# Kepler's Third Law

1. Nov 13, 2013

### KVat390

1. The problem statement, all variables and given/known data
Find the period of a satellite that is in orbit 6.7×10^6 meters from the center of the earth?

2. Relevant equations
P^2=R^3 P=period and R=average distance

3. The attempt at a solution
so far I have tried P^2=(6.7×10^6)^3
then sqrt of (P^2)=sqrt of (3.00763×10^20)
My answer is the period of the satellite=1.73425×10^10

2. Nov 13, 2013

### Staff: Mentor

3. Nov 13, 2013

### KVat390

4∏/T^2=GM/R^3
4∏/T^2=(6.67×10^-11)(5.98×10^24)/(6.7×10^6)^3
12.57/T^2=(3.98866E14)/(3.00763E20)
12.57/T^2=1.326180414E-6
T^2=1.66700878E-5
T=.0040829019

4. Nov 13, 2013

### Staff: Mentor

I don't think so. How did you get T^2= ?

I would have solved for T^2 first and then inserted the values. It always makes things easier.

GM*T^2 = 4*pi^2 * R^3

T^2 = 4*pi^2*R^3 / G*M

Last edited: Nov 13, 2013
5. Nov 13, 2013

### SteamKing

Staff Emeritus
Unit-free calculations almost never end well.

6. Nov 13, 2013

### KVat390

A Revision to my previous post

The equation is 4pi^2/T^2=GM/R^3 not 4pi/T^2=GM/R^3
I changed my answer to 5.46 periods
39.48/T^2=(3.98866E14)/(3.00763E20)
T^2=39.48/1.33x10^-6
sqrt of T=sqrt of 39.48/1.33x10^-6
T=5.45×10^3 periods/earth years

Last edited: Nov 13, 2013
7. Nov 13, 2013

### Staff: Mentor

I fixed my eqns to say pi^2

so that T^2 = 4 * pi^2 * R^3 / (G * M) = 4 * pi^2 (6.7E6)^3 / ((6.67E-11) * (5.98E24)) = 2.98E7

and T =5.46E3

When I did my calculations I got tripped up by a lack of parentheses around the denominator terms which meant that I divided by the G and then multiplied by the M instead of dividing by (G * M)

Last edited: Nov 14, 2013
8. Nov 13, 2013

### SteamKing

Staff Emeritus
Still won't knuckle under and use units, eh? Good Luck with the rest of your course work!

9. Nov 13, 2013

### Staff: Mentor

Klingon programmers have no need of units, we use junits...

10. Nov 13, 2013

### Staff: Mentor

Edit: To the OP I forgot the pesky pi factor again but fixed my post above.

Having gotten the answer for T and knowing R does it seem reasonable?

What object might have a periodicity like this?

Oh and as SteamKing said where is your unit analysis? What units is used for T?

Last edited: Nov 14, 2013
11. Nov 13, 2013

### D H

Staff Emeritus
That result is incorrect. You dropped a factor of pi.

You are being sloppy and it is getting you in trouble.

You also are not following instructions. You didn't read the instructions on where to post your physics problems.

This is not an advanced physics homework problem. I'm moving this to the introductory physics homework section.

Last edited: Nov 13, 2013
12. Nov 14, 2013

### SteamKing

Staff Emeritus
'Advanced Physics' also doesn't mean, "Units? Units? I don't need no stinkin' units!"