Gravitational fields

Question 1

Give three properties of the field lines in a uniform field.

Answer 1

Straight
Parallel
Equally spaced

Question 2

How does the gravitational field strength change as you move through a uniform field?

Answer 2

It doesn’t

Field strength constant no matter the position: same density field lines

Question 3

How would you calculate gravitational field strength in a uniform field?

Answer 3

g = F / m

Question 4

How does the gravitational field strength change as you move awayfrom the centre of a radial field?

Answer 4

The field strength decreases exponentially

g ∝ 1/r²
g is related to r by the inverse square law

Question 5

How would you calculate gravitational field strength in a radial field?

Answer 5

g = GM / r²

g = -ΔV / Δr

M - mass of object creating field
r - distance between objects’ centres

Question 6

Define Gravitational Potential Energy (GPE)

Answer 6

The energy that an object has due to its position in a gravitational field.

Question 7

Where does an object have 0 GPE?

Answer 7

At infinity.

A Gravitational field has infinite range, must leave the field for 0 GPE

Question 8

In terms of a positive or negative change, how does the GPE of an object change as it moves from infinity?

Answer 8

Negative change

It decreases, remember EP is zero at infinity and negative anywhere else

Question 9

In terms of a positive or negative change, how does the GPE of an object change as it moves to infinity?

Answer 9

Positive change

It increases, remember EP is zero at infinity and negative anywhere else

Question 10

Define Gravitational Potential at a position in a field

Answer 10

The work done on each unit of mass of an object in order to move it from infinity to that position in the field

Remember the units for gravitational potential: Jkg (Energy x mass)

Question 11

Is the point of zero potential between the Earth and Moon closer to the Earth or the Moon?

Answer 11

The Moon

The Moon has a weaker field, so you need to get closer to it than Earth

Question 12

Define lines of equipotential

Answer 12

The line across a gravitational field where gravitational potential is constant

It also takes no energy to move across a line of equipotential

Question 13

Define escape velocity

Answer 13

The minimum velocity an object requires to escape the gravitational field from the surface of a mass

(Only affected by gravity, not air resistance. Measured from the ground)

Question 14

Give the equation for escape velocity

Answer 14

v = √2GM/R = √2gR

Be careful with the capitals:
R = the radius of the planet
v = velocity

Question 15

What is Kepler’s Third Law?

Answer 15

r³/T² = GM/4π²

Question 16

What relationship does Kepler’s Third Law show for objects orbiting the sun (or any large object)?

Answer 16

The square of the orbital period is directly proportional to the cube of the radius of the orbit
(T² ∝ r³)

→The period of an objects orbit (and by extenstion its velocity) is only dependant on the radius of its orbit and not the objects own mass

Remember: T²/r³ is constant for all objects orbiting the sun (=GM/4π²)

Question 17

What is the first step in the derivation of Kepler’s Third Law

Answer 17

Centripetal Force = Force due to gravity

F(c) = F(g)

Orbits are circular - centripetal force is caused by gravitational force

Remember the scenario - a small test mass is orbiting a larger body circularly