Gravitational Fields Flashcards
What is a force field
A region in which a body experiences a non-contact force
How are force fields represented
As vectors
How do force fields arise
From the interactions of mass, static charge and between moving charges
What are the similarities between gravitational and electrostatic forces
Both have inverse square force laws that have many common features such as :
use of field lines
use of potential concepts
What are the differences between gravitational and electrostatic forces
Masses always attract but charges may attract or repel
What is gravity
A universal attractive force acting between all matter
gravitational field strength at a point =
force due to gravity (weight) / mass
F=mg
what does the equation g = F/m show
The larger the mass of an object, the greater its pull on another object
What factors affect the gravitational field strength at the surface of a planet
The radius/diameter of a planet
The mass of the planet
What is the direction of a gravitational field represented by
Gravitational field lines
In what direction do gravitational field lines around a point mass act
Radially inwards
How are gravitational field lines of a uniform field represented
By equally spaced parallel lines
What are radial/non-uniform fields
When the gravitational field strength is different depending on how far you are from the centre
What is a uniform sphere
One where its mass is distributed evenly
How do the gravitational field lines around a uniform sphere and a point mass compare
They are identical
How do the directions of the field lines differ for radial and uniform fields
Radial fields : Towards the centre of the sphere or point charge
Uniform fields : Towards the surface of the object
What is the mass of a uniform sphere considered to be at its centre
A point mass at its centre
Newtons law of Gravitation
The gravitational force between 2 point masses is proportional to the product of the masses and inversely proportional to the square of their separation
Gravitational force between two masses =
Newtons gravitational constant x point mass(1) x point mass (2) / distance between the centres of the 2 masses ^2
gravitational field strength in a radial field =
G x M / r^2
What would the graph of g against r look like
When r < R (the radius of the planet) g is directly proportional to r
When r > R, g is inversely proportional to r^2
What is GPE
The energy an object has when lifted off the ground
What is the GPE on the surface of the Earth
0
What is GPE outside Earth’s surface
The energy an object possesses due to its position in a gravitational field
What is gravitational potential at a point also know as
the gravitational potential energy per unit mass at that point
Definition of gravitiational potential energy per unit mass at that point
The work done per unit mass in bringing a test mass from infinity to a defined point
Why is gravitational potential always a negative value
It is defined as 0 at infinity
Since the gravitational force is attractive, work must be done on a mass to reach infinity
Why do two points at different distances from a mass have different gravitational potentials
The gravitational potential increases with distance from a mass
gravitational potential difference =
final gravitational potential - initial gravitational potential
Gravitational potential, V =
- GM / r
Why is the gravitational potential always negative near an isolated mass such as a planet
The potential when r is at infinity is defined as 0
Work must be done to move a mass away from a planet
What happens to gravitational potential when a mass is closer to a planet
Becomes smaller (more negative)
inverse square law for g
g is directly proportional to 1/r^2
is gravitational potential scalar or vector quantity
Scalar, unlike gravitational field strength which is a vector
Are gravitational forces attractive or repulsive and what does this mean as r decreases
Always attractive.
This means that as r decreases, positive work is done by the mass when moving from infinity to that point
What happens to gravitational potential when a mass is closer to a planet
Gravitational potential becomes smaller and more negative
What happens to gravitational potential when a mass moves away from a planet
Its gravitational potential becomes larger and less negative until it reaches 0 at infinity
equation relating V and g
g = - change in gravitational potential (V) / distance from the centre of a point mass (r)
Key characteristics of the graph of V against r for a planet
Values for V are all negative
As r increases, V against r follows a -1/r relation
Gradient is g at that point
Gradient has shallow increase as r increases
(graph bends to the right and is always under x axis)
Key characteristics of the graph of g against r for a planet
Values of g all positive
As r increases, g against r follows a 1/r^2 relation - inverse square law
Area under the graph is equal to the change in gravitational potential
Graph has steep decline as r increases
Looks like a ski slope
work done in moving a mass against the force of gravity =
Mass x change in gravitational potential
∆W = m∆V
Change in work done =
Change in GPE
Change in GPE for an object at a distance from a larger mass to another distance
GMm/r1- GMm/r2
GPE when V = 0
GPE = 0
Why does the equation for change in GPE for an object at a distance from a larger mass to another distance not involve g
g varies for different planets and is no longer a constant outside the surface of a planet
Characteristics of equipotential lines
Join together points with same gravitational potential
Perpendicular to gravitational field lines in both radial and uniform fields
Represented by dotted lines
NOT VECTORS SO HAVE NO DIRECTION
Equipotential lines in a radial field
Concentric circles around the planet
Further apart further away from the planet
Equipotential lines in a uniform field (near Earth’s surface)
Horizontal straight lines
Parallel
Equally spaced
Work done moving along an equipotential line or surface
No work is done moving along it only between equipotential lines or surfaces as there is no change in gravitational potential along an equipotential line
What is the centripetal force needed by a planet to stay in orbit
The gravitational force between the Sun and the planet
Kepler’s third law
For planets or satellites in a circular orbit about the same central body, the square of the time period is proportional to the cube of the radius of the orbit.
T^2 is proportional to r^3
Derivation of Kepler’s third law
- GMm/r^2 = mv^2 /r
- v^2 = GM/r
- v = 2pi x r / T
- v^2 = (2pi x r / T)^2 = GM/r
- T^2 = 4pi^2r^3 / GM
How can we graphically show the relationship between T and r
using log graphs
Total energy of an orbiting satellite =
KE + GPE
Total energy is always constant
What happens to the satellite’s KE and GPE if orbital radius decreases
KE increases and GPE decreases
What happens to the satellite’s KE and GPE if orbital radius increases
KE decreases and GPE increases
What happens to the satellite when the radius of the orbit is smaller
Larger gravitational force on it
Higher speed
Higher KE
Lower GPE
Shorter orbital timer period
Escape velocity
The minimum speed that will allow an object to escape a gravitational field with no further energy input
What happens to an objects kinetic energy when it reaches escape velocity
it has been transferred to gravitational potential energy
1/2 x m x v^2 = GMm / r
escape velocity =
root ( 2GM /r)
Why do rockets launched from Earth’s surface not need to achieve escape velocity to reach their orbit around Earth
They are continuously given energy through fuel and thrust to help them move.
Less energy is needed to achieve orbit than to escape from Earth’s gravitational field
Synchronous orbit
When an orbiting body has a time period equal to that of the body being orbited and in the same direction of rotation as that body
Geosynchronous orbit
When the plane of the orbit is directly above the equator.
Always orbits at the same point above Earth’s surface
Orbital time period equal to 24 hours
Moves west to east
What are geostationary satellites used for
Telecommunication transmissions
Television broadcast
Low orbits
When the altitude of the satellite is closer to the Earth’s surface
Example of low orbits
Polar orbit where the satellite orbits around the north and south poles
Uses of low orbits
Weather
Military applications
This is because they can take high quality photos of the Earth’s surface
