5.4 Gravitational Fields Flashcards

You may prefer our related Brainscape-certified flashcards:
1
Q

what is a gravitational field?

A

a gravitational field is the region around a body in which other bodies will feel a force due to the mass of the body

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

gravitational fields are due

A

To objects having a mass

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

The field lines around a spherical mass, like a planet, form a

A

Radial field

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

what do gravitational field lines show?

A

Field lines show the direction the force would act on an object placed at that point in space. The magnitude of the field is represented by the spacing of the lines. The closer the lines are to each other, the higher the magnitude.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

what is gravitational field strength defined as?

A

the gravitational field strength at any point in a gravitational field is the force acting per unit mass at that point, g = F / m (units are NKg^-1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

how do gravitational field lines act around a spherical mass?

A

they act radially inwards, towards the centre because spherical objects can be modelled as a point mass at its centre

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

what happens to the field lines of Earth as you get closer and closer to the surface of the Earth?

A

the gravitational field lines become uniform and straight, the lines converge to become almost parallel, the radial field becomes apparent the further we move away from the Earth and observe it from space

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

state Newton’s law of gravitation?

A

Newton’s law of gravitation states that the gravitational force of attraction between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

what is the equation for Newton’s law of gravitation?

A

F = - GMm / r^2
where M and m are the masses of the two bodies and r is the separation of their centres
(the minus shows it is an attractive force)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

what is G?

A

the universal gravitational constant, 6.67 x 10^-11

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

what law does Newton’s law of gravitation follow in terms of force? (think of intensity)

A

follows an inverse square law, forces gets smaller with distance because the strength changes

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

a spherical mass is often assumed to be what?

A

a point mass with all its mass concentrated at the centre

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

what is the other equation for gravitational field strength for a point mass and how can you get to it?

A

first g = F / m
F = - GMm / r^2, equate Fs
leading to g = - GMm / mr^2, cancel little m
leading to g = - GM / r^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what is gravitational field strength equal to on earth?

A

g = 9.81 ms^-2 (acceleration due to freefall)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

what are Kepler’s three laws of planetary motion?

A
  1. planets travel orbit around the sun in elliptical orbits and the sun located at one of the two foci
  2. equal area covered in equal time
    dtT1 = dtT2
    Then
    dtA1 = dtA2
  3. the time period of the orbit squared is proportional to the mean radius of the orbit cubed, or T^2 ∝ r^3
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

what is Kepler’s third law?

A

kepler’s third law states that the square of the period of a planet orbiting the Sun is proportional to the mean radius of its orbit cubed (his law also applies to other planetary stems, to the orbits of moons around planets and to binary stars)

17
Q

what is a geostationary orbit?

A

a geostationary orbit is an orbit of the Earth made by a satellite that has the same time period and orbital direction as the rotation of the Earth (i.e 24 hours) and is in the equatorial plane

18
Q

what are geostationary satellites used for?

A
  • broadcasting TV signals and relating mobile telephone signals
  • monitoring the weather and changes in the environment
  • monitoring air traffic
19
Q

what is the equation that relates time period to mean radius (kepler’s third law)?

A

T^2 = (4π^2 / GM ) x r^3

20
Q

how do you derive the equation or get to T^2 = (4π^2 / GM ) x r^3 ?

A
F = - GMm / r^2
equate the gravitational force to centripetal force
mrω^2/ r = GMm / r^
substituting ω = 2π / T gets you to...
T^2 = (4π^2 / GM ) x r^3
21
Q

what is gravitational potential?

A

gravitational potential at a point in a gravitational field is defined a the work done in moving unit mass from infinity (where the gravitational potential is zero) to that point

22
Q

what is gravitational potential energy?

A

the gravitational potential energy, E, of a body in a gravitational field is the work/energy required to move a body of mass, m, from infinity to that point in the field

23
Q

what is the equation for gravitational potential?

A

Vg = - GM / r

at a distance r from a point mass M

24
Q

what is the equation for gravitational potential energy?

A
E = mVg (bit like V = E / Q but for mass)
E = - GMm / r
25
Q

what does a force-distance graph for a point or spherical mass look like? (for moving a mass in a radial gravitational field, force varies with position)

A

curve exponential from negative y axis going up to x axis (x axis is asymptote), the area underneath is equal to the work done to move a mass

26
Q

what is escape velocity?

A

the minimum velocity required of an object to escape Earth’s gravitational field and not return to the ground

27
Q

how can you calculate escape velocity?

A

equate the initial kinetic energy of the object with the change in gravitational potential energy as it is thrown up,
0.5mv^2 ≥ GMm / r
rearranging vies us v ≥ (2GM / r)^0.5

28
Q

Explain why the direction of gravitational field strength at any point around a planet is always towards the centre of the planet

A

Gravitational field strength is always attractive and points towards the centre of mass of the objects causing the gravitational field

29
Q

Describe how you can use a newton meter and a known mass to determine the gravitational field strength on top of a mountain

A

Hold the newton meter vertically in a fixed position and suspend the known mass from it

Measure the value of force then use this equation

g = f/m

30
Q

State Newton’s third law

A

When two objects interact, they exert equal and opposite forces on each other

31
Q

What is aphelion

A

at aphelion it is the furthest point from the sun

32
Q

what is perihelion

A

at perihelion it is the closest point to the sun

33
Q

what is eccentricity

A

A measure of how elongated the circle is

34
Q

If radius is infinite, whats is vg

A

0