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  Home : Math & Science : Physics Study Guides : Gravitation : Newton : Problems for Newton's Law
Newton and Gravitation
  
 
Problems for Newton's Law
Problem 1.1: What is the force exerted by Big Ben on the Empire State building? Assume that Big Ben has a mass of 108 kilograms and the Empire State building 109 kilograms. The distance between them is about 5000 kilometers and Big Ben is due east of the Empire State building. [Solution]
Problem 1.2: What is the gravitational force that the sun exerts on the earth? The earth on the sun? In what direction do these act? (Me = 5.98×1024 and Ms = 1.99×1030 and the earth-sun distance is 150×109 meters). [Solution]
Problem 1.3:
Figure E.1: alignment of Mercury, Venus and the Sun.
If Mercury, Venus and the sun are aligned in a right triangle, as shown, then calculate the vector sum of the forces on Venus due to both Mercury and the Sun. What is the direction and magnitude of the resulting force? (Sun-Venus distance rv = 108×109 meters, Sun-Mercury distance rm = 57.6×109 meters, mass of Sun Ms = 1.99×1030 kilograms, mass of Mercury Mm = 3.3×1023 kilograms, mass of Venus Mv = 4.87×1024 kilograms). [Solution]
Problem 1.4: It is possible to simulate "weightless" conditions by flying a plane in an arc such that the centripetal acceleration exactly cancels the acceleration due to gravity. Such a plane was used by NASA when training astronauts. What would be the required speed at the top of an arc of radius 1000 metres? [Solution]
Problem 1.5: Show using Newton's Universal Law of Gravitation that the period of orbit of a binary star system is given by:

T2 =
   

Where m1 and m2 are the masses of the respective stars and d is the distance between them. Notice that we derived the same result in a problem in the previous section, using the reduced mass and Kepler's Third Law. [Solution]
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