# Two orbiting body problems

## Homework Statement

A. NASA sends a satellite to another planet by placing the satellite in a Keplerian orbit such that the perihelion is at the radius of the Earth's orbit (1 AU) and the aphelion is at the radius of the planet's orbit. The gravitational effects may be neglected. Suppose a new planet were to appear in a circular orbit of radius 7.30 AU around the Sun. Calculate the time it would take a NASA satellite to travel from Earth to this planet. Express the result in years.

B. A Global Positioning System (GPS) satellite is placed in a high circular orbit around the earth. The period of revolution is 12 hours. Calculate the radius r of the orbit.

## Homework Equations

A. Kepler's third law

B. T^2=(4*pi^2*r^3)/GM

## The Attempt at a Solution

A.
1^2 yr x^2 yr
------- = --------
1^3 au 7.03^3 au

X would be 18.639 years but this seems to be incorrect.

B. I think T needs to be in seconds as that's what the other units are in. Thus:
43200^2=(4*pi^2*x^3)/(6.674E-11*5.9742E24) Thus, X=2.6613E7 m but again no luck.

Any help on either would be greatly appreciated! Thanks!

lightgrav
Homework Helper
"SEMI" -major axis of this orbit is HOW far?

by the way, they only want the trip time OUT, not the entire orbit time.

You'll have to bear with me because I'm not too great with these types of problems. I have a problem conceptualizing them or something. Anyways...

I got the satellite-to-planet one. That was really stupid (wasn't halving it at the end and was using 7.3/2 instead of 8.3/2. Final answer came out to be 4.277 AU.

Thank you very much for the help on that one.

Now for the other one which I'm sure I'm just being stupid about again. It seems like it should be really easy with how short it is but I'm just not able to understand what I'm messing up.