Question

the international space station has a mass of 419,455 kg. when the station orbits at an altitude of 330,000 m, what is the approximate gravitational force on the station due to earths gravity? (recall that earth has a radius of 6.37 × 10^6 m, it has a mass of 5.97 × 10^24 kg, and g = 6.67 × 10^-11 n·m²/kg².)
a. 2.9 × 10^6 n
b. 3.1 × 10^6 n
c. 3.7 × 10^6 n
d. 3.4 × 10^6 n

Explanation:

Step1: Calculate the distance from the center of the Earth to the station

The radius of the Earth \(R = 6.37\times10^{6}\text{ m}\), and the altitude \(h=330000\text{ m}=3.3\times 10^{5}\text{ m}\). The distance \(r = R + h=(6.37\times 10^{6}+3.3\times 10^{5})\text{ m}=6.7\times10^{6}\text{ m}\)

Step2: Use the formula for gravitational force

The formula for gravitational force \(F = G\frac{Mm}{r^{2}}\), where \(G = 6.67\times10^{-11}\text{ N}\cdot\text{m}^{2}/\text{kg}^{2}\), \(M = 5.97\times10^{24}\text{ kg}\), \(m = 419455\text{ kg}\), and \(r = 6.7\times10^{6}\text{ m}\)

Substitute the values into the formula:

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Answer:

C. \(3.7\times 10^{6}\text{ N}\)