Gravitational Fields

For uniform fields (e.g close to the surface of the Earth), what formula can we use?

Change in potential = gh

Explain why we choose to define the zero point of gravitational potential at an infinite distance from any planet.

This definition ensure that all planets and stars have the same zero point for their potentials.

What are key points about gravitational field strength?

-The gravitational field strength at a point in a field is independent of the mass placed there - it's is a property of the field. Thus two objects of different mass placed at the same point in the field will experience the same field strength, but feel different gravitational forces.

What is a gravitational field?

A region in which a massive object experiences a gravitational force. Any object of mass produced a gravitational field but we often use the term to describe the region of space around large celestial objects like galaxies, stars, planets and moons. The gravitational field only becomes noticeable when one of the masses is of planetary size.

What is a geostationary orbit?

A satellite that appears to be stationary over a point in the Earth's equator. The orbit of such a satelitte is circular and over the Earth's equator, and the only points on Earth that orbits its centre are those on the equator.

Explain the term equipotential

An equipotential is a line of surface where the gravitational potential is the same.

Give a summary of what gravitational force depends on

Depends on the mass of the Earth and your mass, it wreaks with distance.

Give the uses of geostationary satellites

Geostationary satellites are predominantly used for communications. Satellite TV companies use geostationary satellites to cover a constant area on the Earth's surface - hence you point your satellite dish receiver in the direction of the geostationary satellite.

What causes the weight that you feel?

Gravitational attraction by the Earth

Explain what is meant by geosynchronous

Have an orbital period of 24 hours. For an orbit to be geostationary, it must first be geosynchronous.

What does it mean if lines of equipotential are close together?

If equipotentials are close together, a lot of work must be done over a relatively short distance to move a mass (g is strong) - against the field - i.e the field is very strong

Does gravitational potential depend on mass?

Potential, like field strength is a property of the field at a point, and is independent of the mass places there. Two objects with different masses at the same point in a field are subject to the same potential, but have different potential energies.

If you plot T^2 against R^3, what is the gradient equal to?

T^2 / R^3 = 4*pi^2 / G*M

State what is represented by gravitational field lines.

The direction of gravitational force on a mass placed in the field.

If you plot a graph of V against r, what would the gradient give you?

The gradient would give -g g at that point = -potential gradient

What is Kepler's third law?

The square of the period of a planet's orbit is directly proportional to the cube of its mean distance from the Sun.

Close to the surface of the Earth, describe the field lines

Uniform field lines. They are directed downwards (the direction in which a body near the Earth surface would feel a gravitational force) and they are parallel and of equal distance apart indicating that the field is constant or uniform.

When is the gravitational force 0?

When gravitational force on object 1 equals to gravitational force on object 2

What affects the size of the Earth's pull on you?

Your mass, it's mass

What does Newton's Law of gravitation tell us?

-The gravitational force of attraction is directly proportional to the product of the masses and is inversely proportional to the square of the separation between the masses. -Every object with a mass in the universe attracts every other according to this law. But the actual size of the force becomes very small for objects very far away.

What are the key points to note about field line diagrams?

1. Field lines do not start or stop in empty space (even though on diagrams they have to stop somewhere). They end on a mass and extended all the way to infinity. 2. Field lines never cross. (If they did, then an object placed at the point where they crossed would feel forces in more than one direction. These forces could be resolved into one direction, the direction of the field line there).

What is meant by action at a distance ?

Action at a distance is the concept that an object can be moved, changed or otherwise affected without being physically touched (as in mechanical contact) by another object. That is, it is the non-local interaction of objects that are separated in space.

What is the relationship between g and radius ?

An inverse square law, g is proportional to 1/ r^2 therefore product of gr^2 must be a constant

What is the relationship between gravitational force (force of gravity) and radius?

An inverse square law. Gravitational force is inversely proportional to r^2.

When will the gravitational potential energy be zero?

At a distance of infinity away, Ep has a maximum value of 0.

Why does potential energy always have a negative value?

At a distance of infinity away, Ep has a maximum value of 0. Therefore, at any distance closer than infinity, Ep must have a negative value.

When is the gravitational potential equals to zero?

At a distance of infinity gravitational potential is zero. Going from the point to infinity, the potential energy increase therefore all values for potential are negative.

What are the main problems with launching geostationary satellites into orbit?

Because geostationary satellites have to be launched so high (other satellites orbit as low as a few hundred km), the energy and costs required for launching a satellite into geostationary orbit are high.

What is the first step in the derivation of Kepler's third Law ?

Equate centripetal force to gravitational force. The centripetal force is provided by gravitational force ?

How would you draw equipotential lines?

Equipotentials are always perpendicular to field lines

In what direction are field lines directed for the Earth?

Field lines are directed rapidly onwards because at any point in the Earth's field, a body will feel a force directed towards the centre of the earth.

What happens to the strength of the pull of the Earth as you go further away?

It gets weaker

What energy is needed for a mass to completely escape the gravitational field of a planet of mass M and radius r?

It is equal to the work done in moving the mass from a planet's surface to a point where gravitational field is zero (infinity)

Close to the mass would be the potential be large or small?

Large and negative because you do loads of work to move the mass away

What happens to lines of equipotential further way from a mass?

Lines of equipotential get further away as you get further away from the mass.

How much work is done if you move around an equipotential surface ?

No work is done, 0

Describe three essential features of the orbit needed for a satellite to appear geostationary.

Period of 24 hours Moving west to east equatorial orbit

Explain what is meant by potential gradient

Potential gradient a point in a gravitational field is the change of potential per metre at that point

What is the gravitational field strength, g ?

The gravitational force exerted on an object placed at that point, per kg of the object's mass. It is just the number of Newton's of attractive force acting per kg of the object's mass. Since the attractive force is simply what we call weight we write it as: force / mass

What extent do gravitational fields have?

The gravitational force is infinite in range, although it becomes very weak at large distances as it is an inverse square Law. The gravitational field due to a body is this also infinite.

When does Newton's Law of Universal Gravitation force apply?

The law applies between point masses, but spherical masses can be treated as though they were point masses with all their mass concentrated at the centre.

Explain why a spacecraft orbiting on the one equipotential can stay in orbit round a planet indefinitely.

The spacecraft stays in orbit at a constant speed because no work is done by the planet's field to change its direction. It is on an equipotential so its energy remains unchanged.

What is the escape velocity?

The velocity at which an object needs to be travelling away from an astronomical body in order to break free from the gravitational field, without further propulsion.

What is gravitational potential?

The work done per unit mass in moving the mass from infinity to the point. Work done / mass

What happens to field lines further away from the Earth?

They become more spread out as the distance from the Earth increases, indicating the diminishing strength of the field.

If the Earth is pulling down on you, then what else must be occurring by Newton's 3rd Law ?

You must be pulling up on the Earth with a force equal to your weight.

What is g?

gravitational field strength AND acceleration