Gravitational Fields

Question 1

What is a gravitational field?

Answer 1

A gravitational field is a force field. A force field is a region in which a body experiences a non-contact force.

Question 2

What is Newton’s law of gravitation in words?

Answer 2

The force of attraction between two point masses is proportional to the product of their masses and inversely proportional to the square of their distances apart.

Question 3

What is an inverse square law and what does this mean for Newton’s law of gravitation?

Answer 3

An inverse square law means as one value increases, the other decreases at an exponential rate. For Newton’s law, it means as distance between the centres of the objects increases, the force between the masses decreases by 1/this value squared.

Question 4

What is the equation for gravitational field strength, g?

Answer 4

g = F / m where g is the gravitational field strength, F is the force experienced by a mass in the gravitational field, and m is mass in kg.

Question 5

What is the equation for gravity in a radial field?

Answer 5

g = GM / r^2 where M is the mass of object creating gravitational field and r is the distance from the point mass in m.

Question 6

What kind of graph do you get if you plot a graph of g against r?

Answer 6

A curve with a negative gradient (as r increases, g decreases). - inverse square law

Question 7

Is a gravitational field a scalar or a vector and can they be combined?

Answer 7

It is a vector and gravitational fields can be combined.

Question 8

What is gravitational potential?

Answer 8

Gravitational potential at a point is the gravitational potential energy that a unit mass would have. For example, if a 1kg mass has -10J of potential energy at point Z, the gravitational potential at point Z is -10Jkg^-1.

Question 9

What is the equation for gravitational potential in a radial field?

Answer 9

V = -GM / r where M is the mass of the object creating the field and r is the distance from the centre of the object in m.

Question 10

Why is gravitational potential negative? What will the gravitational potential be at infinite distance?

Answer 10

Because you can think of it as doing work against the gravitational field to move an object out of it. At infinite distance the gravitational potential will be zero (becomes less negative as the object moves up).

Question 11

What kind of graph do you get if you plot a graph of gravitational potential against distance to the centre of the object?

Answer 11

A curve in the negative quadrant with a positive decreasing gradient: Gravitational potential is proportional to 1 / r.

Question 12

What is the gradient of the graph of gravitational potential against distance to centre of object equal to?

Answer 12

The gradient is equal to the value of -g : g = -ΔV / Δr

Question 13

What is the area under a g - r graph?

Answer 13

The area under a g -r graph is equal to ΔV, the change in gravitational potential.

Question 14

What is gravitational potential difference?

Answer 14

Gravitational potential difference is the energy needed to move a unit mass.

Question 15

What does the amount of energy needed to move an object and do work against gravity depend on?

Answer 15

The mass of the object and the gravitational field strength.

Question 16

What are equipotentials?

Answer 16

Equipotentials are lines (in 2D) and surfaces (in 3D) that join together all of the points with the same gravitational potential, V.

Question 17

What is the first step in deriving Kepler’s 3rd Law?

Answer 17

Making the centripetal force (mv^2 / r) equal to the gravitational force (GMm / r^2).

Question 18

What is the second step in deriving Kepler’s 3rd Law?

Answer 18

After rearranging, you substitute the equation for velocity (2πr / T). You then make T the subject.

Question 19

What is the equation for gravitational potential energy and which equation is it derived from?

Answer 19

Ep = -GMm / r. It is derived from the equation ΔW = mΔV by substituting in the equation for gravitational potential (-GM / r).

Question 20

What do you need to do to derive an equation for escape velocity?

Answer 20

Make kinetic energy equal gravitational potential energy (because kinetic energy lost equals GPE gained).

Question 21

What is a synchronous orbit?

Answer 21

When an orbiting object has an orbital period equal to the rotational period of the object it is orbiting.

Question 22

What is a geostationary satellite?

Answer 22

Satellites with a synchronous orbit but lie on the equator and therefore appear in the same place in the sky all the time.

Question 23

What are geostationary satellites useful for?

Answer 23

Very useful for sending TV and telephone signals as you don’t have to alter the angle of your receiver.

Question 24

What are low orbiting satellites and what are they useful for?

Answer 24

Satellites which orbit between 180 and 2000km. They are useful for communications and imaging of the Earth’s surface in high detail.