Gravitational Fields Flashcards
What is a gravitational field
A gravitational field is a force field - a region where an object will experience a non-contact force.
What do force fields cause
Force fields cause interactions between objects or particles - e.g. static or moving charges interact through electric fields and objects with mass interact through gravitational fields.
What type of force (attractive or repulsive) will an object with mass experience when put in a gravitational field
Any object with mass will experience an attractive force if you put it in the gravitational field of another object.
What is a point mass
M and m are uniform spheres, which behave as point masses
- as if all their mass is concentrated at the centre.
What is newton’s law of gravitational equation
F=-GMm/r^2
Where F is the force acting on mass m due to mass M,
M and m are point masses
G is the gravitational constant
r is the distance between the centre of two masses
Note: the negative sign shows that the vector F is in the opposite direction to r (displacement of m from M)
What can you say about the force point mass M experiences if point mass m experiences a force due to point mass M
The force on M due to m is equal but in the opposite direction
What is the relationship between force by a point mass on a gravitational field and the distance the masses (r)
The law of gravitation is an inverse square law so: F ∝ 1/r^2
If the distance r between the masses increases then the force ~ will decrease.
If the distance doubles then the force will be one quarter the strength of the original force.
What are gravitational field lines
Gravitational field lines (or lines of force) are arrows showing the direction of the force that masses would feel in a gravitational field.
What does radial mean in relation to a gravitational field
The Earth’s gravitational field is radial - the lines of force meet at the centre of the Earth.
What happens a on object in a gravitational field is moved further from the centre of the field on a diagram
If you move mass m further away from the Earth - where the lines of force (in the diagram) are further apart - the force it experiences decreases.
Why don’t you draw lines of force for the small object often
The small mass, m, has a gravitational field of its own. This doesn’t have a noticeable effect on the Earth though, hecause the Earth is so much more massive
On a diagram showing field lines close to an object such as the earths surface what can be assumed
Close to the Earth’s surface, the field is (almost) uniform the field lines are (almost) parallel and equally spaced. You can usually assume that the field is perfectly uniform.
Close to the surface field lines show the direction of force of a small mass
Look at CGP to see what this looks like
How can gravitational field strength be calculated?
Gravitonal field strength can be thought as the force per unit mass. It value depend on where you can in the field but can be calculated by
g=F/m
Where F is the force expired by mass m in a gravitational field
Measured in NKg^-1
Is g a vector or scalar
g is a vector quantity, always pointing towards the centre of the mass whose field you’re describing. Depending on the direction defined to be positive, it could be negative.
What can be assumed about the gravitational field strength at the Earth’s surface
Since the gravitational field is almost uniform at the Earth’s surface, you can assume g is a constant if you don’t go too high.
What can be assumed about g since F=ma
g is just the acceleration of a mass in a gravitational field. It’s often called the acceleration due to gravity.
How do you calculate the gravitational field strength in a radial field. What can be said about this law in terms of proportionality
When the gravitational field is being caused by a point mass the field is radial. Therefore the value of g depend on the distance (r) from the point mass.
g=-GM/r^2
It is an inverse square law. As r increase, g decrease
What is the gravitational field potential
The gravitational field potential at a point is the work done moving a unit mass from infinity to that point
What is the symbol and unit for gravitational field potential
V subscript g Nkg^-1
What is the equation for graviton field potential in a radial field
Vg=-GM/r
Vg is the gravitational potential (Jkg^-1)
G is the gravitational constant
M is the mass of the object causing the gravitational field (kg)
r is the distance from the centre of the object (m)
Why is gravitational potential a negative value
Gravitational potential is negative - you have to do work against the gravitational field to
move an opiect out of it. the further vou are from the centre of a radial nield. the smaller the magnitude of Vg. At an infinite distance from the mass, the gravitational potential will be zero
Electric potential works the same this with attractive charged particles
What does the gradient of the graph of gravitational potential against r find
If you find the gradient you get the value of -g
g=-change in Vg / change in r
Since when you move an object against gravity work in done, how do you calculate the amount of energy you need to move an object a distance ?
Change in energy (W) = m x change in gravitational potential
(Note that you gave to calculate the graviton potential acting on the object before and after it is moved)
On a graph of force on an object due to the gravitational field of a point mass, against distance of that object from the point mass (r) what does the area under the graph represent between two values of r
Work done to the move the object away from the point mass
How to calculate an objects gravitational potential energy at a point in the gravitational field is
E = m Vg
Or
E=-GMm/r
Where r is the distance from the centre of mass m to M
What is escape velocity?
The escape velocity is defined as the velocity needed so an object has just enough kinetic energy to escape a gravitational field. This is when an object’s kinetic energy is equal and opposite to its gravitational potential energy - so the total energy is zero. The formula for escape velocity is:
v = square root of [2GM/r]
Note can easily be derived from the fact at the escape velocity 1/2mv^2 = GMm/r
What is a satellite with an example
A satellite is just any smaller mass which orbits a much larger mass - the Moon is a satellite of the Earth.
Are planets orbits circular ?
Almost (their actually elliptical)
In our Solar System, the planets have nearly circular orbits… so you can use the equations of circular motion.
How do you calculate the speed of orbit of the Earth
Since the centripetal force is equal to the force due to the suns gravitational pull
mv^2/ r = GMm/r^2
Which rearranges to be become v = square root [GM/r]
Where v is the orbital speed in ms^-1
G is the gravitational constant
M is the mass of the object being orbited
r is the distance from the centre of the object being orbited to the centre of the satellite
How do you calculate the period of a orbiting satellite
Since speed = distance / time
T = 2pi r/v
Subbing into v= square root [GM/r]
T^2= (4 pi^2 / GM) r^3
What are geostationary satellites
Geostationary satellites are those that orbit directly over the equator and are always above the same point on Earth
What is the angular speed of a geostationary velocity the same as
A geostationary satellite travels at the same angular speed as the Earth turns below it.
Their orbit takes exactly one day.
How long does 1 geostationary orbit take
1 day
Uses of geostationary satellites
These satellites are really useful for sending TV and telephone signals and have improved communication around the world. The satellite is stationary relative to a certain point on the Earth, so you don’t have to alter the angle of your receiver (or transmitter) to keep up.
What are the cons of a geostationary satellite
There are downsides though - they are expensive and pose a small risk of something going wrong and the satellite falling back to Earth.
What’s Kepler’s 1st law
FIRST LAW: Each planet moves in an ellipse around the Sun, with the Sun at one focus (a circle is just a special kind of ellipse).
What’s Keplers 2nd law
SECOND LAW: A line joining the Sun to a planet will sweep out equal areas in equal times. (So if moving from A to B takes the same amount of time as moving from C to D, the two shaded sections will have equal areas.)
See CGP diagram
What’s Keplers 3rd law
THIRD LAW: The period of the orbit and the mean distance between the Sun and the planet are related by Kepler’s third law:
T^2 ∝ r^3
Other than predicting the motion of satellites, what else can newtons law of gravitation be used for?
Newton’s law of gravitation can also help to explain how thick a planet’s atmosphere is.
The planet’s gravitational field exerts a force on everything around it, including the particles which make up its atmosphere. Otherwise, the particles would float off into space.
For a planet of a fixed density, the more massive the planet is, the larger the force is further away from it’s surface - so the more atmosphere particles it can stop escaping into space, leading to a thicker atmosphere.
