Chapter 18 - Gravitational Fields

State Kepler's second law of planetary motion. [1]

A line segment joining a planet and the Sun sweeps our equal areas during equal time intervals.

This question is about orbits around the Sun. The special case where the Earth and the space observatory are positioned so that both orbit the Sun in exactly one year. Explain how it is possible for the observatory to have an orbital period of one year. Suggest why this is convenient. [3]

Centripetal pull towards the Sun is smaller allows resultant force to give required F = mv2/r (i.e. where v is the correct value to give a period of one year) so the observatory stays at the same point relative to Earth so aerial directions fixed/convenience of positioning aerials to pick up signals from observatory.

State two features of geostationary orbits. [2]

Equatorial orbit Period is 24 hours (same as Earth)

Explain why in order for there to be a change in gravitational potential energy a mass needs to move vertically in a uniform field. [2]

For there to be a change in gravitational potential energy a fixed mass must experience a change in gravitational potential. At a fixed height in a uniform field the gravitational potential is constant. Only a change in vertical height will results in a change in gravitational potential and so a change in gravitational potential energy.

Define gravitational field strength, g. [1]

Force per unit mass at that point.

Explain why the acceleration due to gravity and the gravitational field strength at the Earth's surface have the same value. [2]

From Newton's second law: F = ma; a = F/m = W/m for a freely falling object (without air resistance etc.). This is the same value as g = F/m = W/m , as measured by a spring balance.

Explain why the resultant gravitational field strength changes from a negative value near the Earth to a positive value near the Moon. [2]

Gravitational field strength is a vector quantity. Since gravitational fields are always attractive, the gravitational fields of the Earth and Moon are in opposite directions.

Explain why the direction of the gravitational field strength at any point around a planet is always towards the centre of the planet. [1]

Gravitational field strength is always attractive and points towards the centre of mass of the object causing the gravitational field.

Describe how you can use a newton-meter and a known mass to determine the gravitational field strength on top of a mountain. [2]

Hold the newton-meter vertically in a fixed position and suspend the known mass from it. Measure the value of force shown in the newton-meter and use this, along with the known mass m, to find g using g=F/m.

The planet Mars has a gravitational potential of -12.7 MJkg-1 on its surface. Explainthe significance of the minus sign in the value of the potential. [2]

The negative sign implies that gravitational field is an attractive field, therefore work has to be done to move an object further away from a gravitating mass. The potential at infinity is (maximum and) equal to 0.

State Kepler's first law of planetary motion. [1]

The orbit of a planet is an ellipse with the Sun at one of the two foci.

State Kepler's third law of planetary motion. [1]

The square of the orbital period of a planet is directly proportional to the cube of its average distance from the Sun.

Define gravitational potential at a point in space around a gravitating mass. [1]

The work done per unit mass to move a small object from infinity to that point

Suggest why geostationary satellites are used for satellite television. [2]

They remain above the same point on the surface of the Earth. Providing continuous coverage for a certain area.