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Phase Difference > C18 Gravitational Field > Flashcards

C18 Gravitational Field Flashcards

Poop

1
Q

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

A

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

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2
Q

Formula for gravitational field strength using mass and force

A

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

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3
Q

Uniform gravitational field

A

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

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4
Q

Newton’s Law Of Gravitation

A

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.

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5
Q

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

A

F = - [ GMm / r^2 ]

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6
Q

Universal Gravitational Constant, G

A

6.67 x 10^-11

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7
Q

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

A

F ∝ 1/r^2
If r x2, force x1/4.

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8
Q

Mass of the Sun

A

1.99 x 10^30 kg

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9
Q

Mass of the Earth

A

5.97 x 10^24 kg

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10
Q

Formula for calculating the gravitational field strength, g

A

g = - [ GM / r^2 ]

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11
Q

Kepler’s First Law

A

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

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12
Q

What is the ‘eccentricity’ of an orbit?

A
  • A measure of how elongated the circle is.
  • So an orbit with a low eccentricity is almost a circle.
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13
Q

Kepler’s Second Law

A

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

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14
Q

Kepler’s Third Law

A

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

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15
Q

Relationship for Kepler’s Third Law including a constant

A

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

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16
Q

Astronomical Unit

A

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

17
Q

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

A

mv^2 / r = GMm / r^2

18
Q

How to calculate the orbital speed of a planet in orbit

A

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

19
Q

Mathematical version of Kepler’s third law

A

T^2 = (4π^2 / GM) r^3

20
Q

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

A

4π^2 / GM

21
Q

Deriving Kepler’s Third Law

A

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

22
Q

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

A

v = √ (GM / r)

23
Q

Different industries modern satellites are used in

A

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

24
Q

Requirements for a satellite to be geostationary

A
  • 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.
25
Q

Why are polar satellites useful for mapping/reconnaissance?

A

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

26
Q

Define Natural Satellite

A

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

27
Q

Define Artificial Satellite

A

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

28
Q

Define Gravitational Potential

A

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

29
Q

Formula for gravitational potential, Vg

A

Vg = - [ GM / r ]

30
Q

Graph of Vg against 1/r

A

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

31
Q

How do changes in gravitational potential work

A
  • 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
32
Q

Define gravitational potential energy

A

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

33
Q

Formulas for GPE related to Vg, M, r

A

E = mVg
E = - [ GMm / r ]

34
Q

Define escape velocity

A

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

35
Q

Formula for escape velocity

A

v^2 = 2GM / r

36
Q

NEW CARDS FROM HERE ONWARD XDDDDDDDDDDDDDDD

A
37
Q

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

A

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

38
Q

How do you derive the formula for escape velocity?

A

GPE must equal KE.

Phase Difference (18 decks)

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