Question

Problem 3: The Rosetta spacecraft landed a probe on the comet Churyumov-Gerasimenko. It has a mass of appeoximately 1 x 10 kg and has an average density of approximately 400 kg/m. It is far from spherical, but for this problem go ahead and assume it is spherical. Estimate the radius, the acceleration due to gravity at the surface and the escape velocity from its surface. (10 points) Problem 4: A GPS satellite has a mass of 1940 kg and is in a circular orbit around the Earth at a distance of 20,200 km above the surface of the Earth (this is standard GPS satellite height). How much energy is required to double the radius of this satellite's orbit and keep the orbit circular? (10 points) locast distance to the Earth

Answer 1

Ans: 3 mass of the comet m= 10's kg. Density of the comet s = 400 kg/m3 since shape of the comet is assumed spherical. volume of the comet it its radius is or V= 2 X R3 = m = 1013 Hence, - = 25 x 109 400 R= 75x109 47 R= 1.8142 x 103 m the Now gravitational acceleration at the surface of comet is - ag = m = 6.678101x1013 (1,8142 x103)2 Tag = 2.0265 x 104 m R? Now we will calculate escape velocity of comet Escape velocity Ve = 1 VR 1013 Ve = 2X6.67X10" x 10" 2x 6.67 x 10 1.8142 x x 103 ve = 8.575 m/s