Year 11 Preliminary Physics The Cosmic Engine NEWTON’S LAW OF UNIVERSAL GRAVITATION Year 11 Preliminary Physics The Cosmic Engine

Universal Gravitation From Kepler’s Law of Periods Newton deduced that the force between bodies was an inverse square law. From Kepler’s Law of Areas he deduced the force to be a central force (i.e. it acts along the line joining the Sun and the planet). Combining these ideas Newton proposed his Law of Universal Gravitation.

The Law of Universal Gravitation G= 6.67x10-11 N.m2.kg-2

Gravitational Fields An object of mass m1 for example produces a gravitational field in the space around it. A second object of mass m2 placed in the field will experience a force due to the field. Similarly m2 produces a field that acts on m1. Gravitational fields are force fields.

Gravitational Field Mathematics We define the gravitational field as the force per unit mass. At the Earth’s surface g = 9.8 N.kg-1. (same as 9.8ms-2 acceleration due to gravity.) The g refers to the strength of the field rather than any acceleration of the mass. Gravitational Field Mathematics

Kepler’s 3rd Law and Newton’s Law of Universal Gravitation For a planet revolving around the Sun in a circular orbit or radius r, the centripetal force is provided by the gravitational attraction between the planet and the Sun. If the mass of the planet is m and the mass of the sun is M then:

Kepler and Newton (cont) F = G Mm = mv2 r2 r G Mm = m (2/T)2 r2 r GM = 42r r2 T That is : r3 = GM T2 42 Brilliant