Gravitational fields

Question 1

Gravitational field

Answer 1

All objects with mass create a gravitational field around them. The field extends all the way to infinity but gets weaker as the distance increases, eventually becoming negligible. Gravitational force is always attractive

Question 2

Gravitational field strength

Answer 2

The gravitational force exerted per unit mass on a small object placed at a point within that field
g = F/m
F=-GMm/r^2
g=-GM/r^2

Question 3

Gravitational field patterns

Answer 3

Field lines around a spherical mass form a radial field
For a large sphere like a planet, the field lines can be modelled as a uniform gravitational field - change is negligible at any height

Question 4

Newton’s law of gravitation

Answer 4

F∝Mm
F∝1/r^2
f∝Mn/r^2
F= -GMm/r^2

Question 5

Kepler’s first law

Answer 5

The orbit of a planet is an ellipse with the sun at one of the two foci
(Most orbits have low eccentricity so can be modelled as a circle)

Question 6

Kepler’s second law

Answer 6

A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time (i.e. when a planet is closer to the sun, it moves faster)

Question 7

Kepler’s third law

Answer 7

The square of the orbital period T of a planet is directly proportional to the cube of the average distance r from the sun
T^2 ∝ r^3

Question 8

Kepler’s third law derrivation

Answer 8

F=mv^2/r
F=GMm/r^2
mv^2/r = GMm/r^2
v^2 =GM/r
v=2πr/T
4π^2/T^2 = GM/r
T^2 = (4π^2/GM) r^3
T^2 ∝ r^3

Question 9

Uses of satellites

Answer 9

Communications (satellite pjones, TV, radio)
Military reconnaisance
Scientific research
Weather and climate predicting/monitoring
GPS

Question 10

How does a satellite stay in orbit

Answer 10

The only force acting is gravitational attraction - it is always falling towards the Earth
v= square root(GM/r)

Question 11

Geostationary satellite

Answer 11

Have an orbital period of 24 hours so they remain in a fixed position above the Earth
For this to happen, they must orbit above the Earth’s equator and rotate in the same direction as the Earth

Question 12

Gravitational potential

Answer 12

Vg at a point in a gravitational field is defined as the work done per unit mass to move an object to that point from infinity
“infinity” is the point where gravitational force of attraction is 0
At infinity, Vg =0 so all other values are negative

Question 13

Gravitational potential energy

Answer 13

E=mVg =GMm/r

Question 14

Escape velocity

Answer 14

The velocity needed to leave the gravitational field
1/2 m v^2 = GMm/r
v = sqrroot(2GM/r)