1. Feb 2, 2005

Format

I need to find the orbital radius of a satilite, while only knowing its orbital period.

i tried..

a = 4π²r/T²
Fnet = Fg
a = Gm/r²

Gm/r² = 4π²r/T²
r = cuberoot(T²Gm/4π²)

didnt work out..

2. Feb 2, 2005

dextercioby

What??What are u saying by "didn't work out" ?Your formula is okay for a circular orbit...

Daniel.

3. Feb 2, 2005

Format

Hmm..i keep getting 3.19x10^7

4. Feb 2, 2005

christinono

Try this:
From the period, find the speed (simple calculation). Then, use this formula to find the radius:

$$v=\sqrt{\frac{Gm_E}{r}}$$

5. Feb 2, 2005

Format

hmm, in order to find the speed dont you need the radius?

like v = 2πr/T ?

6. Feb 2, 2005

Gokul43201

Staff Emeritus
I see nothing wrong with your approach. Why don't you post the numbers given (actually just the value of T), so we can check the calculation ?

7. Feb 2, 2005

8. Feb 2, 2005

Format

i guess that would help lol..

A satilite has an orbital period of T = 5760 s. What is the average orbital radius of its orbit?

Last edited: Feb 2, 2005
9. Feb 2, 2005

dextercioby

Please post the initial text of the problem...

Daniel.

10. Feb 2, 2005

Gokul43201

Staff Emeritus
I get 6.95 * 10^6 m.

You must have made a calculation error. Show us your working, and we'll show you what's wrong.

11. Feb 2, 2005

christinono

I did exactly that and got 6.95 x 10^6 m. Maybe you punched in the numbers wrong...

12. Feb 2, 2005

Format

well isnt this anoying..
k i put the cube root of..

( (5760²)(6.67x10^(-11)(5.98x10^24) ) / 4π²

13. Feb 2, 2005

Format

wait...i see a missing bracket, one sec lol

damn didnt make a difference...wut am i doin wrong?

Last edited: Feb 2, 2005
14. Feb 2, 2005

dextercioby

Without using the calculator i could show that the result is
$$6\cdot 10^{6} <r<7\cdot 10^{6}$$

So how about pluggng in the numbers properly...

Daniel.

15. Feb 2, 2005

christinono

yeah, you're missing a bracket. :tongue2:

16. Feb 2, 2005

Format

ive done this like 10 times now and added the brackets...still gettin 3.2x10^7 lol

17. Feb 2, 2005

christinono

OK, show me exactly what you typed into you calculator.

18. Feb 2, 2005

Gokul43201

Staff Emeritus
19. Feb 2, 2005

dextercioby

Okay:U need to take 3-rd order root from:
$$\frac{(5.76)^{2}\cdot 1000^{2}\cdot 6.67\cdot 10^{-11}\cdot 5.98\cdot 10^{-24}}{4\pi^{2}} \simeq 300\cdot 10^{18}$$

Daniel.

20. Feb 2, 2005

Format

ok i got it to work haha, thx for the help guys