Imagine you are an astronaut in a circular orbit around the Earth. Let's say you have a mass of 100 kg. You are orbiting at a radial distance of 10,000 km (10 km, or 10' m) from the center of the Earth (Radius of Earth is 6400 km (6.4 x 10° km, or 6.4 x 10 m), so you are 3600 km above the surface). It takes you two hours and 45 minutes to complete each orbit. 7. What is the acceleration of gravity at your location (in m/s)? (Hint: "G*M" for Earth = 4 x 1014)

A landing craft with mass M is in a circular orbit a distance d above the surface of a planet. The period ofthe orbit is T. The astronauts in the landing craft measure the diameter of the planet to be D. The landing craft sets down at the north pole of the planet. a)What is the weight of a person of mass m as they step out onto the plant’s surface? b)Suppose days on this planet last t seconds (i.e. the planet rotates about its axis once every t seconds).Write an expression for the astronaut’s perceived weight at the equator in terms of their weight at the north pole. (Hint: think about centripetal force)

The gas-giant planet Rom (mass 5.7⨯1026 kg) goes around the star Galla (mass 2.0⨯1030 kg) in a circular orbit.  If the orbital radius of Rom is 2.5×1011 m … Note: G = 6.67⨯10-11 N·m2/kg2 i) What is the gravitational force of Rom on Galla?

(a) Based on the observations, determine the total mass M of the planet. (b) Which moon and planet of our solar system is the team observing? (Use literature.)