TJC 8 Gravitational Fields

Unit 8: Newton’s Law of Gravitation Learning Outcomes Candidates should be able to: (a) recall and use Newton's law of gravitation in the form F = 2 21 r mGm . (b) derive, from Newton's law of gravitation and the definition of gravitational field strength, the field strength due to a point mass, g = 2r GM . (c) recall and use g = 2r GM for the gravitational field strength due to a point mass to solve problems. (d) 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. (e) define the gravitational potential at a point as the work done per unit mass by an external force in bringing a small test mass from infinity to the point. (f) solve problems using the equation  = r GM for the gravitational potential in the field due to a point mass. (g) show an understanding that the gravitational potential energy of a system of two point masses is UG = GMm r (h) recall that gravitational field strength at a point is equal to the negative potential gradient at that point and use this to solve problems. (i) analyse problems related to escape velocity by considering energy stores and transfers. (j) 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. Student’s copy

Temasek Junior College 2025 2 1. NEWTON’S LAW OF GRAVITATION LO(a) You may have heard the legend that Newton was struck on the head by a falling apple while napping under a tree. This alleged accident supposedly prompted him to imagine that perhaps all objects in the Universe were attracted to each other in the same way the apple was attracted to the Earth. It was in 1687 that Newton first published his work on the law of gravitation. Gravitational force F = 2 21 r mGm where m1 and m2 are the two point masses and r the distance between them. The constant of proportionality G is called the universal gravitational constant. G = 6.67  10-11 N m2 kg-2. Note: 1. The expression is applicable ONLY between point masses or spheres of uniform density. 2. For spheres, r is the distance between their centres and NOT surface to surface. 3. The gravitational force is directed along the line joining their centres. 4. The gravitational forces acting on the two masses form an action-reaction pair. 5. By the usual convention in Physics, an attractive force should have a negative sign (i.e. F = - 2 21 r mGm ). But since gravitational repulsion does not exist, the negative sign is omitted. 6. Newton’s law of gravitation is an e