How Does the Time Period Change with Orbit Radius in Satellite Motion?

[Deebu R]

Homework Statement

If the time period of a satellite in the orbit of radius r around a planet is T, then the time period of a satellite in the orbit of radius 4r is T'= ?

2. The attempt at a solution
To be honest I have no idea how to solve this. First I thought Keplers third law may be the solution but even if it is the solution I have no idea how to apply it to solve this question.
Thank you for your time and help.

 

[drvrm]

To be honest I have no idea how to solve this. First I thought Keplers third law may be the solution but even if it is the solution I have no idea how to apply it to solve this question.
Thank you for your time and help.

the time period must be time taken to complete one rotation-
so first relate the time period to the radius of the orbit
ask what is the path covered in time T- length of path divided by speed will give time T.

 

[BvU]

Homework Statement

If the time period of a satellite in the orbit of radius r around a planet is T, then the time period of a satellite in the orbit of radius 4r is T'= ?

2. The attempt at a solution
To be honest I have no idea how to solve this. First I thought Keplers third law may be the solution but even if it is the solution I have no idea how to apply it to solve this question.
Thank you for your time and help.

Hi Deebu,

Kepler 3 is indeed, but we are going to 'discover' it ourselves. You may assume the orbits are circular (it says r and 4r in the problem statement).
What keeps the thing in this circular orbit ? -- You have an expression for that
How much of that is needed for an orbit of radius r -- you have an experssion for that too, I hope ? (See why the template is so useful? Don't throw away parts of it !)

(Note: All 'calculations' are with symbols -- that's what keeps it simple and elegant and no larger or more complicated than necessary )

 

[Deebu R]

Is it staying in the path because angular momentum and velocity is a constent?
Should I be looking for orbital velocity?

 

[BvU]

I don't see the relationship between my question and your post ?
My answer to your new questions:
a) no. angular momentum is radius x momentum. There is no question of consistency or inconsistency. Or do you mean something else ?
b) orbital velocity does come into the relevant equations, yes.

 

[Deebu R]

I don't see the relationship between my question and your post ?
My answer to your new questions:
a) no. angular momentum is radius x momentum. There is no question of consistency or inconsistency. Or do you mean something else ?
b) orbital velocity does come into the relevant equations, yes.

?

 

[Deebu R]

I don't understand.Sorry.

 

[QuantumQuest]

Homework Statement

If the time period of a satellite in the orbit of radius r around a planet is T, then the time period of a satellite in the orbit of radius 4r is T'= ?

2. The attempt at a solution
To be honest I have no idea how to solve this. First I thought Keplers third law may be the solution but even if it is the solution I have no idea how to apply it to solve this question.
Thank you for your time and help.

To be honest I have no idea how to solve this. First I thought Keplers third law may be the solution but even if it is the solution I have no idea how to apply it to solve this question.

In order to solve any problem, you must understand what is given, what is asked and develop a path, in order to reach a solution.
Now, although obvious,I'd ask why did you think that Kepler's third law may be the solution, because I see some misunderstanding there. If you answer this, you'll see immediately the sketch of the solution. What you have to do then, is throw in what is given into this sketch and walk the path to the solution. As a second piece of advice, physical laws in the context of problems are not a magic wand. You have to apply them.

 

[kuruman]

Since you mentioned Kepler's 3rd law, why don't you start by writing it down twice? Once adapted for the orbit at r and once for the orbit at 4r. Do that first and we'll continue from there.

 

[Deebu R]

Since you mentioned Kepler's 3rd law, why don't you start by writing it down twice? Once adapted for the orbit at r and once for the orbit at 4r. Do that first and we'll continue from there.

Ah! I get it

T^2 directly preportional R^3
T^2 directly preportional to (4R)^3

T = root(64) = 8. Right?

 

[kuruman]

Almost, but not quite right. When you write T = 8, you say that the new period (actually it should be T' not T because symbol T is reserved for the initial period) is 8. The number 8 is correct, but 8 what? You can't have a period on one side of the equation and a pure number on the other. Also, it is a good habit to write equations explicitly in terms of symbols. You say "directly proportional", but you assume that the proportionality constant is the same in the two orbits. Is it really? Here it is, but in other situations it may not be and you need its symbolic representation to see what is going on.