The distance of the Earth to the Sun is 1 AU. Suppose an steroid is in circular orbit around the sun at a distance of 2 AU. How long does it take the asteroid to orbit the sun once?

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)

Calculate the period of a satellite orbiting a planet with the mass 8.7 x 1022 kg given the height of the satellite's orbit is 300 km and the radius of the planet is 2000 km. Provide your answer in Sl units.

GeoEye-1 is an Earth-observation satellite that provides high-resolution images for Google. The orbital period and eccentricity of GeoEye-1 are 98.33 min and 0.001027, respectively. Determine the perigee and apogee altitudes of GeoEye-1.