Question

The physics of satellite motion around Jupiter.
A satellite is placed in orbit 5.00 x 10⁵ m above the surface of Jupiter. Jupiter has a mass of 1.80 x 10²⁷ kg and a radius of 8.14 x 10⁷ m.

1. Determine the radius of motion of the satellite.
2. What force is providing the centripetal force necessary for the satellite to stay in orbit?
3. In what direction is the centripetal force always acting?
4. Derive the mathematical equation that allows you to calculate the orbital speed of the satellite.
5. Calculate the orbital speed of the satellite.

Answer 1

1 ) The satelitte is revolving around the jupiter of radius r = 8.14 X 10 7 m and at height of h = 5.0 X 10 5 m

so the radius of the orbit is R = r+ h = 8.19 X 10 7 m

2 ) The gravitational force of the jupiter and the satelite is providing the necessary centripetal force for the motion

3 ) the force is acting in the dirction perpendicular to the jupiter surface and towards jupiter , the motion is guided by the centrifugal reaction force of the motion

4 ) The force of gravitation between jupiter and satelite is equal to the centripeteal force

the force of gravitaiton is Fg

where G is the universal gravitaional constant 6.67 X 10 -11 N m2 /kg 2

Mj is the mass of jupiter , Ms mass of satellite

The centripetal force is Fc

where v is the velocity of the satelitte

equating both the sides we have

this is the relation of orbital velocity

5) putting the value Mj = 1.8 X 10 27 kg , G = 6.67 X 10 -11 N m2 /kg2 , R = 8.19 X 10 7 m

we get orbital velocity v = 3.83 X 10 4 m/s