If NASA wants to put a satellite in a circular orbit around the sun so it will make 2.0 orbits per year, at what distance (in astronomical units, AU) from the sun should that satellite orbit? The
Earth's orbit is 1.0 AU from the sun.
A) 0.63 AU
B) 2.0 AU
C) 0.50 AU
D) 0.71 AU
E) 7.6 AU

Question

Quizplus · Accepted Answer

The orbital period of a satellite around the sun (or any central body) is determined by Kepler's Third Law, which states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. If the satellite makes 2.0 orbits per year, its orbital period is half that of Earth's. To find the distance in AU, we use the relation $T^2 \propto r^3$, where $T$ is the orbital period and $r$ is the distance from the sun in AU. For Earth, $T = 1$ year and $r = 1$ AU. For the satellite, $T = 0.5$ years. Rearranging the proportionality for the satellite and solving for $r$, we find that $r$ is approximately $0.63$ AU, making choice A correct.

If NASA Wants to Put a Satellite in a Circular