s

b)

R = radius of earth at equator = 6.378 x 10⁶ m

r = orbital radius = R = 6.378 x 10⁶ m

M = mass of earth = 5.98 x 10²⁴ kg

orbital velocity of the antenna is given as

v' = sqrt(GM/r)

v' = sqrt((6.67 x 10^-11) (5.98 x 10²⁴)/(6.378 x 10⁶))

v' = 7.91 x 10³ m/s