Define a gravitational field

A field is a region in which a force may be exerted by an object.

What are the rules for drawing gravitational field lines?

Gravitational Field lines represent the direction of force on a mass at a point.

The separation between fields lines represents their strength Field lines drawn for a single mass (gravitational or otherwise) never cross each other.

Gravitational field lines always point towards the centre of mass. (Gravitational force is always attractive).

Define the strength of a gravitational field (g)

The force per unit mass on a small test mass placed in the field.

Describe a radial field

The field lines are like the spokes of a wheel, towards the centre.

What happens to g in a radial field?

Decreases with increasing distance from the massive body.

Describe a uniform field

Field lines are parallel and equally spaced.

What happens to g in a uniform field?

Magnitude and direction of g is constant.

Sketch a graph of gravitational field strength against separation.

State what can be calculated from this graph

See diagram

Area = Gravitational potential

Explain why mass of an object is constant but weight may change

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- Mass only depends on the number of particles present.
- Weight is a force which depends on gravitational field strength
- Gravitational fields strength varies on every planet

Define Newton's law of gravitation?

Attractive force

Proportional to the mass of each object

Inversley Proportional to r^{2} (r is distance between objects)

When using Newtons law of atteaction equation why can planets be assumed to be point masses?

The diamater of a planet is much smaller than the distance between the two planets.

Sketch a graph of force against separation.

State what can be found from this graph

See diagram

Area = work done = GPE

State Kepler's first law

The orbital path of a planet around the Sun is an ellipse, not a perfect circle. The Sun lies at one of the foci of the ellipse

State Kepler's second law

An imaginary line connecting the Sun to any planet sweeps out equal areas of the ellipse over equal intervals of time.

KE + PE = a constant

If the radius of a orbit decreases what happens to the speed, kinetic energy, potential energy and total energy?

Total energy is constant

Total energy = kinetic + potential

Potential energy - decreases so

Kinetic energy and speed increases

If the radius of a orbit increases what happens to the speed, kinetic energy, potential energy and total energy?

Total energy is constant

Total energy = kinetic + potential

Potential energy - increases so

Kinetic energy and speed decreases

What is Kepler's Third Law?

The period of planet's orbit squared is proportional to the cube of the average radius of its orbit.

T^{2 }proportional r^{3}

State the equations needed to derive the orbital velocity equation

F = mv^{2}/r and

F = GM_{1}M_{2}/r^{2}

State the equations needed to derive the orbital time period equation equation (Keplers 3rd Law)

F = mv^{2}/r and

F = GM_{1}M_{2}/r^{2} and

v = 2πr/T

State the orbital time period for a geostationary satellite

24 hours

State the criteria for a geostationary orbit

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- Have a time period of 24 hours
- Be at a height of 36 000 km above the Earths surface
- Be circular
- Be equatorial (in the plane of the equator)
- Rotate in the same direction of the earth (west to east)

State some benefits of a polar (low) orbit

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- A cheaper launch cost
- Eventually cover the whole earth as the satellite doesn’t stay above the same point

Define gravitational potential energy

The gravitational potential energy (W) at a point in a field, is the work done to move an object from infinity to that point.

It is measured in joules

State the equation for gravitational potential energy

E_{p} = - GMm / r

Sketch a graph of GPE against separation. What can be found from this graph?

see diagram

Gradient = force

Sketch a graph of GPE against seperation for a journey from the Earth to the Moon.

See diagram.

Define gravitational potential

Gravitational potential at a point is the work done per unit mass to move a small object from infinity to that point.

It is measured in Jkg^{-1}

Is gravitational potential a vector or scalar?

Scalar

Why is gravitational potential always negative?

GPE is zero at infinity.

The further you raise the object, the more work you do and the greater the change in gpe.

GPE increase with distance but can only increase to 0 at infinity.

Sketch a graph of gravitational potential against separation.

What can be found from this graph?

see diagram

Gradient = g