Chapter 18 - Gravitational Fields Flashcards
What is the weight of an object
Any object placed in a gravitational field will experience an attractive force towards the centre of mass that’s creating the field.
What is the gravitational field strength
At a point within a gravitational field is defined as the gravitational force exerted per unit mass on a test mass placed at that point.
How to calculate g?
g= F/m
What are gravitational field lines?
They are directed towards the centre of the mass, around a spherical mass forming a radial field.
The stronger the field, the closer together the lines will be.
What type of quantity is g?
It’s a vector quantity and it always points to the centre of mass.
What is Newton’s Law of Gravitation
It states the attractive force between 2 point masses is:
directly proportional to the product of their masses
And inversely proportional to the square of their separation.
What is the Gravitational Constant
6.67 x 10-11 Nm2kg2
How can you derive the expression for Gravitational field strength in a radial field.
Use the F= -GMm/r2. Take the f and put it into the g=F/m.
What is a electrostatic field?
A region of space within which a positive test mass experiences a force per unit charge.
What is a positive test mass
It has no fields; so its fields can’t interact with the field that your trying to measure in the first place. This way you can get an accurate measure of the field that you are trying to measure.
What is a magnetic field?
An region around bodies that are magnetic and exert a force on other magnetic bodies.
What is Keplar’s 1st Law of Motion
All planets move about the Sun in an elliptical orbit, having the Sun as one of the foci.
What are the implications of a point body
By treating bodies as point bodies, for any given displacement w.r.t, the displacement will stay the same.
What is the eccentricity
The ellipticity of an ellipse.
Keplar’s 2 Law of Motion
A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths in time.
It implies the the speed of a planet about its orbit IS NOT CONSTANT. So, closer to the Sun, the Earth will move faster and cover more distance in 1 month, than it will when it if further away and travels slower, and covers less distance.
Keplar’s 3 Law of Motion
The square of the orbital period, T of a planet is directly proportional to the cube of its average distance form the Sun.
Derivation of Keplar’s 3rd Law
You say that GMm/r2 = mv2/r.
Rearrange to find v.
V= 2πr/T. Rearrange to get:
r3/T2 = GM/4π2 = k.
Geostationary satellites
They have the same time period as the Earth (24 hours)
They can only orbit above the equator.
Polar orbits
Goes from North to South.
Has a lattitude of 90 degrees.
What are Geostationary satellites used for
GPS.
What are polar satellites used for
Spys, cameras , weather.
Determining the r for Geostationary satellites
Since T is the same as the Earth, and for them all, then the radius that they travel at is also equal.
Uses of satellites
Communications Military uses Scientific research Weather and climte GPS
GPS
There are 32 satellites, in the lower orbit. Each satellite gives info about the time of transmission and current position etc.
1 position needs at least 4 satellites.
Equation for Gravitation potential - Vg
-GM/r.
How can you calculate Vg
Integrate the (-GMm/r2) from limits infinity to r.
What is the Vg- definition
Work done per unit mass in moving a body from infinity to the a point in a gravitational field.
What do you lose energy in Vg
Because at infinity, you will have 0J. So anywhere away from it, will be negative.
Graph for Vg
X axis: r/Mm.
Y axis: Vg
You would get a graph thats an upside down curve. It would have a limit at the line x=r, which it would touch at the correct Vg. The gradient would be -GM/r.
If there are 2 equipotential lines of 2 planets intersecting at -40MJ/kg, what would the Vg at this point
-40+-40 = 80 MJ/kg.
What is the GPE
m Δ Vg.
Derivation for Vg
Integrate the (GMm/r2) over the limits of rb and ra.
This gives you:
-GMm/ra – GMm/rb.
-m (GM/ra + GM/rb)
= b (Va - Vb)
What is the escape velocity
The minimum velocity required in order for a non-propelled body to escape the gravitational pull of a planet.
Assumptions in escape velocity
It is the least minimum velocity.
all KE is transferred to GPE.
The object is non-propelled. Only impart energy, so one big boost, and a lot of force in a small amount of time.
Escape
You need to just no longer feel the gravitational pull of the planet.
How to calculate the escape velocity
V= √2GM/r
Derivation for escape velocity
m Vg = mv2 / r
GMm/ r = mv2/r
V= √2GM/r
Graph for escape velocity
Plot Vg against1/r.
Gradient = -GM.
How can you calculate the total energy in moving an object from the surface of a planet to a point?
Kinetic energy + (- GMm/r)
Why will lg-lg graphs stay a straight line?
Because GM is constant, and so the gradient will always be -2.
Why is the gradient always -2 on a lg-lg graph
Because g = k/r^2. This means that for every planet, the gradient will always be -2.
