Does Mass Affect Orbital Velocity for Satellites in Similar Earth Orbits?

[samaank]

Can someone help me with this question?

A science group put 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 simmilar orbit at the same altitude. Its mass is 3 times 'm'. What orbital velocity would it need to be given? give reasons why using mathematical reasoning.

thanks, i really appreciate it

 

[StatusX]

Any ideas? We're not going to do it for you.

 

[Tide]

Can you think of any reasons why the orbital speed would depend on the mass of the satellite?

 

[samaank]

this is my theory, its more conceptual that it is mathematical and i could be wrong.
If you have a 1kg marble tied at the end of a string and spin it, it will have a certain amount of centrifugal force, however if you had a 10k marble on the end of a string and spun it at the same speed it would have a greater outward centrifugal force. and if we say that gravity is that string then the same idea applies. so the heavier the object the more/less velocity is needed to keep it in orbit, otherwise it would spiral out getting further and further from the Earth with every orbit. any ideas? I'm totally lost and being bombarded with work.

 

[samaank]

do any of kepler's laws apply here?

 

[samaank]

just point me in the right direction with some tips or momentum

 

[gnpatterson]

Now I understand why I was so lucky to have been taught motion properly, if you are taught the idea of orbit as balanced forces you really have no chance of developing a reliable insight into the physics of the situation. The motion of any object in free fall is (neglecting air resistance) not dependent on the mass.

If you imagine a spaceship that can separate into two halves in orbit, it does not suddenly change speed when separation occurs.

If you have a mass on a number of strings and swing it round your head (a very stupid thing to do) it does not speed up or slow down if separated from itself (as long as all the parts stay on some string obviously)

 

[mukundpa]

Just think, if the mass of an object is three times of the other, what will be the ratio of free fall acceleration?

 

[samaank]

i know that the forces have to be balanced to have orbit, u didnt understand my analogy. can someone please actually help me?

 

[da_willem]

If you imagine a spaceship that can separate into two halves in orbit, it does not suddenly change speed when separation occurs.

This was not helpful ?!

 

[H_man]

If you start with the equation for the gravitational force between two objects. You can then equate this to the equation for centripetal acceleration.

With these two equations it is then just a case of cancelling out.

I assume that given that you have been given this question you will also have been told the relevant formulae.
$$F = \frac {GMm} {r^2}$$

For the Gravitational force.

And

$$F = \frac {m v^2} {r}$$

For the centripetal force.

Hope this puts you on the right track

 

[gnpatterson]

Why not do the sensible thing and realize that gravity produces an acceleration field and simply say that the craft moves in freefall. Then you have a huge advantage of being certain about the velocity no matter the shape of the orbit is. If you start down this route of having write out equations and then cancel something out you are going to be a slave to it in the future. Just stretch that little bit further with your imagination and visualise the motion so that you can "see" that the mass is irrelevant. A little bit of verbal skill can construct an argument to communicate the point.

The correct use of the maths is to work out the velocity, using it to think about the nature of the situation is just lazy. And pretending that it "explains" anything is not going to help you in the long run.