A satellite of mass 220 kg is placed into Earth orbit at a height of 850 km abov

Question

A satellite of mass 220 kg is placed into Earth orbit at a height of 850 km above the surface. (a) Assuming a circular orbit, how long does the satellite take to complete one orbit? Incorrect: Your answer is incorrect. It may be easiest to answer part (b) (find the speed of the satellite) first. h (b) What is the satellite's speed? m/s (c) Starting from the satellite on the Earth's surface, what is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the planet's daily rotation. J

Explanation / Answer

(A) r = R + h = 6371 + 850 = 7221 km

r = 7.221 x 10^6 m

for circular motion,

G M m / r^2 = m w^2 r

w^2 = (6.67 x 10^-11)(5.972 x 10^24) / (7.221 x 10^6)^3

w = 1.029 x 10^-3 rad/s

T = 2pi / w = 6109 sec Or 1.70 hrs

(b) v = w r = 7430 m/s

(c) energy input = Ef - Ei

= - (6.67 x 10^-11)(5.972 x 10^24)/2(7.221 x 10^6) + (6.67 x 10^-11)(5.972 x 10^24)/2(6.371 x 10^6)

=3.68 x 10^6 J

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