Gravitational Feilds

Question 1

State newtons 3d law for gravitational fields

Answer 1

Force on M due to m is equal in size, same type and opposite to the direction to force on m

Question 2

Explain why 2 objects of mass M an mass m have an attractive force towards eachother

Answer 2

Each mass gives rise to its own gravitational field and their interaction results in an attractive force which is equal and opposite and the same type f force

Question 3

What does the -ve sign represent in the GF force equation

Answer 3

To indicate that F is an attractive force an in the opposite direction

Question 4

Definition of gravitational field

Answer 4

For a certain point in the field of a mass the field strength is defined as the gravitational force (weight) acting on an object per unit of the objects ass

Question 5

Explain the characteristics of field lines acting on an object , field lines represent GF

Answer 5

The density of feild lines represent the strength of feild
The feild lines never cross
They are directed radially toward the centre of mass of the object
They are parallel to eachother and perpendicular to the objects surface
They are uniform, same mag

Question 6

State Kepler’s 1st law

Answer 6

Planets have elliptical orbits with the sun at 1 foci
For any point on the eclipse the sum of the distances of the 2 foci is away the same

Question 7

State keplers 2nd law

Answer 7

A line segment joining the planet and the star sweeps out equal areas in equal time segments

Question 8

How can you derive keplers 3d law

Answer 8

Gravitational force=centripetal force
Sub v using v=2pir/T
Simplify

Question 9

State keplers 3d law

Answer 9

The square of the orbital period of the planet T is proportional to the cube of the planets orbital radius r

Question 10

Define work

Answer 10

What is done when a force moves its point of application through some distance in the direction of the force

Question 11

Define gravitational potential

Answer 11

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

Question 12

Explain why gravitational potential is always negative

Answer 12

When the mass is at infinity force would equal zero. ASR squared equals zero therefore the mass cannot fall/gravitate towards any mass and so it’s gravitational potential is also zero however when the mass is at a distance are from another mass we would have to do work to return this mass to infinity where gravitational potential is zero this means it must have less than zero energy, as gravitational potential is worked done divided by mass. This would also mean the potential is less than zero so gravitational potential is always negative.

Question 13

Give another equation for gravitational potential energy

Answer 13

Work done divided by mass

Question 14

How can we find the change of work done using gravitational potential

Answer 14

Change of work done equals mass times the change of gravitational potential

Question 15

Explain why work done is negative or positive in some cases

Answer 15

When moving closer to a mass this means the mass is moving to a more negative potential as it is losing gravitational potential energy so the work done is negative and energy is transferred for example kinetic energy of the falling object
When the mass is moving away from a point of mass this means it is moving to a less negative potential as it is gaining gravitational potential energy therefore work done will be positive

Question 16

Give a characteristics of a geostationary orbit

Answer 16

Orbital period of 24 hours in the same direction as the rotation of earth

Question 17

Derive equation for escape velocity

Answer 17

Gravitational energy = KE
Rearrange for v
Gpe= GMm/r

Question 18

Explain why the force of gravitational attraction is not noticeable between two cars but it is noticeable between two planets

Answer 18

The mass of two cars is far smaller than the mass of two planets therefore as gravitational force is directly proportional to the product of the two masses the gravitational force between the light occurs will be much smaller compared to the force between the two planets

Question 19

What can the field lines around a planet show about the nature of the gravitational field?

Answer 19

The gravitational force is attractive and act towards the centre of the planet. The gravitational field is radial and the gravitational field decreases with distance from the surface of the planet.

Question 20

Explain why there is no noticeable difference in the value g at the Heights reached by aeroplanes

Answer 20

The distance is measured from the centre of the body and we know that G and inverse square relationship with distance heights from the surface of earth reached by aeroplanes are very small in comparison to the distance from the centre of the earth to the earth surface therefore this increase in distance from the centre of the Earth only has a small effect on the value of g

Question 21

Describe the gravitational field and the gravitational field strength close to the surface of the earth

Answer 21

The gravitational feud strength is approximately 9.81 m/s squared close to the surface of the Earth and the field lines are approximately parallel

Question 22

Explain how the gravitational force changes with the distance from the centre of earth when it is doubled

Answer 22

When the distance from the centre of earth is doubled, the gravitational force gets four times smaller

Question 23

Explain why planets move faster at smaller orbits

Answer 23

According to capless third law, the square of a planets period is directly proportional to the cube of the planets orbital radius this means that if the planet has a smaller orbit it will have a smaller period and we know that velocity equals two pi divided by time period therefore the smaller time period means the bigger velocity

Question 24

A planet is orbiting the Sun describe the forces acting on the planet

Answer 24

The only force acting on the planet is the gravitational attraction

Question 25

Describe what forces caused the centripetal force acting on a planet

Answer 25

The gravitational attraction force

Question 26

Give three uses of geostationary satellites

Answer 26

Spying telecommunication and whether

Question 27

State the properties of a geostationary orbit

Answer 27

It’s orbit is above the equator. It stays at the same position relative to the surface of earth therefore has a circular orbit and it has an orbital period equal to 24 hours.

Question 28

Explain why gravitational potential is relative to 0

Answer 28

At all points at a distance of infinity the potential energy is equal to 0 as r squared equals infinity therefore as the distance moves to infinity the force equals zero

Question 29

State three factors that Gravett potential energy is dependent on

Answer 29

The mass of object 1
The mass of object two
The separation of the two objects

Question 30

Using Kepler second law explain why when an astroid orbits the Sun it will move at maximum speed when it is at the closest distance to the Sun

Answer 30

Second law states that a line segment connected between the astroid and the Sun will sweep out equal areas in equal time segments therefore when it is closest to the Sun it will have to travel a larger distance for the same time period. As velocity equals overtime the velocity will be larger.

Question 31

Define gravitational potential energy

Answer 31

The work done in bringing an object from Infinity to that point

Question 32

Why would launching a satellite from the equator require min enrgy

Answer 32

At equator the satellite has largest kinetic enrgy due to the earths rotation

Question 33

Explain how the linear speed of a satellite vary with circular orbit

Answer 33

A higher circular orbit leads to a smaller linear speed as v= root GM/r therfore v is prop. To 1/square root r

Question 34

What is the equation for escape velocity and how to derive

Answer 34

V= square root (2GM/r )
Ek= GPE rearrange for v

Question 35

Impulse engines are used to place the satellite into an orbit with a longer period what changes does this make to the orbital motion of satellite

Answer 35

Velocity decreases as velocity is proportional to to 1/T therfore radius increases as velocity is proportional to 1/ square root r
And r increases as r^3 is proportional to T^2

Question 36

Describe 2 prop of a radial gravitational field

Answer 36

It is always attractive
Inverse square variation with distance g is prop to 1/r^2

Question 37

Explain how newtons law of gravity is applied between 2 non-spherical asteroids

Answer 37

The force is inversely prop to the distance squared between the centres of mass of the asteroids

Question 38

Explain what is meant by the grav potential at the earths surface is -6.27x10^6

Answer 38

The force is attractive so the work done is neagtive
Vg is 0 at infinity therfore the value is more negative closer to earth