Topic 2A.2 - Gravitation

Question 1

What is gravitational field strength?

Answer 1

The force experienced per unit mass with a particle of small mass when placed at a point within the field.

Question 2

What are the units of gravitational field strength?

Answer 2

Newtons per kilogram

Question 3

What is Newton’s Universal Law of Gravitation?

Answer 3

Every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses, inversely proportional to the square of thr distance between them and acts on the line joining their centres.

Question 4

Equation for gravitational attraction

Answer 4

F = Gmm/ d(squared)

Force = Gravitational constant x mass 1 x mass 2 / squared distance

Question 5

In what direction is gravitational force?

Answer 5

Always attractive no matter the charge

Question 6

What the units for the period of an orbit?

Answer 6

Seconds

Question 7

Kepler’s 1st law

Answer 7

All planets move in an elliptical orbit with the sun at one foci

Question 8

Kepler’s 2nd law

Answer 8

The radius vector drawn from the sun to the planet sweeps equal area in equal time intervals.

Question 9

Kepler’s 3rd law

Answer 9

The period of revolution of a satellite is proportional to the radius of the orbit cubed

Question 10

polar orbits
(4 key points)

Answer 10

pass over both the north and south poles
very small altitude over the Earth
gather very detailed images of the earth’s surface
orbit Earth 14.2 times per day

Question 11

geostationary orbits

Answer 11

fixed over one place on the Earth’s surface
move in same direction as the earth with the same period of revolution
have an equatorial orbit
7 x radius of the Earth

Question 12

Use of geostationary satellites

Answer 12

communication

internet

Question 13

Use of polar satellites

Answer 13

weather???
surveillance
research

Question 14

How to derive the gravitational field equation

g of planet

Answer 14

F = Gm1m2/d2
F = ma = mg

mg = Gm1m2/d2

g = Gm/d2

Question 15

How to derive the velocity equation

Answer 15

For a satellite F (centripetal) = F (gravity)
Therefore,
mv2/r = Gm1m2/r2

v2=Gm/r
v = `|Gm/r

Question 16

Why is the centre of the earth always the centre of a satellites orbit?

Answer 16

1. satellites are moving with UCM
2. UCM requires a force directed towards the centre of the circular path
3. Gravity provides the force for the satellite
4. Gravity is directed towards the centre of the Earth
5. Therefore, the centre of the Earth coincides with the centre of the orbit

Question 17

Derive Kepler’s 3rd law

Answer 17

Fc = Fg
mv2/r = GMm/r2
v2 = GM/r
v = `|GM/r

v = 2 x pi x r/T
substitute v into equation and solve for T