Gravitational Fields COPY Flashcards
Define Newton’s Law of Gravitation
The gravitational force of attraction between two masses is inversely proportional to the distance between their centre of masses squared and is directly proportional to the product of the two masses.
What effect on the gravitational force will doubling the distance have?
It will 1/4 the force
What is the equation for Newtons Law of gravitation?
What value is the gravitational constant?
6.67 x 10-11 Nm^2kg^-2
What does a graph of Force against distance look like for a mass affected by Newtons Law of gravitation?
What does a graph of Force against 1/distance^2 look like for a mass affected by Newtons Law of gravitation?
Define gravitational field strength (uniform field)
The gravitational field strength at a point in a gravitational field is the force acting per unit mass at that point
Give the formula for the gravitational field strength in a uniform field
g = F/m
What are the units of gravitational field strength?
N/Kg
Is gravitational field strength a vector or scalar quantity?
Vector
What is the gravitational field strength at a point equal to?
The acceleration due to gravity at that point
What does Newtons 2nd Law state in relation to acceleration and gravitational field strength?
a = g
F/m = a
F/m = g
What is a radial field?
A field around a spherical object like a planet or a star
What does how far apart the gravitational field lines are around a spherical object in a radial field say about the strength of the field?
The closer the field lines, the larger the gravitational field strength (g)
How should radial field lines around a planet/star be drawn?
- The direction of the field lines at a point being the same direction of the force at that point (towards the centre)
- The lines are equally spaced
If we consider a mass m placed at a point at a distance, r, from a spherical body of mass M and radius R, the the force due to gravity acting on m due to the body is ?
If we consider a mass m placed at a point at a distance, r, from a spherical body of mass M and radius R, the the gravitational field strength acting on m due to the body is ?
g = GM / r^2
If g = 9.81 N/Kg at the surface of the earth, which has radius R, sketch a graph od g against distance, with R, 2R and 3R labelled on the distance axis.
Derive the equation for g on the surface in relation to density
Define gravitational potential
The gravitational potential at a point is defined as the work done in bringing unit mass from infinity to that point.
What symbol does gravitational potential use?
V
What are the units of gravitational potential?
J/Kg
What is the potential an infinite distance from an object. Explain.
- The potential is linked to position where the gravitational field becomes 0
- This happens at infinity
- Thus, the potential at infinite distance from an object = 0 J/Kg
How much energy is required to move 1kg from infinity to a potential of -30MJ/Kg?
It will need 30 MJ of energy
What are the key points to remember when moving a mass from infinity to a point with a potential of -30MJ/Kg?
- 30 MJ of energy is transferred
- The gravitational potentiakl around a mass will always be negitive since no work is done getting thw mass from infinity to a point as the gravitational force does no work
- The work done by the gravitational force will be the same regardless of route from infinity to the point
The work done moving between 2 points in a field is given by what equation?
/\W = m/\V
/\ = delta
What is the equation for gravitational potential in a radial field?
V = -GM / r
Sketch a graph of potential against distance from the centre of the earth if the potential at the surface of the earth is -62.5 MJ/Kg. Label the distance axis with R, 2R, 3R, where R is the radius of the earth.
What are the key things to remember about gravitational equipotentials? (4)
- These are a set of points all at the same potential
- They are aleays at right angles to the field lines
- The closer they are, the greater the field strength
- No work is donemoving along an equipotential
What is the equation linking Potential and gravitational field strength?
g = -/\V / /\r
/\ = delta
What is the formula for GPE in a uniform field?
GPE = mgh
What does the gradient represent on a V against r graph where r is distance?
The gradient is g.
What does the area under the graph represent on a g against r graph where r is radial displacement (distance)?
/\V
/\ = delta
How do you calculate work done / GPE in a non-uniform field?
/\W = m/\V
/\ = delta
Describe the orbit of a satellite
A satellite will move around a planet / star at constant speed but will be constantly accelerating
How can a satellite in orbit be travelling at a constant speed but be accelerating?
- The centripetal force on the satellite is at right anglkes to the velocity
- Therefore there is no component of the force in the direction of the velocity to increase or decrease the size of it
- The force does no work on the satellite and so there is no change in the kinetic energy of the satellity
Which direction is the satellite accelerating in?
Towards the centre of the star / planet which it is orbiting
Why does the astronaught feel a sense of weightlessness when in a satellite?
The satellite can be thought of as being in a state of free fall towards the centre of the star / planet but because its velocity is at right angles to this direction, it never makes it.
The velocity is just right for it to follow the curveature of the planet.
What does the size of the acceleration in a satellite equal to?
The g field strength at that point
What is Kepler’s 3rd law?
The time period of orbit can be shown to be linked to the radius or orbit so that T^2 is directly proportional to r ^3.
Derive:
T^2 = (4)(pi^2)(r^3) / (G)(M)
Derive:
T1^2 / r1^3 = T2^2 / r2^3
Prove T^2 = (4)(pi^2)(r^3) / GM by taking logs abnd plotting a graph
Describe the energy chenges on a satellite in an elliptical orbit aroung a planet or star, providing there are no external forces acting on it.
- The sum of its kinetic energy and gravitational potential energy will always be the same, so as it moves towards the planet / star it will lose GPE but gain an equal amount of KE.
HOWEVER
If a satellite is in a circular orbit and moves to another cricular orbit then the sum of potential and kinetic energy will not be the same
What is the velocity of a satellite equal to?
v^2 = GM / r
What is the GPE of a satellite in a circular orbit?
GPE = -GMm / r
What is the KE of a satellite in a circular orbit?
KE = GMm / 2r
What is the total energy of a satellite in a circular orbit equal to?
GPE + KE = -GMm / 2r
Describe how the total energy of a satellite in a circular orbit changes as r changes. Link this to work done.
- The total energy gets bigger the further away the satellite is from earth
- Therefore work needs to be done on an object to get ot to a higher orbit and work work needs to be done against an object (breaking force) to get it to a lower orbit
Derive a formula for the escape velocity of the earth
Describe a synchronous orbit (2)
- Orbits with the same orbital period as the planets rotational period that it is orbiting
- For earth, T is 1 day.
Give the three main points for a geostationary satellite
- 24 hour time period
- Above the equator
- Above same point
What are geostationary satellites used for?
- GPS and TV signals as the position is fixed
- Can take pictures of the earth (though not detailed)
- Because they stay in the same position in relation to the surface of the earth signals can be reflected off them and so transmitted across the earth.
Describe a geosynchronous orbit
- Have a time period of 24 hours
- Do not orbit above equator (the cross equator twice a day)
- Are above the same point once a day
How would you calculate the distance abouve the earth of a satellite?
Kepler’s 3rd Law
What orbit ranges classes a satellite as “low orbit”?
180 - 2000km
What are low orbit satellites used for?
- Remote sensing (weather mapping, spy photographs)
Describe a low orbit satellite
- Orbit between 180 - 2000km
- Rotate at much higher angular speeds than the planet they orbit and so can scan the whole surface of the earth
What equation do you use when adding g-fields?
g = GM / r^2
