The Mass of the Earth

1. Write down the expression for the force of attraction between two uniform spheres of unequal masses.
2. Assume that one of the spheres is the Earth, and the other is a small sphere at the surface of the Earth.
3. Express the force of attraction in terms of the small sphere's weight.
4. Find an expression for the mass of the Earth in terms of the acceleration due to gravity, the Universal Gravitational constant G, and the radius of the Earth.
   

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5. If you are told that two verticals drawn to the surface of the Earth at two points which are 300 km apart form an angle of 2.69 degrees, calculate the radius of the Earth. If you can't visualize this, look at the The Size of The Earth video clip.
   
6. Put all these pieces together and calculate the mass of the Earth.