AQA Edexcel A Level Physics Gravitational Fields Answers 2

1. The graph below shows the variation of the orbital period squared with the radius cubed for Jupiter’s moons. Total for Question 1: 10 (a) Define a gravitational field. (b) By equating the centripetal force and the gravitational force on a planet, show that T 2 = 4π2 r3. [1] [4] (c) Use the result from the previous part and the graph above to calculate Jupiter’s mass. [3] (d) Kepler’s second law states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. Use this to explain why we rarely see great comets, whose orbits are highly elliptical. [2] 2. Satellites can also be analysed using the various laws of gravitation and circular motion. For this question, assume that Earth’s mass is 6.0 × 1024 kg and that it has a radius of 6400 km. Total for Question 2: 10 (a) By equating gravitational and centripetal forces, show that the mass of a satellite in orbit does not affect its speed. [2] (b) Calculate the speed at which a satellite must be released into orbit if it is to maintain a height of 100 km above Earth’s surface. [2] (c) Define a geostationary orbit. [3] (d) Calculate the altitude of a geostationary orbit. [3] 3. All vector fields have an associated scalar potential. For this question, assume Earth has a radius of 6400 km and a mass of 6.0 × 1024 kg. (a) Define, in words, the gravitational potential. Total for Question 3: 10 [1] (b) Given that the gravitational potential, Vg, is 63 MJkg−1 at Earth’s surface, calculate the following: i. Vg at infinity. [1] ii. Vg at an altitude equal to Earth’s radius. [1] (c) Calculate the gravitational potential energy of a 10 kg ball at an altitude equal to three times Earth’s radius. [2] (d) Sketch a graph to show how the magnitude of the gravitational force varies with the distance from the centre of the spherical object creating the field. What is represented by the area underneath the graph? [1] (e) The average kinetic energy of an H2 molecule is given by the equation 1 mc¯2 = 3 kT , where m is the [4] 2 2 mass of the molecule, c is the r.m.s. speed, k is the Boltzmann constant and T is temperature. By calculating the r.m.s. speed and the escape velocity, determine whether or not a helium molecule at 300 K can escape Earth’s atmosphere. The mass of one atom of helium is 6.6 × 10−27 kg.