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)7.6 AU
B)0.63 AU
C)0.50 AU
D)2.0 AU
E)0.71 AU

Question

Quizplus · Accepted Answer

The period of an orbit (the time it takes to make one complete orbit) is related to the distance from the sun by Kepler's Third Law, which states that the square of the orbital period is directly proportional to the cube of the semi-major axis of its orbit. If the satellite makes 2.0 orbits per year, its period is 0.5 years (since 1 orbit/year is Earth's period). To maintain the same proportionality as Earth (1 AU, 1 year), the distance for a 0.5-year orbit would be the cube root of 0.5 squared (since T^2 ∝ R^3), which simplifies to the cube root of 0.25. This calculation gives a value close to 0.63 AU, making option B the correct choice.

If NASA Wants to Put a Satellite in a Circular