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?

Answer 1

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.

Answer 2

is 8 the correct answer