Gravitational Fields

A force field is a region in which a body experiences a non-contact force.

Gravitational fields are regions where objects with mass experience an attractive force due to gravity.

This force is determined by Newton's Law of Gravitation, which states that:

‣ The force is directly proportional to product of the masses involved

‣ The force is inversely proportional to the square of the separation between two masses

As an equation this is:

F = GMm/r²

(G = Gravitational Constant)

Field lines can be drawn to represent a gravitational field. The lines:

‣ Always point towards the centre of the mass producing the field

‣ Show the direction in which a mass would experience a force if placed at a point in that field

‣ Are closer together at points where the field is stronger

‣ Are further apart at points where the field is weaker

‣ Never cross over each other

A useful way to compare gravitational fields is by comparing gravitational field strengths. Gravitational field strength is defined as the attractive gravitational force that a unit mass would experience, at a given point in the field.

The gravitational field strength at the surface of Earth is roughly 9.81 N/kg. This means that a mass of 1kg would experience a force of 9.81N.

As an equation, gravitational field strength is:

g = F/m

which for a radial field gives...

g = GM/r²

Gravitational potential at a point is the amount of work done in moving a unit mass from infinity to that point in a gravitational field.

As an equation this is:

V = -GM/r

‣ Gravitational potential is defined as being zero at infinity

‣ Work is done to move an object closer to the centre of the field, and so gravitational potential is always a negative value.

‣ Equipotentials are planes containing points with equal gravitational potential. This means that the amount of work done when an object is moved around these planes is zero.

Orbits:

The orbits of planets and satellites are a result of the gravitational force produced by the body they are orbiting. This force acts as a centripetal force, which results in circular motion. There are many different types of orbit.

Know that:

‣ Synchronous orbits have a time period of one day, and so return to the same place in the sky each day.

‣ Low orbits at heights of between 160 km and 2000 km.

‣ Geostationary orbits have a time period of one day and stay over the same point on the Earth's surface. They must be directly above the equator and travel in the same direction as the earth's rotation.

Gravitational Fields:

Similarities:

‣ Gravitational field strength (g) is a force per unit mass.

‣ Newton's Law of gravitation for force between 2 masses is an inverse square law.

‣ The field lines around a point mass show the force acting on a point mass, and is 0 at infinity.

‣ Gravitational potential (V₉ᵣₐᵥ) is the potential energy per unit mass, and is 0 at infinity.

Differences:

‣ Forces are always attractive.

‣ Objects cannot be shielded from the field.

‣ The size of the force doesn't depend on the medium between masses.

Electric Fields:

Similarities:

‣ Electric field strength (E) is force per unit +ve charge.

‣ Coulomb's Law for electric force between 2 +ve point charges is an inverse square law.

‣ The field lines around a point charge show the force acting on a positive point charge.

‣ Electric potential (V) is the potential energy per unit positive charge, and is 0 at infinity.

Differences:

‣ Force can be attractive or repulsive.

‣ Objects can be shielded from the field.

‣ The size of the force does depend on the medium between charges.

What does Newton's Law of Gravitation state?

The gravitational force between two point masses is proportional to the product of their masses and is inversely proportional to the square of the separation of their centres.

State the defining equation for Newton's Law of Gravitation.

F = -GMm/r²

What does 'G' represent?

The universal gravitational constant, which is equal to 6.67 x 10⁻¹¹ N m²kg⁻².

What is always true about the gravitational force between two masses?

It is always an attractive force.

What is a gravitational field?

A region in which any object with mass will experience a non-contact force.

What is gravitational field strength?

The force per unit mass felt by the object.

What is the unit for gravitational field strength?

Nkg⁻¹

State the equation for gravitational field strength.

g = GM/r²

or

g = F/m

What is the gravitational potential at a point?

The energy transferred per unit mass when moving an object from infinity to that point.

State the equation for gravitational potential.

V = -GM/r

State the equation for gravitational potential energy.

E = -GMm/r

What is an equipotential?

A plane in which all points have the same potential.

What is true when a mass moves along an equipotential?

No work is done when along an equipotential.

What does the area under a force-separation graph represent?

Energy

What is gravity?

Gravity is the universal attractive force which acts between all matter.

What can field lines tell you about a field?

The direction of the arrows show the direction of the field. The strength of the field is represented by the density of the field lines.

What is gravitational potential?

The potential energy per unit mass, at any point in the field. Zero potential is defined at infinity, hence at a point close to a mass the potential of an object would be negative.

How do you calculate the work done by moving a mass in a field?

Work Done = Mass x Change in Gravitational Potential

What is gravitational potential difference?

Gravitational potential difference is the difference in the gravitational potentials of two points in a gravitational field.

How much work is done per unit distance when you move along an equipotential?

No work is done when moving across equipotentials, as the potential at each point is the same.

Why is gravitational potential a negative value?

Work needs to be done to move an object from the inside the field to outside the field. Since outside the field's potential is defined as zero then the potential inside the field must be negative.

How is the orbital period related to the radius of a circular orbit?

T²∝ R³

Compare the PE and KE of a lower orbit to a higher one.

A lower orbit (smaller m) has less potential energy and more kinetic energy than a higher orbit (bigger r).

What is the period of a geosynchronous orbit?

Geosynchronous orbits have a period of one day.

What type of matter is affected by a gravitational field?

Any object or matter with mass will experience an attractive force.

What is a point mass?

A point mass is a theoretical object that has a mass but no dimensions. This means that all of its mass acts at a single point.

What is the relationship between the field strength and the field lines that represent it?

The closer the lines are together, the stronger the gravitational field strength. The further apart the lines are, the weaker the field strength.