DHS 07 Gravitational Field (Lecture Notes)

Dunman High School (Senior High Physics) 9749 Physics (2024) Topic 7: Gravitational Field Page 1 of 20 Guiding Questions • How do two masses interact? Do they need to be in physical contact to do so? • What do field lines represent? Do field lines represent similar things for gravitational fields and electric fields? • How can we understand the motion of planets and satellites? Are we at the centre of the universe? Content • Gravitational field • Gravitational force between point masses • Gravitational field of a point mass • Gravitational field near to the surface of the Earth • Gravitation potential • Circular orbits Learning Outcomes Students should be able to: Gravitational field (a) show an understanding of the concept of a gravitational field as an example of field of force and define gravitational field strength at a point as the gravitational force exerted per unit mass placed at that point (b) recognise the analogy between certain qualitative and quantitative aspects of gravitational and electric fields. [To be taught in the topic of “Electric Field”] Gravitational force between point masses (c) recall and use Newton's law of gravitation in the form 12 2 Gm mF r= Gravitational field of a point mass (d) derive, from Newton's law of gravitation and the definition of gravitational field strength, the equation 2 GMg r= for the gravitational field strength of a point mass (e) recall and apply the equation 2 GMg r = for the gravitational field strength of a point mass to new situations or to solve related problems Gravitational field near the surface of the Earth (f) show an understanding that near the surface of the Earth, gravitational field strength is approximately constant and is equal to the acceleration of free fall Gravitational potential (g) define the gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to that point (h) solve problems using the equation GM rφ = − for the gravitational potential in the field of a point mass Circular orbits (i) analyse circular orbits in inverse square law fields by relating the gravitational force to the centripetal acceleration it causes (j) show an understanding of geostationary orbits and their application 9749 H2 Physics Topic 7 Gravitational Field Year 5 (2024) DUNMAN HIGH SCHOOL

Dunman High School (Senior High Physics) 9749 Physics (2024) Topic 7: Gravitational Field Page 2 of 20 0. Field Concepts 1. Introduction Gravitational force is a force that is evident in our everyday lives and plays a crucial role in many processes on Earth. For instance, the ocean tides are caused by the gravitational attraction of both the Moon and Sun on the Earth’s oceans. The falling of objects when released is also caused by the gravitational pull of the Earth on all objects. In terms of planetary motion, gravitational force is responsible for ke