C18 Gravitational Field

Question 1

Define gravitational field strength g at a point within a gravitational field

Answer 1

The gravitational force exerted per unit mass on a small object placed at that point within the field.

Question 2

Formula for gravitational field strength using mass and force

Answer 2

g = F / m
F = gravitational force
m = mass of object in the field

Question 3

Uniform gravitational field

Answer 3

Field lines will be parallel and equidistant, perpendicular to the surface and the field strength does not change.

Question 4

Newton’s Law Of Gravitation

Answer 4

The force between two point masses is:
- Directly proportional to the product of the masses, F ∝ Mm.
- Inversely proportional to the square of their separation, F ∝ 1/r^2.

Question 5

Equation for Newton’s law of gravitation, calculating force of attraction

Answer 5

F = - [ GMm / r^2 ]

Question 6

Universal Gravitational Constant, G

Answer 6

6.67 x 10^-11

Question 7

Relationship between the attractive force, F and distance between objects, r

Answer 7

F ∝ 1/r^2
If r x2, force x1/4.

Question 8

Mass of the Sun

Answer 8

1.99 x 10^30 kg

Question 9

Mass of the Earth

Answer 9

5.97 x 10^24 kg

Question 10

Formula for calculating the gravitational field strength, g

Answer 10

g = - [ GM / r^2 ]

Question 11

Kepler’s First Law

Answer 11

The orbit of a planet is an ellipse with the Sun at one of the two foci.

Question 12

What is the ‘eccentricity’ of an orbit?

Answer 12

• A measure of how elongated the circle is.
• So an orbit with a low eccentricity is almost a circle.

Question 13

Kepler’s Second Law

Answer 13

A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

Question 14

Kepler’s Third Law

Answer 14

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

Question 15

Relationship for Kepler’s Third Law including a constant

Answer 15

T^2 / r^3 = K
They are directly proportional, K is a constant.

Question 16

Astronomical Unit

Answer 16

Defined as the mean distance between the Earth and the Sun.

Question 17

Formula relating centripetal force on planet and gravitational force acting on a planet

Answer 17

mv^2 / r = GMm / r^2

Question 18

How to calculate the orbital speed of a planet in orbit

Answer 18

Dividing the circumference of its orbit by its orbital period, 2πr / T

Question 19

Mathematical version of Kepler’s third law

Answer 19

T^2 = (4π^2 / GM) r^3

Question 20

What is the gradient of a graph of T^2 against R^3?

Answer 20

4π^2 / GM

Question 21

Deriving Kepler’s Third Law

Answer 21

start with:
mv^2 / r = GMm / r^2
substitute v = 2πr / T

rest you can do in the exam:
4π^2r^2 / T^2 = GM / r
T^2 = (4π^2 / GM) r^3

Question 22

Formula for orbital speed v, given M and r (not given)

Answer 22

v = √ (GM / r)

Question 23

Different industries modern satellites are used in

Answer 23

Communications, military uses, scientific research, weather and climate, global positioning.

Question 24

Requirements for a satellite to be geostationary

Answer 24

• Be in orbit above the Earth’s equator.
• Rotate in the same direction as the Earth’s rotation.
• Have an orbital period of 24 hours.

Question 25

Why are polar satellites useful for mapping/reconnaissance?

Answer 25

The Earth rotates beneath their path, so after a number of orbits they can map all parts of the globe.

Question 26

Define Natural Satellite

Answer 26

Celestial bodies that orbit around a planet or another larger body.

Question 27

Define Artificial Satellite

Answer 27

Human-made objects that are intentionally placed into orbit around Earth or other celestial bodies.

Question 28

Define Gravitational Potential

Answer 28

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

Question 29

Formula for gravitational potential, Vg

Answer 29

Vg = - [ GM / r ]

Question 30

Graph of Vg against 1/r

Answer 30

A straight line through the origin, with gradient, -GM

Question 31

How do changes in gravitational potential work

Answer 31

- Moving toward a point mass will decrease it, e.g. from -40 MJ kg to -70MJ kg - Moving away from a point mass will increase it, e.g. from -30 MJ kg to -20MJ kg

Question 32

Define gravitational potential energy

Answer 32

The work done to move a mass from infinity to a point in a gravitational field.

Question 33

Formulas for GPE related to Vg, M, r

Answer 33

E = mVg E = - [ GMm / r ]

Question 34

Define escape velocity

Answer 34

The lowest velocity which a body must have in order to escape the gravitational attraction of a particular planet or other object.

Question 35

Formula for escape velocity

Answer 35

v^2 = 2GM / r

Question 36

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Question 37

What are the units used in Kepler's Third Law?

Answer 37

T² / R^3 = K T = time period in years R = distance in AU

Question 38

How do you derive the formula for escape velocity?

Answer 38

GPE must equal KE.