Gravitational Field JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS Gravitational Field Learning Outcomes Candidates 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 the gravitational field strength at a point as the gravitational force exerted per unit mass placed at that point. (b) recognise the analogy between cer tain qualitative and quantitative aspects of gravitational and electric fields (*To be taught in Electric Fields) Gravitational force between point masses (c) recall and use Newton's law of gravitation in the form F = 12 2 Gm m r Gravitational field of a point mass (d) derive, from Newton's law of gravitation and the definition of gravitational field strength, the equation g = 2 GM r for the gravitational field strength of a point mass (e) recall and apply t he equation g = 2r GM for the gravitational field strength of a point mass to new situations or to solve related problems Gravitational field near to 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  = r GM− 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.

2 Introduction ▪ Isaac Newton (1642 –1726), published Philosophiæ Naturalis Principia Mathematica ("Mathematical Principles of Natural Philosophy") in 1687. In it, he formulated the Newton’s laws of motion (Dynamics), and the Newton’s law of gravitation (Gravitational Field). ▪ Newton’s studies in gravitation started when he observed an apple falling to the ground and he began to ask himself questions. Why does a falling apple always descend perpendicularly to the ground? Did the force that pulled an apple to the Earth also extend further and pull bodies like the Moon towards the Earth? Would this force affect the orbit of the moon? We will answer these questions and more in this chapter. 1 GRAVITATIONAL FORCE (c) Candidates should be able to recall and use Newton’s law of gravitation in the form 12 2 Gm mF r= . . 1.1 Newton’s law of gravitation Newton’s law of gravitation states that the force of attraction between two point masses is directly proportion al to the product of the masses and inversely proportional to the square of the distance between them.