Need help with finding the Kinetic energy of a satellite

[Gardamun]

Greetings.

I have been a bit confused with kinetic energy and potential energy but I thought I was over my confusion until satellites in orbit appeared. I'm dealing with a problem with a few parts and I'm stuck on part B. Part A asked me to calculate the PEg of the satellite, with I could easily do using the equation PEg= - (Gm1m2)/R^2 . The following question then asked me what the kinetic energy and velocity of the satellite is. I only have the mass of the satellite and the answer from the first part to work with. I don't need the answer, just a point in the right direction. Thank you in advance!

 

[gneill]

What keeps a body moving in a circle? Can you draw a FBD for the satellite?

 

[Gardamun]

The gravitational pull keeps the satellite moving in a circle (centripetal force). I still don't see how that helps me and how I can use Potential Energy or find Kinetic energy. Can the PEg be used to determine ac? All the equations I have that use ac have another variable in it that I can't determine. Is the answer staring at me in the face?

 

[gneill]

The gravitational pull keeps the satellite moving in a circle (centripetal force). I still don't see how that helps me and how I can use Potential Energy or find Kinetic energy. Can the PEg be used to determine ac? All the equations I have that use ac have another variable in it that I can't determine. Is the answer staring at me in the face?

What do you need to know if you want to find KE?

What are the formulas for gravitational acceleration and centripetal acceleration?

 

[Gardamun]

I guess what I'm trying to figure out is if there is a formula for calculating Kinetic energy for objects in orbit? I've gotten a few different answers. One person said the formula is 1/2 (Gm1m2/R) and another answer I got is that the kinetic energy is = to the total work done to move the satellite from Earth into orbit, but those 2 ways seem to produce different answers. Do either of these ways work?

 

[gneill]

I guess what I'm trying to figure out is if there is a formula for calculating Kinetic energy for objects in orbit? I've gotten a few different answers. One person said the formula is 1/2 (Gm1m2/R) and another answer I got is that the kinetic energy is = to the total work done to move the satellite from Earth into orbit, but those 2 ways seem to produce different answers. Do either of these ways work?

All those energies are related for something in orbit, but you need to be careful about it. 1/2 (Gm1m2/R) is gravitational potential energy that is referenced to a location off at infinity. The second "definition" you got, "the total work done to move the satellite from Earth into orbit", includes the change in potential energy from the Earth's surface to the orbital height. So that's not just kinetic energy.

The kinetic energy of a satellite in orbit is tied to its orbital speed. As always, KE = (1/2)MV². So, find the orbital velocity and you'll be able to find the KE.

That's why I was asking you if you knew formulas for gravitational acceleration and centripetal acceleration -- you can find the orbital velocity by considering the acceleration (or force) balance that keeps the satellite traveling in a circular path.

 

[technician]

The potential energy at a distance R is -GM/R where M is mass of Earth (or planet) and R is distance from centre of planet
Potential energy is m x potential where m is mass of satellite

 

[Gardamun]

First gneil I have forgotten to thank you for your responses, I apologize for that. I've been a bit grumpy about this problem because I'm doing this course by distance education and the explanations about quite a few different topics is flimsy and inadequate in the textbook. So thank your for your help. The way I've gone about it now, is that I've combined a few different formulas, (the ones you suggested) and manage to end up with a formula V^2=Gm1/R this way I was able to determine V with the information I had and then could easily get Kinetic energy. I'm still a bit baffled by all the strange answers I find online and also the explanations in my textbook but do you think I'm on the right path here?

 

[gneill]

First gneil I have forgotten to thank you for your responses, I apologize for that. I've been a bit grumpy about this problem because I'm doing this course by distance education and the explanations about quite a few different topics is flimsy and inadequate in the textbook. So thank your for your help. The way I've gone about it now, is that I've combined a few different formulas, (the ones you suggested) and manage to end up with a formula V^2=Gm1/R this way I was able to determine V with the information I had and then could easily get Kinetic energy. I'm still a bit baffled by all the strange answers I find online and also the explanations in my textbook but do you think I'm on the right path here?

You're quite welcome. Glad to help out.

Yes, the formula that you found (V²=GM/R where M is the mass of the central body and R the orbit radius) is correct and one that's handy to remember. It can be derived by considering the centripetal acceleration and gravitational acceleration of the orbiting body. You're doing fine.