- #1

tuki

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## Homework Statement

A Satellite is brought up into a geostationary orbit (altitude 35800km measured from the surface of the earth). Satellite weights 1000.0kg. How much work is required to bring satellite from a surface of the Earth to

geostationary orbit?

## Homework Equations

Newton's law of universal gravitation

$$ F = G \frac{m_1m_2}{r^2} $$

Work is defined as:

$$ W \int F \cdot s ds $$

## The Attempt at a Solution

I want to compute work done by Newton's law of universal gravitation when

moving satellite from the surface of the Earth to the orbit. It should be done with:h0 is surface of the Earth (about 6371 km)

h1 is geostationary orbit (about 6371 km + 35800 km = 42171km)

m1 is mass of the satellite (about 1000 kg)

m2 is mass of the Earth (about 5.972E24)

$$ W = \int_{h_0}^{h_1} G \frac{m_1 m_2}{r^2} dr = - G \frac{m_1 m_2}{h_1} - (- G \frac{m_1 m_2}{h_0} $$

$$ = G m_1 m_2 (\frac{1}{h_1} - \frac{1}{h_0}) \approx 5.3108\cdot 10^{10} \text{ J} $$

However, our textbook suggests that the correct answer would be 5.77E10 Joules. I can't exactly spot out where the mistake is.