Field Theory Answers

A passenger in a spaceship going round the earth in a circular orbit of radius 2Re has a mass of 60.0kg. Given that Re is the average radius of the earth, calculate the gravitational potential energy of the astronaut.

An object of mass, m, is loacted at a height, h above the earth's surface in a region where the gravitational field strength of the earth is g. Under what circumstance(s) can the expression U = mgh be used, to calculate its gravitational potential energy, U?

A proposed communication satellite would revolve round the earth in a circular orbit in the equitorial plane, at a height of 35880 km above the earth's surface. Find the period of revolution of the satellite in hours, and comment on the result. (Radius of earth= 6370 km, mass of earth = 5.98 x 10^24 , constant of gravition = 6.66 x 10^-11 Nm^2kg^-2)

Assuming the earth to be perfectly spherical, give sketch graphs to show how (a) the acceleration due to gravity , (b) the gravitational potential due to the earth's mass, vary with distance from the surface of the earth for points external to it.

Assuming that the planets are moving in circular orbits, apply Kepler's laws to show that the acceleration of a planet is inversely proportional to the square of its distance from the sun.

Briefly describe an experiment by which the value of g may be determined. Indicate the measurements taken and how to calculate the result.

Distinguish between the gravitational constant (G) and the acceleration due to gravity (g) and show the relation between them.

How can you account for the sensation of 'weightlessness' experienced by the occupant of a space capsule
(a) in a circular orbit round the earth
(b) in outer space? Give one other instance in which an object would be 'weightless'.

Assuming that the mean density of the earth is 5500kgm^-3, that the constant gravitation is 6.7 x 10^-11 Nm^2kg^-2, and that the radius of the earth is 6400km, find a value for the acceleration due to gravity at the earth's surface.

If the acceleration due to gravity is 98m/s^2 and the radius of the earth is 6400km, calculate a value for the mass of the earth.