EJC Physics H207 Gravitational Field 2023_1. Notes (FULL)

9749(2023) H2 Physics H207 Gravitational Field – Notes Page 1 of 26 H2 Topic 07 – Gravitational Field Despite the apparent “weightlessness” of astronauts at the International Space Station (ISS), they are still subject to a gravitational acceleration of 8.7 m s-1, or about 89% of “1 g”. If the Earth’s gravity were to suddenly stop acting on ISS, the ISS will move away from Earth tangentially at a constant velocity instead. Find out more here in this topic. Content: • Gravitational field • Gravitational force between point masses • Gravitational field of a point mass • Gravitational field near to the surface of the earth • Gravitational potential • Circular Orbits Learning Objectives: Candidates should be able to: (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 place at that point. (b) recognise the analogy between certain qualitative and quantitative aspect of gravitational and electric fields. (c) recall and use Newton's law of gravitation in the form 12 2 Gm mF r = . (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. (f) show an understanding that on the surface of the Earth g is approximately constant and equal to the acceleration of free fall. (g) define the gravitational potential at a point as the work done per unit mass in bringing small test mass from infinity to the point. (h) solve problems using the equation GM r φ = − for the potential in the field of a point mass. (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. (bold) items are needed for 8867 H1 Physics

9749(2023) H2 Physics H207 Gravitational Field – Notes Page 2 of 26 7.1 Gravitational Field A “field” is a region of space where a force is experienced by an “entity” without contact. A mass experiences a gravitational force when placed in a gravitational field. Forces are vector quantities so the direction has to be well-defined. Gravitational force is a purely attractive force. An isolated mass generates its gravitational field in the region surrounding the mass and it permeates all of space (“to infinity”). When another mass is inside this region, that mass interacts with the existing gravitational field and both masses experience gravitational force. 7.1.1 Field Lines Field lines represent a field visually. Arrows show the direction of force acting on a test mass. A test particle is an idealized object which does not al