Titania, the largest moon of the planet Uranus, has 1818 the radius of the earth and 1170011700 the mass of the earth. What is the acceleration due to gravity at the surface of Titania? Data: G = 6.67××10−1110−11 N m22/kg22, RE = 6.38 ×× 106106 m, mEmE = 5.97 ×× 10241024 kg

Two stars each of one solar mass (= 2 ×× 10301030 kg) are approaching each other for a head on collision. When they are a distance 109109 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 104 km. assume the stars to remain undistorted until they collide. (Use the known value of G)

Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface.It is necessary to have the spacecraft escape from the earth completely. If the spacecraft’s rockets are fired at perigee, by how much would the speed have to be increased to achieve this?If the spacecraft’s rockets are fired at apogee, by how much would the speed have to be increased to achieve this?

A rocket is fired ‘vertically’ from the surface of mars with a speed of 2 km s−1s−1 . If 20 percent of its initial energy is lost due to Martian atmospheric resistance, how far will the rocket go from the surface of mars before returning to it? Mass of mars = 6.4 ×× 10231023 kg; radius of mars = 3395 km; G = 6.67 ×× 10−1110−11 N m2m2 kg−2−2.