Chapter 21 - Gravitational fields

Question 1

What is a force field?

Answer 1

Region in which a body experiences a non-contact force

Question 2

What is a gravitational field?

Answer 2

Force field around a mass

Question 3

What is a (gravitational) field line?

Answer 3

Path a smaller mass would follow if pulled towards a larger mass.

Question 4

Define the strength of a gravitational field(g)

Answer 4

Force per unit mass on a smaller test mass placed in the field

Question 5

Give the equation for gravitational field strength (g)

Answer 5

g = F/m (NKg^-1)

Question 6

Give the equation for acceleration of free fall in a gravitational field.

Answer 6

a = force/ mass = mg/m = g

Question 7

What’s a radial field?

Answer 7

Where field lines are like spokes of a wheel. Towards the centre

Question 8

What happens to g in a radial field?

Answer 8

Decreases with increasing distance from the massive body.

Question 9

What is a uniform field?

Answer 9

Field lines are parallel and equally spaced.

Question 10

What happens to g in a uniform field?

Answer 10

Magnitude + direction of g is constant throughout the field

Question 11

Is earth’s gravitational field uniform or radial?

Answer 11

• Radial (Uniform over a very small distance)
• g decreases with distance from the earth increasing

Question 12

Define gravitational potential energy

Answer 12

Energy of an object due to its position in a gravitational field

Question 13

Define gravitational potential (V)? Give the equation

Answer 13

The gravitational potential at a point is the work done per unit mass to move a small object from infinity to that point. (As gravitational potential is zero at infinity)

V = W/m (unit: JKg^-1)

Question 14

What’s the equation for change in gpe (Ep) if a small object of mass m is moved from gravitational potential V1 to gravitational potential V2?

Answer 14

Change in Ep = m(V2-V1)

Question 15

What are equipotentials?

Answer 15

• Surfaces of constant potential. So no work needs to be done to move along an equipotential surface.

Question 16

Define potential gradient (gravitational)

Answer 16

Potential gradient at a point in a gravitational field is the change of potential per metre at that point

Question 17

Draw the equipotentials on a diagram of a planet

Answer 17

Question 18

Why do the equipotential get further apart as the distance increases from the planet?

Answer 18

gravitational fields become weaker so gain of gravitational potential energy per metre of height gain becomes less.

Question 19

Give the equation for potential gradient for change in V and change in r (small distance

Answer 19

potential gradient = change in V/ change in r

Question 20

Give the equation for g (gravitational field strength) using potential gradient

Answer 20

g = - change in V/ change in r = - potential gradient

Question 21

What is Kepler’s third law?

Answer 21

• The value of r^3/T^2 was the same for all planets.
  where r = average radius of it’s orbit and T = time period

Question 22

What are the assumptions in Newton’s laws of gravitation?

Answer 22

Gravitational force between any 2 point objects (planets were taken to be point masses) is:

• always an attractive force
• Proportional to the product of the masses of each object
• Proportional to 1/r^2 where r is their distance apart

Question 23

What is G and give a value and units

Answer 23

Universal constant of gravitation, G
6.67x10^-11 Nm^2Kg^-2

Question 24

Give the equation for gravitational force, F, using Newton’s laws of gravitation.

Answer 24

Gravitational force F = Gm1m2/r^2

Question 25

What is the equation for magnitude of the gravitational field strength (g) at distance r from a point object or from the centre of a sphere of mass M?

Answer 25

g = GM/r^2
as f = F/m:
F = Gm1m2/r^2
F/m = GM/r^2

Question 26

How do you calculate the gravitational potential near a spherical planet (at or beyond the surface)?

Answer 26

V = -GM/r

Question 27

Define escape velocity

Answer 27

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

Question 28

What is the formula for escape velocity?

Answer 28

v(esc) = (2gR)^1/2 where R = radius of planet 
or = (2GM/R)^1/2

Question 29

What does the area under a g-r graph represent? where r is the distance from surface

Answer 29

Gravitational potential (V) at the surface

Question 30

What’s the relationship between gravitational potential, V, and distance r from the centre of the planet?

Answer 30

V is inversely proportional to r

Question 31

What’s a geostationary satellite?

Answer 31

• Satellite that orbits the earth directly above the equator and has a time period of exactly 24 hours.
• Remains in fixed position above the equator

Question 32

What advantage does a geostationary satellite offer when used for communications?

Answer 32

Maintains fixed position relative to earth’s surface, so offers uninterrupted communication between transmitter and reciever

steerable dish not necessary

Question 33

What’s the height of a geostationary wave above the earth?

Answer 33

36000 Km

Question 34

For a satellite in circular orbit of radius r, how do you calculate it’s total energy?

Answer 34

E = -GMm/2r

Question 35

What’s the equation for radius of the orbit of a geostationary satellite?

Answer 35

r³ / T² = GM/4π²

as F = GMm/r² : v²/r = GM/r²

therefore speed, v² = GM/r

v = 2πr/T so: (2πr)² / T² = GM/r

so: r³/T² = GM/4π²

Question 36

What happens to the speed of a satellite when it moves to an orbit that’s closer to earth?

Answer 36

Speed increases as:
- as GMm/r² = mv²/r:

v = (GM/r)^1/2 so as r decreases, velocity increases. V proportional to 1/r

• Loses potential energy, so gains kinetic

Question 37

Whats the equation for increase in potential energy, when a satellite is raised from planets surface to a height

Answer 37

change in Ep = m x change in V

= GMm(1/R - 1/r)

where R = radius of planet and r = radius of orbit