5.4 Gravitational Fields

Question 1

Describe gravity

Answer 1

A universal attractive force, experienced by objects with mass.
It is weak.
It has infinite range.

Question 2

Objects placed within a gravitational field will be attracted towards the ____________ of an object.

Answer 2

centre of mass

Question 3

Define gravitational field strength, g.

Answer 3

The gravitational force experienced per unit mass by an object at a point in a gravitational field.
g = F/m

Question 4

Is gravitational field strength vector or scalar?

Answer 4

Vector.

Question 5

Units of gravitational field strength

Answer 5

Nkg-1
OR
ms-2

Question 6

What are the two types of field?

Answer 6

Uniform and radial.

Question 7

What can field lines tell you about a field?

Answer 7

Their direction, as well as the strength of the field (depending on density of field lines)

Question 8

When is g = F/M only applicable?

Answer 8

When the object’s own gravitational field is negligible compared to the external field it is currently in.

Question 9

Newton’s law of gravitation

Answer 9

The force between two point masses is directly proportional to the product of the two masses, and inversely proportional to the square of their separation.

F = -GMm / r^2

Question 10

Why is there a negative sign in F = -GMm / r^2?

Answer 10

To show the attractive nature of the force.

Question 11

What is G?

Answer 11

The universal gravitational constant (6.67x10^-11 m3 kg-1 s-2)

Question 12

What equation for g features the mass of an object with a field, and the distance from the C.E.M of that object?

Answer 12

g = GM / r^2

Question 13

When considering the gravitational field strength close to the earth’s surface, how might we model the field?

Answer 13

Uniform

Question 14

Kepler’s first law

Answer 14

Planets travel in elliptical orbits, centred around the sun.
(The eccentricity of the ellipse is very low, so the motion can be modelled as circular)

Question 15

Kepler’s second law

Answer 15

A line segment joining a planet and the sun sweeps out equal areas during intervals of equal time.
(This is because the speed of the planet is not constant - it moves faster when it is closer to the sun).

Question 16

Kepler’s third law

Answer 16

The square of the orbital period T is proportional to the cube of the average distance r from the sun.

Question 17

How can Kepler’s third law be proved?

Answer 17

By considering the forces acting on the planet. Centripetal force is required to keep the planet in orbit, and this force is provided by the gravitational field of the sun.

Question 18

Satellite

Answer 18

Objects that orbit other, larger objects. These can be natural, or manmade.

Question 19

Uses of satellites

Answer 19

Communications, scientific research, and Global Positioning Systems (GPS)

Question 20

Geostationary satellite

Answer 20

• Satellites with an orbital period of 1 day.
• They travel in the same direction as the rotation of the Earth, along the equatorial plane.
• This means they remain above the same point on the Earth’s surface, making them useful for communications and surveying, as they provide continuous coverage.

Question 21

Gravitational Potential (Vg) at a point

Answer 21

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

Question 22

How does Vg vary within a field.

Answer 22

At infinity, it is 0 (minimum). At all other points, it is negative, which represents how energy is required to move the object out of the field.

Question 23

How is Vg calculated?

Answer 23

Vg = -GM/r

M: Mass of object being moved away from
r: Separation distance

Question 24

Gravitational Potential Energy
(verify definition with one from textbook)

Answer 24

The work done to move an object with mass m from infinity to a point in a gravitational field.

Question 25

Equation for GPE

Answer 25

E = -GMm / r

Question 26

What is the required condition for an object to escape a gravitational field produced by mass M?

(verify this card, gpt wasnt too keen)

Answer 26

The KE of the object at any point in the field must be greater than or equal to the GPE required to lift the object to infinity.

ChatGPT said:
The total energy of the object, which is the sum of its kinetic and potential energy, must be greater than or equal to zero. This means that the object’s kinetic energy at any given point in the field must be greater than or equal to the gravitational potential energy required to lift the object to infinity, which is equivalent to zero potential energy.

Question 27

Does escape velocity differ depending on the mass m of the object?
(needs teacher verification, gpt didnt really work)

Answer 27

Yes.

Question 28

Escape velocity

Answer 28

The minimum velocity an object requires in order to escape the gfield of an object when projected vertically from its surface.

Question 29

Equation for escape velocity

Answer 29

v = sqrt[ 2GM / r ]

Question 30

Prove T2 is proportional to r3

Answer 30

Start off by equating the formula for centripetal force with the formula for gravitational force.
F = mv2 / r = GMm / r2

We can rearrange it to produce:
GM / r = v2

The velocity of an object in circular motion is 2πr / T. Sub this in to get:
GM / r = 4π2r3 / t2

This can be rearranged to show:
T2 = 4π2r3 / Gm.

Because G and M are constants, this formula shows T2 is proportional to r3.

Question 31

Describe uniform fields.

Answer 31

Parallel lines towards the surface.
The lines are perpendicular to the surface.
The lines are spaced at equal intervals from each other.

Question 32

Describe radial fields (in terms of gravitational fields)

Answer 32

The field lines point towards a central point
The field lines are perpendicular to the equipotential surfaces
The field line density decreases the further away we get from the central point.