5.4, 5.6-5.8 Circular Motion, Gravitational Fields, Planetary Motion

Explain how the speed of an object undergoing circular motion remains constant even though there is a resultant force acting on it.

• The resultant force acts at a right angle to the motion of the object;

• and so no work is done by the force

• hence, the kinetic energy (and speed) of the object does not change.

Explain what is meant by a radian.

The angle subtended at the centre of a circle when the arc is equal in length to the radius.

Explain what is meant by the angular speed of an object about a point.

The angle swept out per unit time by the object.

State, in terms of force, the conditions necessary for an object to move in a circular path at constant speed.

The resultant force acts on the object in a direction which is perpendicular to the direction of motion (velocity).

State what is meant by a geostationary orbit.

The spaceship/satellite is always vertically above the same point on the surface of the Earth/planet.

State some of the properties of a geostationary orbit.

• The orbit is equatorial (that is it is above the equator);

• The velocity of the satellite is parallel to the velocity of a point on the surface of the planet at all times;

• The satellite orbits in the same direction as the rotation of the planet.

Polar-orbiting satellites are used for communication on Earth. State and explain one advantage and one disadvantage of polar-orbiting satellites as compared with geostationary satellites.

• Advantage: the whole Earth may be covered/mapped in several orbits; there is a much shorter time delay as the orbit is much lower,

• Disadvantage: They must be tracked and more satellites are needed for continuous operation.

Suggest one advantage of launching geostationary satellites from the Equator in the direction of rotation of the Earth.

Satellite will already have some speed in the correct direction.

Describe the pattern of gravitational field lines in a uniform field.

• The field lines are parallel to each other;

• The field lines are equally spaced.

State, in words, Newton's law of gravitation.

• The gravitational force exerted on one object due to another object is proportional to the product of their masses;

• and inversely proportional to the square of the distance between their centres of mass.

Define gravitational field strength.

Force per unit mass at a point in a gravitational field.

Explain why, although the planets and the Sun are not point masses, Newton's Law of Gravitation applies to planets orbiting the Sun.

• The orbital separation of the planets and the Sun is much greater than the diameter of the Sun or the planets.

• Explain why there is a point between the Earth and the Moon at which the gravitational field strength is zero.

• The gravitational fields of the Earth and the Moon are in opposite directions;

• The resultant gravitational field is found by subtracting the field strength of each of the Earth's and Moon's gravitational field;

• so there is a point where the two fields exactly cancel, making the resultant field zero.

The total energy of the satellite gradually decreases. State and explain the effect of this decrease on:

The radius of the orbit;

• The total energy of the satellite is proportional to -r^-1;

• so as the total energy decreases/becomes more negative, r^-1 becomes larger, so r becomes smaller

The linear speed of the satellite

• GMm/r^2 = mv^2/r;

• v^2 = GM/r;

• As r decreases, v increases.

State Kepler's First Law.

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

State Kepler's Second Law.

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

State Kepler's Third Law.

The cube of the planets distance from the Sun divided by the square of the orbital period is the same (for all planets).

Explain why values of gravitational potential near to an isolated mass are all negative.

• The potential at infinity is defined as being zero;

• Gravitational forces are always attractive;

• So work is done on a mass by the gravitational field/force to move it closer to an isolated mass, which decreases the gravitational potential energy/gravitational potential of the system.

Explain why values of gravitational potential are always negative whereas values of electric potential may be positive or negative.

• Gravitational forces are always attractive, whereas electric forces can be attractive or repulsive;

• For gravitational forces, work is done on the masses as they come together;

• For electric forces, work is done by the charges if they have the same sign, work is done on the charges if they have opposite signs.