In recent years, scientists have discovered hundreds of planets orbiting other s

Question

In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of ear, which orbits the sun (Msun = 1.99 x 10^30 kg) at a distance of 1.50 x 10^11 m, called 1 astronomical unit (1 au). Others have extreme orbits that are much different from anything in our solar system. The following problems relates to one of these planets that follows circular orbit around its star.

WASP-32b orbits with a period of only 2.7 days a star with a star with a mass that is 1.1 times that of the sun. How many au from the star is this planet? Assume the orbital period of earth is 365 days.

Explanation / Answer

apply Keplers third law as T^2 = 4pi^2 R^3/GM

R^3 = GMT^2/(4pi^2)

R^3 = 6.67e-11*1.1*1.99e30 * (2.7*24*60*60)^2/(4*3.14*3.14)

R^3 = 201.46 *10^27

R = 5.86 *10^9 m

as 1Au = 1.5 e11

R = 5.86e9/1.5e11

R = 0.039 AU

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