Chapter 21 Gravitational Fields

Question 1

What is a gravitational field?

Answer 1

A force field surrounding an object which attracts other objects towards it/

Question 2

What is a field line.

Answer 2

Field lines line of force through which path the mass pulled by the gravitational field would follow.

Question 3

What is the strength of the gravitational field.

Answer 3

Strength of gravitational field, g is the force per unit mass on a small test mass placed in the field

g = F/m the unit is Nkg-1

Question 4

How can free-fall in a gravitational field be calculated?

Answer 4

if object of mass, m is in a gravitational field, the gravitational force on the object is F = mg

where g is gravitational field strength

If the object is not acted on by anything else its acceleration a = f/m =mg/m = g

There fore acceleration during free-fall is g measured in ms-2

Question 5

what is a radial field?

Answer 5

A radial field is where the field lines are like the spokes of a wheel and are always directed towards the centre.

The magnitude of g decreases with increasing distance from a body

Question 6

What is a uniform field?

Answer 6

The gravitational field strength is the sam in magnitude and direction throughout the field. The field lines are therefore parallel to one another and equally spaced

Question 7

Is the gravitational field of earth uniform or radial?

Answer 7

Radial but it can be considered uniform since the gravitational field strength differences between places are too small to be noticed.

Question 8

What is gravitational potential energy?

Answer 8

The energy of an object due to its position in a gravitational potential field? At the surface of the planet, the gpe is negative, to reach a zero gpe you would need to escape the gravitational field completely such that its effects is negligible. Due to this a zero gpe can be said to be at infinity

Question 9

How is gravitational potential calculated?

Answer 9

Gravitational potential v, is the workdone per unit mass to move a small object from infinity to that point.

V = W/m measured in Jkg-1

since work done is equal to change in gravitational potential energy then ΔW =m ΔV

Question 10

What are equipotentials?

Answer 10

Surfaces of constant potential.

Question 11

What is the relationship between distance from the surface and equipotential?

Answer 11

At a distance from the surface gravitational field becomes weaker, so the gain in gravitational potential energy per meter of height becomes less. The equipotential for equal increases of potential are spaced further when away from earth’s surface.

Near the surface, equipotential are horizontal (parallel to the ground) due to the uniform gravitational field over a small area

Question 12

What is potential gradient?

Answer 12

the potential gradient at A point in the gravitational field is the change of potential per meter at that point.

It becomes less and less the further from earth’s surface.

potential gradient = ΔV(change in potential)/ Δr

Question 13

What is the condition to move a mass m a small distance Δr in the opposite direction to the gravitational force Fgrav?

Answer 13

The gravitation potential energy must be increased by

• an equal and opposite force acting through the distance Δr

-an amount of energy equal to the work done by F, ΔW = FΔr

g = - ΔV/Δr

Question 14

What is the equation for gravitational field strength?

Answer 14

g = -ΔV/r

It is the negative of the potential gradient since it acts in the opposite direction

Question 15

What is Kepler’s Third Law? It’s equation?

Answer 15

The squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits (orbital distance).

r^3/T^2

Question 16

What does Newton’s Law of Gravitation Assume?

Answer 16

The gravitational force between any two point objects is

• always an attractive force
• proportional to the mass of each object
• proportional to 1/r^2 where r is distance apart

F = Gm1m2/r^2

where m1 and m2 are masses of two objects

Question 17

What is the universal constant of gravitation?

Answer 17

The constant of proportionality is gravitational force acting between two bodies of unit mass, kept at a unit distance from each other.

The unit G can be worked out from F = Gm1m2/r^2

G = Fr^2/m1m2

G can be given in Nm^2kg-2

The value of G is 6.67 x 10^-11

Question 18

How can gravitational field strength be calculated using Newtons law?

Answer 18

g = F/m = Gm/r^2 because the distance from the center r is equal to R at the surface.

Question 19

What is escape velocity?

Answer 19

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

Vesc = √2gr

Question 20

How is the gravitational potential at or beyond the surface of a spherical planet calculated?

Answer 20

V = -Gm/r

Question 21

How is the equation for escape velocity derived?

Answer 21

Check textbook page 348 or notes.

Question 22

How is surface gravitational field strength calculated?

Answer 22

g = gsR^2/r^2

Question 23

What is the gradient of a force - distance time? Area under the curve?

Answer 23

Work done is area under the curve while the gradient is g = gsR^2/r^2

Question 24

How is workdone in gravitational field calculated?

Answer 24

ΔW = F Δr = (Δr)Gm1m2/r^2

Question 24

How does the gravitational potential of Earth vary with distance?

Answer 24

V = -GM/r

Gravitational potential is inversely proportional to the distance r from the center of the planet

at distance 2r the center is 1/2 x the potential at distance r from center

at distance 3r the center is 1/3 x the potential distance

at distance 4r the center is 1/4 x the potential distance
etc

Question 24

How can speed of the planet be calculated?

Answer 24

v^2 =GM/r or (2πr^2)/T^2

if rearranged with Kepler’s law r3/T2

then v = GM/4π^2 which will be the same for all planets since keplers law is the same for all planets

Question 24

How can energy of an orbiting satellite be calculated?

Answer 24

Ek = 1/2mv^2 = 1/2m(Gm/r) = GMm/2r

Ep =mV = -GMm/r

Et = Ep +Ek

Et =GMm/r + GMm/2r = -GMm/2r

Question 25

What are the defining characteristics of geostationary orbits?

Answer 25

• orbital period of 24 hours
• equatorial orbit
• remain in a fixed position in the sky to viewers on earth

Question 26

How can you calculate the height of a geostationary orbit?

Answer 26

T^2 = 4π^2/Gm x r^3