Gravitational Fields

Question 1

Define the strength of a gravitational field

Answer 1

The strength of a gravitational field, g, is the force per unit mass on a small test mass placed in the field

g = F / m
where F is the gravitational force acting on mass m

Question 2

What is a field line?

Answer 2

The path which a smaller mass would follow if dropped above a massive body

Question 3

Define a radial field

Answer 3

Where the field lines are like the spokes of a wheel, always directed to the centre

Question 4

Define a uniform

Answer 4

Where the gravitational field strength is the same in magnitude and direction throughout the field. The field lines are therefore parallel to one another and equally spaced.

Question 5

Describe whether the Earth’s gravitational field is uniform or radial

Answer 5

The force of gravity due to the Earth on a small mass decreases with distance from the Earth, the field is therefore radial.
But, over small distances much smaller than the Earth’s radius, the change in gravitational field strength is so insignificant that over small distances the Earth’s field can be considered uniform

Question 6

Define the gravitational potential of an object

Answer 6

The gravitational potential at a point in a gravitational field is the GPE per unit mass of a small test mass. This is equal to the work done per unit mass to move a small object from infinity to that point (since the gravitational potential at infinity is zero)

Question 7

Give the equation for the gravitational potential of an object

Answer 7

V = W / m

Question 8

Give the units for gravitational potential

Answer 8

Jkg⁻¹

Question 9

Define equipotentials

Answer 9

Equipotentials are lines which are at constant gravitational potential (similar to the contours for maps)
Equipotentials become further apart as potential increases (when increasing in regular increments of gravitational potential)

Question 10

Explain why the equipotentials become spaced further apart, the further away from the Earth’s surface for equal increases in potential

Answer 10

Because, at increasing distance from the Earth’s surface, the gravitational field becomes weaker so the gain of gravitational potential energy per metre of height gain becomes less

Question 11

Define potential gradient

Answer 11

The potential gradient at a point in a gravitational field is the change of potential per metre at that point

Question 12

Give the equation for the potential gradient over a small distance

Answer 12

Potential Gradient = ΔV / Δr

Question 13

Give the gravitational field strength in terms of gravitational potential

Answer 13

g = - ( ΔV / Δr )

Question 14

Give the gravitational field strength in terms of potential gradient

Answer 14

g = - potential gradient

Question 15

Give 3 assumptions for Newton’s law of gravitation

Answer 15

The gravitational force between any two point objects is:

1) always an attractive force
2) proportional to the mass of each object
3) proportional to 1/r² where r is their distance apart

Question 16

Give the equation for the gravitational force between two point objects

Answer 16

Gravitational force F = (G m₁ m₂) / r²

Question 17

For Newton’s law of gravitation, what does G stand for and what are its units?

Answer 17

G is the Universal Constant of Gravitation

Nm²kg⁻²

Question 18

Where would an object have to be placed for its gravitational potential energy to be 0?

Answer 18

At infinity

Question 19

Give the magnitude of gravitational field strength for a point mass of M at distance r

Answer 19

F = GMm / r²

g = F / m = GM / r²

Question 20

Describe how the gravitational field strength, g, varies with distance from the centre of a planet with radius R

Answer 20

Between 0 - R, The gravitational field strength increases linearly until it reaches g(s) - the gravitational field strength at the surface of the planet.
At 2R, the gravitational field strength is ¼g(s)
At 3R, the gravitational field strength is ⅟₉g(s)

Question 21

Give the equation for the gravitational potential for an object at distance r from the centre a spherical planet

Answer 21

V = -GM / r

Question 22

Define a satellite

Answer 22

Any smaller mass which orbits a larger mass

Question 23

What is the Earth’s natural satellite?

Answer 23

The moon

Question 24

Define a geostationary satellite

Answer 24

A satellite orbiting the Earth directly above the equator and has a time period of 24hrs. It therefore remains in a fixed position above the equator because it has exactly the same time period as the Earth’s rotation

Question 25

Give the equation to calculate the radius of orbit of a geostationary satellite

Answer 25

r³ / T² = GM / 4π²

r³ = GMT² / 4π²