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.
A. Kepler's third law
The Attempt at a Solution
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!