Planetary Mechanics Question: Determine Kepler's constant for all Earth Satellites

[NDiggity]

1. The problem statement, all variables and given/known data
Determine Kepler's constant for all Earth Satellites. No information is given, only the question.



2. Relevant equations
K=R³/t²



3. The attempt at a solution
I decided to use the moon as a satellite. So I went K=(384,403,000)³/(2,360,594.88)²

For R I used the distance from the moon to earth in meters (384,403km) and for t I used the time it takes the moon to revolve around earth in seconds (27.3 days).

The answer I get is 1.02x10¹³.
The answer is supposed to be 9.85x10¹²

Thanks for any help!

[NDiggity]

Is there any other information I need to provide? Please help, I have a test on Planetary Mechanics tomorrow and my teacher refuses to help me with this question. He told me what the answer should be and said to work it out on my own. I asked some of my classmates and they could not get it either...

[husky88]

I would do it like you did.
These values are very close.
10.2 * 10^12
9.85 * 10^12
So why do you think that is? You and your teacher used different number of significant figures.
3.8 * 10^8
and
2.36 * 10^6
Only two or three significant figures.
Use these values for your calculation and you get your teacher's results. Silly huh? :smile:
It's weird how your teacher would use two significant figures for one and three significant figures for the other.

[NDiggity]

Right on, thank you very much for your help. It seemed strange because I was so close.