5.4 Gravitational Fields

Question 1

what is a gravitational field?

Answer 1

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

Question 2

gravitational fields are due

Answer 2

To objects having a mass

Question 3

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

Answer 3

Radial field

Question 4

what do gravitational field lines show?

Answer 4

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.

Question 5

what is gravitational field strength defined as?

Answer 5

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)

Question 6

how do gravitational field lines act around a spherical mass?

Answer 6

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

Question 7

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

Answer 7

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

Question 8

state Newton’s law of gravitation?

Answer 8

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

Question 9

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

Answer 9

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)

Question 10

what is G?

Answer 10

the universal gravitational constant, 6.67 x 10^-11

Question 11

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

Answer 11

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

Question 12

a spherical mass is often assumed to be what?

Answer 12

a point mass with all its mass concentrated at the centre

Question 13

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

Answer 13

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

Question 14

what is gravitational field strength equal to on earth?

Answer 14

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

Question 15

what are Kepler’s three laws of planetary motion?

Answer 15

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

Question 16

what is Kepler’s third law?

Answer 16

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)

Question 17

what is a geostationary orbit?

Answer 17

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

Question 18

what are geostationary satellites used for?

Answer 18

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

Question 19

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

Answer 19

T^2 = (4π^2 / GM ) x r^3

Question 20

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

Answer 20

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

Question 21

what is gravitational potential?

Answer 21

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

Question 22

what is gravitational potential energy?

Answer 22

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

Question 23

what is the equation for gravitational potential?

Answer 23

Vg = - GM / r

at a distance r from a point mass M

Question 24

what is the equation for gravitational potential energy?

Answer 24

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

Question 25

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)

Answer 25

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

Question 26

what is escape velocity?

Answer 26

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

Question 27

how can you calculate escape velocity?

Answer 27

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

Question 28

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

Answer 28

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

Question 29

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

Answer 29

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

Question 30

State Newton’s third law

Answer 30

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

Question 31

What is aphelion

Answer 31

at aphelion it is the furthest point from the sun

Question 32

what is perihelion

Answer 32

at perihelion it is the closest point to the sun

Question 33

what is eccentricity

Answer 33

A measure of how elongated the circle is

Question 34

If radius is infinite, whats is vg

Answer 34

0