How Can You Find the Mass of a Satellite Without a Given Radius?

[Lemmy]

Okay I understand somewhat of this topic of grav potential energy but i got stumped on this one question. I am to find the mass of a satellite orbiting Earth with the given variables of (F)(units: kN) which is the force the sattelite attracts the earth, and given the gravitational potential energy (-U). You are also givin the gravitational constant (G), and the Earth (m_e)

How could you find the mass (m) of the sattelite without a given radius in the equation U=-(G*m_e*m)/r ?

How would i rewrite this equation

any help would be great thanks
lemmy

 

[Physics Monkey]

Hi Lemmy,

You are correct that if you were given only gravitational potential energy (and the mass of the Earth and G) then you couldn't figure out m or r separately but only in the combination m/r. However, you have an extra piece of information: you know the force. Write out what the force is and see if you can find a way to solve for m and r using both F and U.

 

[quicknote]

To find the mass of the satellite without a given radius, you can use the formula for gravitational potential energy in terms of force and distance: U = -F*r. Rearranging this equation, we get m = -U/(G*m_e*r). This equation can be rewritten as m = -U*G^-1*m_e^-1*r^-1, which shows the relationship between the mass of the satellite and the given variables. It is important to note that this equation assumes that the satellite is in a circular orbit, as the radius is not given. If the satellite is in an elliptical orbit, the calculation would be more complex and would require additional information.