Gravitational Fields

Question 1

Where do gravitational fields exist?

Answer 1

Around any object with mass.

Question 1

What happens when a small mass is placed in a larger mass’ field?

Answer 1

The objects exert an equal an opposite force on each other. Because of the objects larger mass, it doesn’t noticeably move compared to the smaller one.

Question 1

What is a field line in GF?

Answer 1

The path a small object would follow placed in a larger objects GF.

Question 1

Define gravitational field strength:

Answer 1

The force per unit mass on a test mass placed in a field of a larger mass.

Question 1

Define gravitational potential energy:

Answer 1

The energy of an object due to its position in a gravitational field. Zero gpe is treated as an infinity away (the object is so far away field strength is negligible so the work done against gravity is negligible)

Question 1

Prove acceleration under gravity is equal to g.

Answer 1

acceleration = force/mass = mg/m =g

Question 2

Why must a test mass be small?

Answer 2

To prevent it attracting the larger object by a large amount hence changing its position and altering the field strength.

Question 2

Define equipotential:

Answer 2

A surface of constant potential across it therefore no work must be done against gravity to move across it.

Question 2

What is the unit of GF strength?

Answer 2

NKG^-1

Question 2

Define gravitational potential:

Answer 2

The gpe per unit mass of a small test mass which is equal to the work done per unit mass to move a small object from infinity to that point. An object must increase its potential to zero to escape a field, hence potential is negative.

Question 3

Describe a radial field and uniform field:

Answer 3

radial - Acts inwards from the centre of an object. The test mass is directed towards the centre of the object. Inverse square law applies.
uniform - field strength is the same in magnitude and direction throughout the field. The field lines are parallel and evenly spaced.
(in theory g is smaller the higher we go from earth’s surface although the difference is too small to be noticeable)

Question 3

Give Gravitational potential equation and its units:

Answer 3

V = W/m in JKG^-1

Question 4

Define potential gradient:

Answer 4

The change in potential per metre in a gravitational field.

Question 5

What is Kepler’s third law?

Answer 5

r^3/T^2=constant for all planets

Question 5

How does inverse square law work with force and distance?

Answer 5

at a distance d force is F
at 2d, force is F/4
at 3d, force is F/9
It varies inversely with the square of their distance apart.

Question 6

Give the equation for potential gradient:

Answer 6

potential gradient = change in potential / change in distance.

Question 7

Define grav. field strength in terms of potential gradient:

Answer 7

Grav. field strength is the negative of the potential gradient g = - change in potential/ change in distance

Question 8

How does grav. field strength relate to equipotential?

Answer 8

The force due to the field is always at right angles to the equipotential.

Question 9

What 3 things did Newtons Laws of gravitation assume about the gravitational force?

Answer 9

-Always an attractive force.
-Proportional to the mass of each object.
-Proportional to 1/r^2.

Hence F = Gm1m2/r^2

Question 10

Who first discovered a value for G?

Answer 10

Henry Cavendish in 1798

Question 11

What is gravitational field strength at a distance r from a mass?

Answer 11

g = GM/r^2 (g=F/m=GM/r^2 but there is no mass m so g is equal to this)

Question 12

Why is g at the centre of a planet zero?

Answer 12

As r decreases, the mass that contributes to the field strength gets smaller and smaller per g=GM/r^2

Question 13

What is the equation for gravitational potential on a spherical planet?

Answer 13

V = -GM/R (this is negative because energy must be done to remove a point mass from a gravitational field) to make V = 0.

Question 14

Define escape velocity:

Answer 14

Minimum velocity an object needs to escape a planet when projected vertically from the surface.

Question 15

Show how to find escape velocity:

Answer 15

Change in work = mass times by change in potential = mass * GM/R. For an object to escape, 1/2mv^2 must be greater than the potential at the surface. Therefore, v > sqr(rt) 2GM/R for a planet of radius R.

Question 16

How does gravitational potential vary at a distance r from the centre of a planet?

Answer 16

It is inversely proportional (not inverse square law)

Question 17

Define satellite:

Answer 17

any small mass orbiting a larger mass.

Question 18

How did Newton prove Kepler’s 3rd law?

Answer 18

Any force keeping a satellite in orbit must be centripetal force - mv^2/r = GMm/r^2 therefore v = sqr(rt) GM/r. As v = circumference of orbit divided by time it was done in 2pir all squared then r^3 = constant * T^2

Question 19

What is a geostationary satellite?

Answer 19

Orbits the earth directly above the equator and has a time period of 24hr. Therefore, it has a fixed position above the earth as it spins at the same rate.

Question 20

What is a geosynchronous orbit?

Answer 20

It is the same as geostationary but is inclined to the equator so can move in a non-circular shape such as an ellipse.

Question 21

work done - potential equation?

Answer 21

change in work = mass * change in potential

Question 22

What is the equation for energy of an orbiting satellite?

Answer 22

E = -GMm/2r as E =Ep + Ek.

Question 23

What is the gradient of the graph of V against r?

Answer 23

V/r which is -g.