Question

Scientists want to place a 4 × 10³ kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 2.3 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

m_mars = 6.4191 x 10²³ kg
r_mars = 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?

Answer 1

Mass of satellite,

Mass of Mars,

Radius of Mars,

Height of the orbit,

Radius of orbit,

============

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

Gravitational force,

(1) ANSWER:

==============================

2) What speed should the satellite have to be in a perfectly circular orbit?

If the satellite is in a circular orbit, then the gravitational force is equal to the centripetal force of the satellite

(2) ANSWER:

===============================

3) How much time does it take the satellite to complete one revolution?

Orbital speed =Circumference of the orbit/Time period

(3) ANSWER:

==========================================

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?

So time period,

If the satellite is in a circular orbit, then the gravitational force is equal to the centripetal force of the satellite

(4) ANSWER:

==================================