1. Newton’s Law of Gravitation Definition of Newton’s Law of Gravitation: The gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of their separation. All objects with mass attract each other with a gravitational force. The magnitude of this force depends on 2 things: 1)The masses of the 2 bodies. 2)The distance between the two bodies.

2. Newton’s Law of Gravitation F = Gm 1 m 2- r 2 m1m1 m2m2 FF r G is a constant of proportionality known as the gravitational constant and has a value of 6.67 x 10 -11 Nm 2 kg -2. This number is very small. What does this tell us about gravitational forces? The equation was written for point masses but applies to all spherical masses if we assume that the mass of each object is concentrated at the centre of mass and the distance between the masses is measured from the centre of mass.

3. Question The moon orbits the Earth along a path of radius 3.84 x 10 8 m. The mass of the Moon is 7.35 x 10 22 kg and the Earth’s mass is 6.00 x 10 24 kg. G = 6.67 x 10 -11 Nm 2 kg -2. a)Calculate the size of the gravitational force between the Earth and the Moon which keeps the Moon in orbit. b)A rocket of mass 42000kg is fired from Earth to the Moon. What is the resultant gravitational force on the rocket when it is 3.00 x 10 8 m from the centre of the Earth. (Hint: Find the gravitational force between the rocket and the Moon AND the gravitational force between the rocket and the Earth.

4. Solution a) F = Gm E m M- = 6.67x10 -11 x 6.00 x 10 24 x 7.35 x 10 22 = 1.99 x 10 20 N r 2 (3.84 x 10 8 ) 2 b) Gravitational force between rocket and Earth, F E = Gm E m - = 6.67x10 -11 x 6.00 x 10 24 x 42000 = 187N r 2 (3.84 x 10 8 ) 2 Gravitational force between rocket and Moon, F M = Gm m m - = 6.67x10 -11 x 7.35 x 10 22 x 42000 = 29.2N r 2 (3.84 x 10 8 – 3.00 x 10 8 ) 2 The resultant force is therefore 187 – 29.2 = 158N towards the Earth