Orbital Velocity - Satellite

[scientict]

Homework Statement

A science group put in a satellite of mass m kg into a circular Earth orbit of radius r. The orbital velocity it needs to remain in this orbit is v. They now put another satellite into a similar orbit at the same altitude. Its mass is 3 times m. What orbital velocity would it need to be given? Give reasons using mathematical reasoning.

Homework Equations

Newton's law v = 2pi x r/T

The Attempt at a Solution

v^2/r=G m/r^2
Satellite 1:
v=√(G m/r)
Satellite 2:
v=√(G 3m/r)

 

[Shooting Star]

The Attempt at a Solution

v^2/r=G m/r^2

What does 'm' represent here? Can you derive this formula?

When a body moves with constant v in a circular orbit, the centripetal force is constant and equal to the force due to Earth's gravity on the body. Now you can deduce the correct version of the above formula using this.

 

[baba89]

The orbital velocity of a satellite is determined by the mass of the satellite and the radius of its orbit, as shown by the equation v = √(Gm/r). In this scenario, the mass of the second satellite is 3 times that of the first satellite, so we can substitute 3m for m in the equation. This gives us v = √(G(3m)/r), which can be simplified to v = √(3Gm/r). Therefore, the orbital velocity of the second satellite would need to be √3 times the orbital velocity of the first satellite in order to remain in the same orbit. This is because the gravitational force between the Earth and the satellite is proportional to the mass of the satellite, and a larger mass would require a greater velocity to maintain the same orbit.