Scientists want to place a 2600 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 2600 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2.2 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem: m_mars = 4191 times 10^23 kg r_mars 3.397 times 10^6 m G = 6.67428 times 10^-11 N-m^2/kg^2 What is the force of attraction between Mars and the satellite? What speed should the satellite have to be in a perfectly circular orbit? How much time does it take the satellite to complete one revolution? Which of the following quantities would change the speed the satellite needs to orbit at? the mass of the satellite the mass of the planet the radius of the orbit

Explanation / Answer

1)

force of attraction F = G*mmars*msatellite/d^2

d = disance between mars and satellite = 2.2*3.397*10^6 m

F = 6.67428*10^-11*6.4191*10^23*2600/(2.2*3.397*10^6)^2

F = 1994.4 N
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(2)

In circular orbit

Fc = Fg

msatellite*v^2/d = G*msatellite*mmars/d^2

v =sqrt(G*mmars/d)

v = sqrt(6.67*10^-11*6.4191*10^23/(2.2*3.397*10^6))

v = 2393.54 m/s   <<<<<<----answer

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3)

time = 2*pi*d/v = 2*pi*2.2*3.397*10^6/2393.54 = 19618.12 s

1 hr = 3600 s

t = 19618.12/(3600)

t = 5.45 hr

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4)

the radius of the orbit

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