Gravitational Feilds Flashcards
State newtons 3d law for gravitational fields
Force on M due to m is equal in size, same type and opposite to the direction to force on m
Explain why 2 objects of mass M an mass m have an attractive force towards eachother
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
What does the -ve sign represent in the GF force equation
To indicate that F is an attractive force an in the opposite direction
Definition of gravitational field
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
Explain the characteristics of field lines acting on an object , field lines represent GF
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
State Kepler’s 1st law
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
State keplers 2nd law
A line segment joining the planet and the star sweeps out equal areas in equal time segments
How can you derive keplers 3d law
Gravitational force=centripetal force
Sub v using v=2pir/T
Simplify
State keplers 3d law
The square of the orbital period of the planet T is proportional to the cube of the planets orbital radius r
Define work
What is done when a force moves its point of application through some distance in the direction of the force
Define gravitational potential
The work done per unit mass to move an object to that point from infinity
Explain why gravitational potential is always negative
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.
Give another equation for gravitational potential energy
Work done divided by mass
How can we find the change of work done using gravitational potential
Change of work done equals mass times the change of gravitational potential
Explain why work done is negative or positive in some cases
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
Give a characteristics of a geostationary orbit
Orbital period of 24 hours in the same direction as the rotation of earth
Derive equation for escape velocity
Gravitational energy = KE
Rearrange for v
Gpe= GMm/r
Explain why the force of gravitational attraction is not noticeable between two cars but it is noticeable between two planets
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
What can the field lines around a planet show about the nature of the gravitational field?
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.
Explain why there is no noticeable difference in the value g at the Heights reached by aeroplanes
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
Describe the gravitational field and the gravitational field strength close to the surface of the earth
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
Explain how the gravitational force changes with the distance from the centre of earth when it is doubled
When the distance from the centre of earth is doubled, the gravitational force gets four times smaller
Explain why planets move faster at smaller orbits
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
A planet is orbiting the Sun describe the forces acting on the planet
The only force acting on the planet is the gravitational attraction
Describe what forces caused the centripetal force acting on a planet
The gravitational attraction force
Give three uses of geostationary satellites
Spying telecommunication and whether
State the properties of a geostationary orbit
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.
Explain why gravitational potential is relative to 0
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
State three factors that Gravett potential energy is dependent on
The mass of object 1
The mass of object two
The separation of the two objects
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
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.
Define gravitational potential energy
The work done in bringing an object from Infinity to that point
Why would launching a satellite from the equator require min enrgy
At equator the satellite has largest kinetic enrgy due to the earths rotation
Explain how the linear speed of a satellite vary with circular orbit
A higher circular orbit leads to a smaller linear speed as v= root GM/r therfore v is prop. To 1/square root r
What is the equation for escape velocity and how to derive
V= square root (2GM/r )
Ek= GPE rearrange for v
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
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
Describe 2 prop of a radial gravitational field
It is always attractive
Inverse square variation with distance g is prop to 1/r^2
Explain how newtons law of gravity is applied between 2 non-spherical asteroids
The force is inversely prop to the distance squared between the centres of mass of the asteroids
Explain what is meant by the grav potential at the earths surface is -6.27x10^6
The force is attractive so the work done is neagtive
Vg is 0 at infinity therfore the value is more negative closer to earth
