## Question:

The total mass of the Earth is ${ m }_{ e }=5.9736\times { 10 }^{ 24 }kg$. Modeling the Earth (with everything in and on it) as an isolated system and assuming that the center of the Earth is also the center of mass of the Earth, determine the displacement of the center of the Earth due to
(a) a 2m jump off the surface by a 85 kg person;
(b) the Space Shuttle, with a mass of 124.000 kg, reaching an orbit of 200 km;
(c) 170.000 $k{ m }^{ 3 }$ of water being elevated 50m (these numbers are estimates based on publicly available information about the Aswan Dam at the border between Egypt and Sudan). Use 1 $g/c{ m }^{ 3 }$ for the density of water.