Question

A1. The International Space Station (ISS) orbits the Earth at an average altitude of 350 km above Earth's surface. (a) Assuming the ISS is in uniform circular motion, how fast is it moving (in m/s)? (b) How long does it take to complete a full orbit?

Answer 1

Given : Consider Mass of earth Mearth= 5.98 x 10^24 kg, and Radius of earth Rearth = 6.37 x 10^6 m

Answer a)

R = Rearth + height = 6.37 x 10^6 m + 350km = 6.72 x 10^6 m

Mearth = 5.98x10^24 kg

G = 6.673 x 10^-11 N m2/kg2

We will begin by determining the orbital speed of the satellite using the following equation:

v = SQRT [ (G•MCentral ) / R ]

The substitution and solution are as follows:

v = SQRT [ (6.673 x 10^-11 N m2/kg2) • (5.98 x 10^24 kg) / (6.72 x 10^6 m) ]

v = 7.705 x 10^3 m/s

Answer b)

the period can be calculated using the following equation:

The equation can be rearranged to the following form

T = SQRT [(4 • pi^2 • R^3) / (G*Mcentral)]

The substitution and solution are as follows:

T = SQRT [(4 • (3.1415)^2 • (6.72 x 10^6 m)^3) / (6.673 x 10^-11 N m2/kg2) • (5.98x10^24 kg) ]

T = 5479.10 secs = 1.521 hrs