# From the gravitational law, calculate the weight W (gravitational force with respect to the earth) of a 70 kg spacecraft traveling in a circ

Question

From the gravitational law, calculate the weight W (gravitational force with respect to the earth) of a 70 kg spacecraft traveling in a circular orbit 275 km above the earth’s surface. Express W in Newtons and pounds.

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2 years 2021-07-29T20:08:11+00:00 1 Answers 76 views 0

The  value in Newton is $$W = 631.92 \ N$$

The  value in pounds is    $$W = 142 \ lb$$

Explanation:

From the question we are told that

The  mass of the spacecraft is  $$m = 70 \ kg$$

The distance above  the earth is  $$d = 275 \ km = 275000 \ m$$

Generally the gravitational force with respect to the earth is mathematically represented as

$$W = \frac{G * m * m_e}{ (d + r_e)^2}$$

Here $$m_e$$ is the mass of earth with value $$m_e = 5.978 *10^{24} \ kg$$

$$r_e$$ is the radius of the earth with value  $$r_e = 6371 \ km = 6371000 \ m$$

G is the gravitational constant with value $$G = 6.67 *10^{-11} \ m^3/ kg\cdot s^2$$

So

$$W = \frac{ 6.67 *10^{-11} * 70 * 5.978 *10^{24}}{ (275000 + 6371000)^2}$$

$$W = 631.92 \ N$$

Converting to  pounds

$$W = \frac{631.92 }{4.45}$$

$$W = 142 \ lb$$