Problem 4. The following data about the earth is known: Mass of the earth 5.98 x 10" kg Radius of the earth 6.38 x 10" m Mean radius of the earth's orbit ( = 1 astronomical unit, or AU) 1.49 x 10" m Period of the earth's motion about the sun ( = 1 earth year) 365 days and 6 hours Based on this data, calculate: (a) the gravitational acceleration on the surface of the earth (Show calculation!); (b) the mass of the sun (Show calculation!); (c) the gravitational force (weight) acting on an astronaut of mass 60 kilograms when she is in a spacecraft located at a distance of 2.5 earth radii from the earth's surface; (d) the orbital speed and period of a satellite that circles the earth with an orbital radius of 3 earth radi.Problem 5. Confirm your calculation in Problem 4, part (d) using Kepler's Third Law, using the following data Mean radius of the moon's orbit = 3.8 x 10" m (which is 60 times the earth's radius! ); Period of the moon's motion about the earth - 27 days and 8 hours