Gravitational Fields

What is gravity?

A universal attractive force between masses.

Is gravity a strong or weak force?

Weak.

What is the range of gravity?

Infinite.

Do all masses produce a gravitational field?

Yes.

How does gravitational field strength change with distance?

It decreases with increasing distance.

Where do objects experience gravitational attraction towards?

The centre of mass.

How can extended objects be modelled in gravity calculations?

As point masses at their centre of mass.

What does a radial gravitational field look like?

Field lines converge towards the centre.

What do gravitational field arrows show?

Direction of attraction.

What does field line spacing represent?

Field strength.

Do gravitational field lines cross?

No.

When can gravity be modelled as a uniform field?

Close to a planet’s surface.

What do uniform gravitational field lines look like?

Parallel and equally spaced.

Define gravitational field strength (g)

Force per unit mass at a point.

Equation for uniform gravitational field strength

g = F / m.

Unit of gravitational field strength

N kg⁻¹ (or m s⁻²).

Is gravitational field strength a scalar or vector?

Vector.

State Newton’s law of gravitation

F = −GMm / r².

What does G represent?

Gravitational constant.

Value of G

6.67 × 10⁻¹¹ N m² kg⁻².

What does r represent in gravitation equations?

Separation of centres.

Why is there a negative sign in Newton’s law?

Force is attractive.

Equation for gravitational field strength of a point mass

g = −GM / r².

Does g depend on the test mass?

No.

What does g near Earth’s surface equal?

Acceleration of free fall.

State Kepler’s first law

Planets orbit in ellipses with the Sun at one focus.

Why can planetary orbits be approximated as circular?

Low eccentricity.

State Kepler’s second law

Equal areas swept in equal times.

What does Kepler’s second law imply about speed?

Faster when closer to the Sun.

State Kepler’s third law

T² ∝ r³.

What provides centripetal force for planets?

Gravitational force.

Orbital velocity equation

v = √(GM / r).

Orbital period equation

T² = 4π²r³ / GM.

What is a satellite?

An object orbiting a larger body.

Give two types of satellites

Natural and artificial.

Give uses of artificial satellites

Communications, GPS, research.

What is a geostationary satellite?

Satellite fixed above one Earth point.

Geostationary orbital period

24 hours.

Direction of geostationary orbit

Same as Earth’s rotation.

Orbital plane of geostationary satellites

Equatorial.

Define gravitational potential (Vg)

Work done per unit mass from infinity.

Unit of gravitational potential

J kg⁻¹.

What is gravitational potential at infinity?

Zero.

Why is gravitational potential negative?

Energy required to escape field.

Equation for gravitational potential

Vg = −GM / r.

Define gravitational potential energy (Ep)

Work done moving mass from infinity.

Equation linking Ep and Vg

Ep = mVg.

Gravitational potential energy equation

Ep = −GMm / r.

Define escape velocity

Minimum speed to escape a gravitational field.

Does escape velocity depend on object mass?

No.

Escape velocity equation

v = √(2GM / r).

Energy condition for escape

KE ≥ GPE.