Gravitational Field

What is gravity?

A universal attractive force that acts between all matter.

What is a field?

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

What do gravitational field lines show?

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

In which direction does a stationary mass initially move in a gravitational field?

Along the field line towards the source mass.

What represents the strength of a gravitational field?

The density of the field lines.

What happens to the field line density if the mass causing the field increases?

The field line density increases.

State Newton's law of universal gravitation.

Every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of their separation.

What is the equation for gravitational force between two masses?

F = GM₁M₂ / r²

What is the value of the gravitational constant, G?

6.67 × 10⁻¹¹ N m² kg⁻²

What are the units of G?

N m² kg⁻²

What are the SI base units of G?

kg⁻¹ m³ s⁻²

What is gravitational field strength?

Force per unit mass.

What is the equation for gravitational field strength?

g = F / m

What is the gravitational field strength due to a point mass?

g = GM / r²

What does M represent in g = GM / r²?

The mass producing the gravitational field.

What does r represent in g = GM / r²?

The distance from the centre of mass.

Why is gravitational field strength also called gravitational acceleration?

Because F = ma gives a = GM / r² = g.

What is the mass of Earth?

5.97 × 10²⁴ kg

What is the radius of Earth?

6.37 × 10⁶ m

What is the gravitational field strength at Earth's surface?

9.81 m s⁻²

If object X has mass M and radius R, and object Y has mass 5M and radius 2R, what is gₓ : gᵧ?

4 : 5

At what point between masses M and 5M is the gravitational field strength zero?

r = x / (1 + √5)

Approximately what fraction of x is the neutral point between M and 5M?

0.31x

What is gravitational potential?

The work done per unit mass in bringing a mass from infinity to a point.

What is the equation for gravitational potential?

V = −GM / r

What are the units of gravitational potential?

J kg⁻¹

How is gravitational potential related to work done?

ΔW = mΔV

What is the relationship between gravitational field strength and potential gradient?

g = −ΔV / Δr

What is the gravitational potential at infinity?

Zero.

Why is gravitational potential negative?

Because work must be done to move a mass from the field to infinity.

Does gravitational potential increase or decrease with distance from a mass?

It increases towards zero.

What is an equipotential surface?

A surface on which gravitational potential is constant.

What shape are equipotential surfaces around a point mass?

Concentric circles (or spheres in 3D).

How do field lines meet equipotential surfaces?

Perpendicularly.

What is the angle between a field line and an equipotential surface?

90°.

Is work done moving along an equipotential surface?

No.

Why is no work done along an equipotential surface?

Because ΔV = 0.

What does closely spaced equipotential lines indicate?

A stronger gravitational field.

Why do equipotential lines spread out further from a mass?

Because gravitational field strength decreases with distance.

In which direction do gravitational field lines point?

Towards the mass producing the field.

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

Work done.

What does the area under a gravitational field strength-distance graph represent?

Change in gravitational potential.

What does the gradient of a gravitational potential-distance graph represent?

Gravitational field strength.

What is orbital period?

The time taken for one complete orbit.

What symbol is used for orbital period?

T

What is the equation for orbital speed using circumference?

v = 2πr / T

What force provides the centripetal force for a satellite?

Gravity.

What equation links gravitational force and centripetal force?

GMm / r² = mv² / r

What is the equation for orbital speed?

v = √(GM / r)

What is the equation for kinetic energy?

Eₖ = ½mv²

What is the kinetic energy of an orbiting satellite?

Eₖ = GMm / 2r

State Kepler's third law for circular orbits.

T² ∝ r³

What is the full equation for orbital period?

T² = 4π²r³ / GM

What is angular velocity?

The rate of angular motion.

What is the equation linking angular velocity and period?

ω = 2π / T

What is the centripetal force equation using angular velocity?

F = mω²r

What is gravitational potential energy?

Eₚ = −GMm / r

What is the total energy of an orbiting satellite?

Eₜ = Eₖ + Eₚ

What is the equation for total orbital energy?

Eₜ = ½mv² − GMm / r

Is the total energy of an orbiting satellite positive or negative?

Negative.

What does a total energy of zero mean?

The object can escape the gravitational field.

What is escape velocity?

The minimum speed needed to escape a gravitational field.

What is the equation for escape velocity?

vₑ = √(2GM / r)

What happens if a spacecraft exceeds escape velocity?

It escapes the gravitational field.

Why are satellites usually launched near the equator?

Earth's rotation provides extra speed.

What equation explains the advantage of launching from the equator?

v = ωr

What is the rotational speed at the poles?

Zero.

Why is less energy needed to launch from the equator?

The rocket already has kinetic energy from Earth's rotation.

What is a synchronous orbit?

An orbit whose period matches the rotation period of the planet.

What is a geostationary orbit?

A synchronous orbit around Earth that appears fixed in the sky.

What period must a geostationary satellite have?

24 hours.

Where must a geostationary satellite orbit?

Above the equator.

In which direction must a geostationary satellite move?

West to east.

Why does a geostationary satellite appear stationary?

It matches Earth's rotation exactly.

Give one use of geostationary satellites.

Communications.

Give another use of geostationary satellites.

GPS.

What equation is used to calculate the orbital radius of a geostationary satellite?

r³ = GMT² / 4π²

What is the orbital radius of a geostationary satellite?

4.22 × 10⁷ m

What is the height of a geostationary satellite above Earth's surface?

3.6 × 10⁷ m

How is the height of a geostationary orbit found?

Orbital radius minus Earth's radius.

What is the gradient of a log(T) vs log(r) graph?

3/2

Why is log(T) vs log(r) a straight line?

Because T² ∝ r³.

What logarithm rule is used in the derivation?

log(xⁿ) = n log(x)

What logarithm rule is used to separate products?

log(xy) = log(x) + log(y)

What proportional relationship is shown by the log graph?

log T ∝ log r

Which two equations are the most important in AQA gravitational fields?

g = GM / r² and V = −GM / r

Which orbital equation should always be remembered?

T² = 4π²r³ / GM

Which energy equation is not given in the AQA formula booklet but should be memorised?

Eₚ = −GMm / r