What Must the New Orbital Radius Be to Increase the Period to 8T?

[cheeselover87]

Homework Statement

a satellite has a period of T and orbital radius R. If you wish to increase the period to 8T what must the new orbital radius be. (answer= 4T, I just don't know how they got it)

Homework Equations

R1 cubed/ T1 squared = R2 cubed/ T2 squared

The Attempt at a Solution

The answer i got was 8

 

[DaveC426913]

1.
2.
3.
You've got 1. so far. 2 and 3?

 

[blacknovember]

That sounds reasonable.

Check calculation again.

 

[DaveC426913]

That sounds reasonable.

Check calculation again.

Yeeeeah. I think he may have handed that assignment in by now...

 

[paranormal]

T, but after looking at the given answer of 4T, I realized that I made a mistake in my calculations. The correct solution can be found by using the formula R1 cubed/ T1 squared = R2 cubed/ T2 squared. In this case, we are looking for the new orbital radius (R2) when the period is increased to 8T. Therefore, we can rearrange the formula to solve for R2, which gives us the equation R2 = (T2 squared/T1 squared) x R1 cubed. Plugging in the values of T2 = 8T and T1 = T, we get R2 = (8T squared/T squared) x R1 cubed. Simplifying this further, we get R2 = 64R1 cubed/T squared. Since the period is directly proportional to the radius, we can also write this as R2 = 64R1 cubed/T1 squared. From this equation, we can see that the new orbital radius (R2) will be 64 times the original orbital radius (R1). Therefore, if we want to increase the period to 8T, the new orbital radius must be 64 times the original orbital radius, which is equivalent to 4T. This is how the answer of 4T is obtained.