posted by Anonymous .
Suppose you received a message from aliens living on a planet orbiting a star identical to our Sun. They say they live 4 times farther from tier star than Earth is from the sun. What is the length of their year compare to ours?
For all planets orbiting the sun, or another star of the same mass as the sun,
P^2*/R^3 = constant
P is the period and R is the radial distance.
This is called called Kepler's third law. http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law
Since R^3 is 64 times larger for the other star's planet (in your problem), P^2 must be 64 times larger also. The Period ratio is the square root of 64.
is 8 the correct answer