Scientists want to place a 3800 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 3800 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2524 m/s in a perfectly circular orbit. Here is some information that may help solve this problem: mmars 6.4191 x 1025 kg mars 3.397 x 106 m G 6.67428 x 1011 N-m2/kg2 1) What radius should the satellite move at in its orbit? (Measured frrom the center of Mars.) m Submit 2) What is the force of attraction between Mars and the satellite? N Submit 3) What is the acceleration of the satellite in orbit? m/s Submit 4) Which of the following quantities would change the radius the satellite needs to orbit at? the mass of the satellite [y] the mass of the planet the speed of the satellite Submit 5) What should the speed of the orbit be, if we want the satellite to take 8 times longer to complete one full revolution of its orbit? m/s Submit

Explanation / Answer

1) G M m / r^2 = m v^2 / r

r = G M / v^2

r = (6.67 x 10^-11) (6.4191 x 10^23) / (2524^2)

r = 6.72 x 10^6 m

2) F = m v^2 /r = (3800) (2524^2) / (6.72 x 10^6)

F = 3602 N

3) a = F/m = 0.95 m/s^2

4) the mass of planet

the speed of satellite

5) T = 8 (2 pi r / v) = 133828 sec

w = 2pi/T = 4.695 x 10^-5 rad/s

G M / r^2 = w ^2 r

r = 26.9 x 10^6 m

v = w r = 1262 m/s

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