Gravitational Fields

Question 1

What is a gravitational field?

Answer 1

A gravitational field is a region of space where an object with mass experiences a force

Question 2

Define gravitational field strength

Answer 2

At any point in a gravitational field the gravitational field strength is equal to the force per unit mass exerted on a particle at that point in the field
g = F/m

Question 3

What does a line of force show?

Answer 3

The path taken by a mass released in the field

Question 4

What does an equipotential do?

Answer 4

Joins up regions of the same potential

Question 5

Where can you find uniform gravitational fields?

Answer 5

A uniform field may exist in a small region of space, close to a large mass, where the field lines may be considered to be uniform, parallel and equidistant

Question 6

Where can you find a radial gravitational field?

Answer 6

In the region around an isolated mass the field lines are considered radial. The field lines would be drawn radially, with arrows pointing in towards the centre of mass

Question 7

State Newton’s law of universal gravitation

Answer 7

“Every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of their distances apart”

Question 8

State the equation for Newton’s law of universal gravitation

Answer 8

F = -GMm/r²

where G is a universal constant

Question 9

What is the value of G?

Answer 9

6.67x10^-11

Question 10

What does the minus sign in Newton’s law of universal gravitation show?

Answer 10

The minus sign shows that the force is attractive

Question 11

What is the equation for gravitational field strength for a point mass?

Answer 11

g = -GM/r²

Question 12

State the characteristics of g close to Earth

Answer 12

gravitational field strength is uniform close to the surface of the Earth and numerically equal to the acceleration of free fall

Question 13

How is a satellite kept in orbit around a planet?

Answer 13

Gravity provides a centripetal force

Question 14

Derive an equation for the speed of a satellite in orbit

Answer 14

F = GMm/r²
and F = mv²/r

So GMm/r² = mv²/r
GM/r² = v²/r
GM/r = v²
v = √(GM/r)

Question 15

What provides the centripetal force on a planet?

Answer 15

The centripetal force on a planet is provided by the gravitational force between it and the Sun

Question 16

State Kepler’s first law

Answer 16

Each planet moves in an elliptical orbit with the Sun at one focus

Question 17

State Kepler’s second law

Answer 17

A line drawn from the Sun to a planet sweeps out equal areas in equal times

Question 18

State Kepler’s third law

Answer 18

The square of the period, T, of a planet is directly proportional to the cube of its average distance, r, from the Sun

T² ∝ r³

Question 19

Derive an equation for period squared (T²)

Answer 19

v² = GM/r
and v = circumference of sphere/period
v = 2πr/T

So GM/r = (2πr)²/T²
GM/r = 4π²r²/T²
GMT²/r = 4π²r²
T² = 4π²r³/GM

Question 20

Define a geostationary orbit

Answer 20

A geostationary orbit is one such that the period of rotation is the same as that of the Earth. The satellite will therefore always stay in the same place over the Earth provided it orbits in the plane of the equator and rotates in the same direction as the Earth’s rotation.

Question 21

How can geostationary satellites be used?

Answer 21

• Sky TV
• communications
• providing information about the Earth

Question 22

Define gravitational potential in a radial field

Answer 22

Gravitational potential at a point is the work done in bringing unit mass from infinity to that point; a mass at infinity is defined as having zero potential

Question 23

State the equation for gravitational potential

Answer 23

Vg = -GM/r

where r is measured from the centre of the planet

Question 24

Define gravitational potential energy

Answer 24

Gravitational potential energy is the work done in bringing a mass from infinity to the point concerned; a mass at infinity is defined as having zero potential energy

Question 25

State the equation for gravitational potential energy

Answer 25

Ep = mVg and Vg = -GM/r

Therefore Ep = -GMm/r

where r is the distance between the two masses

Question 26

What is the area under a force/distance graph for a point or spherical mass equal to?

Answer 26

Work done

Question 27

Define escape velocity of a planet

Answer 27

The escape velocity of a planet is the velocity which a projectile must be given at the surface of the planet so that it will completely escape from the planet’s gravitational field due to its kinetic energy alone

Question 28

Derive the equation for escape velocity

Answer 28

Ek = 1/2mv²
Ep = -GMm/r

1/2mv² = GMm/r
v = √(2GM/r)

Question 29

State the two equations for escape velocity

Answer 29

v = √(2GM/r)

v = √(2gr)