Gravitational Fields

Question 1

What’s gravitational field?

Answer 1

The force field round a mass.

Question 2

What are field lines?

Answer 2

The lines of the force. Show direction of force on a mass.

Question 3

The strength of a gravitational field, g, is defined as?

Answer 3

The force per unit mass on a small test mass placed in the field.

Question 4

How do we describe an object that falls freely?

Answer 4

Unsupported (weightless) i.e. it’s acted on by the force of gravity alone.

Question 5

What is gravitational potential energy?

Answer 5

The energy of an object due to its position in a gravitational field.
Max at infinity (0). Negative as get closer.

Question 6

What is gravitational potential at a point in a gravitational field?

Answer 6

The work done per unit mass to move a small object from infinity to that point.

(hence always -ve)

Question 7

What is equipotential?

Answer 7

Surfaces of constant potential.

Question 8

What’s the potential gradient?

Answer 8

It’s the change of potential per metre at that point.
For a change of potential ΔV over a small distance Δr, potential gradient = ΔV/Δr.

Question 9

The potential gradient is greater, and the field stronger when equipotential lines are…

Answer 9

closer.

Question 10

Newtons law of gravity assumes that the gravitational force between any two point objects is: (3)
Give eq.

Answer 10

• always an attractive force
• proportional to mass of each
  -proportional to 1/r^2, where r is distance apart (from centres).

Last two points can be summed up as F = Gm1m2/r^2

Question 11

Graph g against r: draw and inc before R and after R.

Explain shape before and after.

Answer 11

Linear increase from origin when r < R rising then at surface (R) curves down in 1/r^2 graph shape.

Inverse square law graph beyond r=R bc g ∝ 1/r^2.

When r<R, only mass in sphere of radius r contributes to g so as r decreases, mass contributing decreases so g decreases.

Question 12

What is the escape velocity from a planet?

Answer 12

The minimum velocity an object must be given to escape from the planet when projected vertically from the surface.

Question 13

To move an object from surface to infinity, the work that must be done is ΔW = mΔV = GMm/R. If the object is projected at speed v then for it to be able to escape from the planet:

Answer 13

it’s initial Ek, 1/2mv^2 ≥ GMm/R
∴ v esc = sqrt 2GM/R = sqrt2gR!

Question 14

Back to the graph g-r (g∝1/r^2), total area under graph from surface to end?

Answer 14

Area is work done to move from surface to infinity i.e. value of gravitational potential at surface.

Area between any two values is change of potential between them (ΔV).

Question 15

What’s the graph of V = -GM/r?

Answer 15

V = -GM/r
V ∝ 1/r graph

X axis and -ve y axis. From surface, curve starting very negative and getting less negative.

Question 16

Compare the two graphs
g ∝ 1/r^2 and V ∝ 1/r:

Answer 16

g changes much more sharply with distance than V does.
g in positive y-axis, V in -ve.

Question 17

What’s a satellite?

Answer 17

Any small mass that orbits a larger mass.

Question 18

What’s Kepler’s third law?

Answer 18

r^3 / T^2 is the same for all planets, where T is time period for one complete orbit of the sun, and r is radius of orbit.

Question 19

When planets orbit the sun, the centripetal force is provided by?

Answer 19

The force of gravitational attraction (F = GMm/r^2)

Question 20

GMm/r^2 = mv^2/r ∴ the speed^2 of the planet is?

Answer 20

v^2 = GM/r

Question 21

Because v = circumference of orbit/T = 2πr/T then..

Answer 21

(2πr/T)^2 = GM/r

Question 22

Therefore r^3/T^2 =?

Answer 22

r^3/T^2 = GM/4π^2

Because GM/4π^2 is the same for all the planets, their r^3/T^2 is the same for all planets.

Question 23

What’s the underlying assumption here?

Answer 23

F ∝ 1/r^2

Question 24

What’s a geostationary satellite?

Answer 24

A satellite that orbits the Earth directly above the equator, with T = 24h.

Question 25

Geostationary satellites remain in fixed positions above the equator because?

Answer 25

Has exactly the same T as the Earth’s rotation.

Question 26

For a satellite in a circular orbit of radius, r its total energy is?

(think Ek and Ep)

Answer 26

Et = Ek + Ep
Ek = 1/2 mv^2 = 1/2mGM/r = GMm/2r
Ep = mV = - GMm/r
∴ Et = -GMm/r + GMm/2r = -GMm/2r!!

Question 27

Why don’t rocket launchers need to achieve escape velocity?

Answer 27

-Continuous thrust added/energy continuously added in flight
-Less energy to receive orbit than to escape gravitational field.

Question 28

Possible use of satellites?

Answer 28

Monitor weather or for surveillance:
- whole Earth may be scanned,
- Earth rotates under orbit,
- can be updated regularly.
Communications:
-limited by intermittent contact.
GPS:
- several satellites needed to fix position on each.