(a) State Newton's law of gravitation in word form. (b) Use the law to show that that the escape velocity for a planet is given by the expression v= √√28, R. You can assume that the gravitational potential per unit - GM mass U, at the surface of the planet, is given by the expression U = where R M and R are the mass and radius of the planet. (c) Assuming that the Earth is a uniform sphere of radius 6.4 x 106 m and mass 6.0 x 1024 kg, calculate: (1) the gravitational potential at the surface of the Earth and the gravitational potential at a point 6.0 x 105 m above the surface of the Earth. (d) A 5 kg mass is to be delivered to a point in space where the gravitational effect on the mass is negligible. Calculate: (1) the escape velocity for the mass. (iii) the work done in taking the mass to a point 6.0 x 105 m above the surface of the Earth. (iii) the work needed to deliver the mass to the point where the gravitational potential is zero. 3

(a) State Newton's law of gravitation in word form. (b) Use the law to show that that the escape velocity for a planet is given by the expression v= √√28, R. You can assume that the gravitational potential per unit - GM mass U, at the surface of the planet, is given by the expression U = where R M and R are the mass and radius of the planet. (c) Assuming that the Earth is a uniform sphere of radius 6.4 x 106 m and mass 6.0 x 1024 kg, calculate: (1) the gravitational potential at the surface of the Earth and the gravitational potential at a point 6.0 x 105 m above the surface of the Earth. (d) A 5 kg mass is to be delivered to a point in space where the gravitational effect on the mass is negligible. Calculate: (1) the escape velocity for the mass. (iii) the work done in taking the mass to a point 6.0 x 105 m above the surface of the Earth. (iii) the work needed to deliver the mass to the point where the gravitational potential is zero. 3

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter11: Angular Momentum

Section: Chapter Questions

Problem 57P: A Molniya orbit is a highly eccentric orbit of a communication satellite so as to provide continuous...

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