Scientists want to place a 2900 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 2900 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 1.7 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:mmars = 6.4191 x 1023 kg
rmars = 3.397 x 106 m
G = 6.67428 x 10-11 N-m2/kg2
1. What is the force of attraction between Mars and the satellite?
2.What speed should the satellite have to be in a perfectly circular orbit?
3. How much time does it take the satellite to complete one revolution?
4. What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?
please show work thanks

Explanation / Answer

1)

force of attraction = G *M * m/d^2

force of attraction = 6.673 *10^-11 * 2900 * 6.419 *10^23/(1.7 * 3.397 *10^6)^2

force of attraction = 3724.8 N

the force of attaction between satellite and moon is 3724.8 N

2.

let the speed of satellte is v

Using second law of motion

Force = m * v^2/d

3724.8 = 2900 * v^2/(1.7 * 3.397 *10^6)

solving for v

v = 2723.5 m/s

the speed of satellite is 2723.5 m/s

3)

time taken to complete one revolution = 2pi * R/v

time taken to complete one revolution = 2pi * 3.397 * 10^6/(2723.5)

time taken to complete one revolution = 7837 s

the time taken to complete one revolution is 7837 s

4)

as time period is given as

T^2/R^3 = 4pi^2/(G * M)

for 8 times longer period

R must be 4 times

the radius of orbit = 4 * 1.7 * 3.397 *10^6 m

radius of orbit = 2.31 *10^7 m

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