## Related questions with answers

A 200-kg communications satellite is placed into a circular orbit around Earth with a radius of $4.23 \times 10^7 \mathrm{~m}$ (26,300 miles) (a) Find the gravitational force on the satellite. (There is some useful information in Section 2.7.) (b) Use the equation for centripetal force to compute the speed of the satellite. (c) Show that the period of the satellite-the time it takes to complete one orbit-is 1 day. (The distance it travels during one orbit is $2 \pi$, or $6.28$, times the radius.) This is a geasynchronous orbit: the satellite stays above a fixed point on Earth's equator.

Solution

VerifiedIn this problem we are given a communications satellite with mass $m = 200 ~\mathrm{kg}$ placed into a circular orbit around the Earth, with radius $r = 4.23 \cdot 10^7 ~\mathrm{m}$. We must find:

$(a)~~$ Gravitational force $F_g$ acting on the satellite

$(b)~~$ Speed $\upsilon$ of the satellite

$(c)~~$ Period $T$ of the satellite (prove that $T = 1 ~\mathrm{day}$)

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