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. The international space station has a mass of 4.2 x 105 kg and it orbits the Earth at an average altitude of 400 km above the Earth's surface. The radius of the Earth is 6400 km, and the mass of the Earth is 6.0 x 1024 kg. Assume the only force acting on the space station is the Universal Gravitational Force, Fo, and assume that the orbit is perfectly circular. How long would it take for the space station to make one complete orbit around the Earth given these assumptions? A. 93 minutes B. 3.5 x 10 minutes C. 85 minutes D. 21 minutes E. 1.3 minutes

Respuesta :

Answer:

A. [tex]93[/tex] min

Explanation:

[tex]M[/tex] = mass of earth = 6.0 x 10²⁴ kg

[tex]R[/tex] = Radius of earth = 6400 km = 6.4 x 10⁶ m

[tex]h[/tex] = Altitude above earth = 400 km = 0.4 x 10⁶ m

Radius of orbit of the space station around earth is given as

[tex]r = R + h[/tex]

[tex]r = 6400 + 400[/tex]

[tex]r = 6800[/tex] km

[tex]r = 6.8 \times 10^{6}[/tex] m

[tex]T[/tex] = Time period of orbit of space station

Here we can use Kepler's third law which is given as

[tex]T^{2} = \frac{4\pi ^{2} r^{3}}{GM}[/tex]

Inserting the above values

[tex]T^{2} = \frac{4(3.14)^{2} (6.8\times10^{6})^{3}}{(6.67\times10^{-11})(6.0\times10^{24})}[/tex]

[tex]T^{2} = 3.1\times 10^{7}[/tex]

[tex]T = 5566.53[/tex] sec

[tex]T = 5566.53 \left ( \frac{1min}{60sec} \right )= 93 min[/tex]

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