Why would prbital velocity slow down when you increase R?

[johnwandering]

Doesnt really make sense. There is no counteracting force...

Orbital velocity is a just linear velocity curved by gravitational force. Centripetal acceleration has no effect on the linear orbital velocity of a satellite.

So when we put the moon out 4x radius to the earth, the orbital speed should Not change at all.
But why does it slow down??

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[deleted103644]

Doesnt really make sense. There is no counteracting force...

Orbital velocity is a just linear velocity curved by gravitational force. Centripetal acceleration has no effect on the linear orbital velocity of a satellite.

So when we put the moon out 4x radius to the earth, the orbital speed should Not change at all.
But why does it slow down??

Orbital velocity is just the velocity required to maintain orbit. This is true when centripetal force is equal to gravitational force.


(r = distance between center of mass of object and center of earth)

g = G * m * M / r^2 = m*v^2 / r = centripetal force

Therefore:

v^2 = GM/r

This decreases as you get further away.

 

[hellocubed]

You are getting confused between the "velocity" generated and the "velocity" necessary to maintain the orbital.

When you read that the satellite was placed in an orbital 4r away, it doesn't mean that the moon was just PLACED 4 R away. In order for it to be in that orbital, its velocity would have had to have been decreased as well.

 

[deleted103644]

You are getting confused between the "velocity" generated and the "velocity" necessary to maintain the orbital.

When you read that the satellite was placed in an orbital 4r away, it doesn't mean that the moon was just PLACED 4 R away. In order for it to be in that orbital, its velocity would have had to have been decreased as well.

Yup, exactly, otherwise it would go flying out of orbit.

 

[dmf2682]

Anyone know if you can think of the system as one where conservation of angular momentum is applied? So if the orbiter and orbitee were one system rotating (about the orbitee ) when radius goes up the velocity drops to conserve? This make sense to anyone? Not sure if this applies to rigid body rotation only, but I was thinking in an ideal sense these would be like point masses.

 

[deleted103644]

Anyone know if you can think of the system as one where conservation of angular momentum is applied? So if the orbiter and orbitee were one system rotating (about the orbitee ) when radius goes up the velocity drops to conserve? This make sense to anyone? Not sure if this applies to rigid body rotation only, but I was thinking in an ideal sense these would be like point masses.

It's different. There's no reason to talk about conservation here, it would take energy to change orbits.

It's actually more complicated the what I said if the two masses are more equal in size. The radii in those equations are not exactly the same, but with Me >>> m, it works out that way.