Scientists want to place a 3200 kg satellite in orbit around Mars. They plan to

Question

Scientists want to place a 3200 kg satellite in orbit around Mars. They plan to have the satellite orbit at a speed of 2640 m/s in a perfectly circular orbit. Here is some information that may 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 radius should the satellite move at in its orbit? (Measured frrom the center of Mars.)m

2)What is the force of attraction between Mars and the satellite?N

3)What is the acceleration of the satellite in orbit?m/s2

4)Which of the following quantities would change the radius the satellite needs to orbit at?

-the mass of the satellite

-the mass of the planet

-the speed of the satellite

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?

Explanation / Answer

1)
v = 2*pi*r/time = 2*pi*r/t
Force between satelite and mars should be providing centrepetal force
G*mmars*m2/r^2 = m2*v^2/r
G*mmars/r = v^2
6.67428*10^-11 * 6.4191*10^23/r = 2640^2
r= 6.15*10^6 m

2)
F= G*mmars*m2/r^2
= 6.67428*10^-11 * 6.4191*10^23 * 3200/ (6.15*10^6)^2
=3625 N

3)
a = F/m
= 3625/3200
= 1.13 m/s^2

4)
G*mmars/r = v^2
r = G*mmars/v^2
Below 2 auantities can change it:
-the mass of the planet
-the speed of the satellite

I am allowed to answer only 4 subparts.please ask remaining as different question

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