Gravitational Fields Flashcards
What is a gravitational field?
A region of space where a mass experiences a force due to the gravitational attraction of another mass.
What is the equation for g?
g=F/m
g = gravitational field strength (N kg-1)
F = force due to gravity, or weight (N)
m = mass (kg)
What is an example of a non-uniform field?
(Description of the field as well)
Radial fields - gravitational field lines around a point mass are radially inwards
What is Newton’s law of gravitation?
Not equation
The gravitational force between two point masses is proportional to the product of the masses and inversely proportional to the square their separation.
What is Newton’s law of gravitation
Equation
F=-GMm/r^2
F = gravitational force between two masses (N)
G = Newton’s gravitational constant
m1and m2 = two points masses (kg)
r = distance between the centre of the two masses (m)
What is a common mistake on calculating the r for newton’s law of gravitation with planets?
A common mistake in exams is to forget to add together the distance from the surface of the planet and its radius to obtain
the value of r. The distance r is measured from the centre of the mass, which is from the centre of the planet.
What is the equation for the Gravitational Field Strength in a Radial Field?
g=-GM/r^2
g = gravitational field strength (N kg-1)
G = Newton’s Gravitational Constant
M = mass of the body producing the gravitational field (kg)
r = distance from the mass where you are calculating the field strength (m)
Is Gravitional field strength a vector or scalar?
Vector
Draw the graph of g against r, label and explain it
r is the distance from the centre of the earth
Check the graphs section of gravity
Equation for Gravitational potential energy
G.P.E = mgΔh
What is gravitational potential defined as?
Not equation/Symbol and units
The gravitational potential energy per unit mass at that point Therefore, it is defined as:
The work done per unit mass in bringing a test mass from infinity to a
defined point. It is represented by the symbol, V and is measured in J kg-1
Why is gravitational potential always negative?
The gravitational potential is always a negative value. This is because:
It is defined as zero at infinity and since the gravitational force is attractive, work must be done on a mass to reach
infinity.
What is the equation for gravitational potential difference?
ΔV = Vf
– Vi
Vf = final gravitational potential (J kg-1)
Vi = initial gravitational potential (J kg-1)
What do you not have to worry about when they talk about difference in potential?
When exam questions ask for the ‘difference’ or ‘change in’ a value (denoted by Δ), they are asking for the magnitude. Therefore, don’t worry too much about negative or positive signs. As long as you consistently calculate the difference in two values as ‘final value initial value‘, a negative difference will mean that the value is decreasing and vice versa
Equation for calculating potential
V=-GM/r
G = Newton’s gravitational constant
V = gravitational potential (J kg-1)
G = Newton’s gravitational constant
M = mass of the body producing the gravitational field (kg)
r = distance from the centre of the mass to the point mass (m
Is gravitational potential a scalar or vector quantity?
Scalar
When calculating gravitational potential at a point what do you need to remember?
Remember to keep the negative sign in your solution for the gravitational potential at a point. However, if you’re asked for the ‘change in’ gravitational potential, no negative sign needs to be included since you are finding a difference in values and just the magnitude is normally required. Rmember to also calculate r as the distance from the centre of the planet, and not just the distance above the planet’s surfac
What is the equation for g in terms of potential?
g=-∆V/∆r
g = gravitational field strength (N kg-1)
ΔV = change in gravitational potential (J kg-1)
Δr = distance from the centre of a point mass (m
Draw, label and explain the graph for V against r
V - Potential r - Distance from the centre of planet
Check the graph section
Draw, label and explain the graph for g against r
g - Gravitational field strength r - Distance from the centre of planet
Check the graph section
The equation for work done against a mass
V is needed
∆W = m∆V
∆W = change in work done (J)
m = mass (kg)
∆V = change in gravitational potential (J kg-1)
The equation for gravitational potential energy
V and M needed
U = mV = -GMm/r
When can you use the mgh equation or -GMm/r equation?
Make sure to not confuse the ΔG.P.E equation with ΔG.P.E = mgΔh
The above equation is only relevant for an object lifted in a uniform gravitational field (close to the Earth’s surface). The new equation for G.P.E will not include g, because this varies for different planets and is no longer a constant (decreases by 1/r^2) outside the surface of a planet.
What are equipotential lines/surfaces and their characteristics?
Equipotential lines (2D) and surfaces (3D) join together points that have the same
gravitational potential
These are always:
Perpendicular to the gravitational field lines in both radial and uniform fields
Represented by dotted lines (unlike field lines, which are solid lines with arrows)
No work is done when moving along an equipotential line or surface, only between
equipotential lines or surface.
How are equipotential lines in a radial and uniform field?
In a radial field (eg. a planet), the equipotential lines:
Are concentric circles around the planet
Become further apart further away from the planet
In a uniform field (eg. near the Earth’s surface), the equipotential lines are:
Horizontal straight lines
Parallel
Equally spaced
How do derive the velocity for orbit?
Make the Fc = Fg and then solve for v
Fc = Centripetal Force
Fg = Gravitational Force
Equation for orbital velocity
v^2=GM/r
v = linear speed of the mass in orbit (m s-1)
G = Newton’s Gravitational Constant
M = mass of the object being orbited (kg)
r = orbital radius (m
How do you derive Kepler’s law?
Make orbital velocity equal to 2(pi)/T and rearrange for T
What is Kepler’s law equation?
T^2=[4(pi)^2][r^3]/GM
T = time period of the orbit (s)
r = orbital radius (m)
G = Newton’s Gravitational Constant
M = mass of the object being orbited (kg
What is Kepler’s law?
The equation shows that the orbital period T is related to the radius r of the orbit. This is also known as 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.
Kepler’s third law can be summarised as:
T^2 ∝ r^3
Draw, Label and explain a graph for smth T against smth R
Smth being a mathematical function
Check the graphs section
Equation for the total energy for an orbiting satellite
ET= Ek+Ep =GMm/2r-GMm/r=-GMm/2r
Ek = Kinetic energy Ep = Gravitational potential energy
What are features of orbit between X and Y
X - Smaller orbit Y - Bigger orbit
At orbit X, where the radius of orbit r is smaller, the satellite has a:
Larger gravitational force on it
Higher speed
Higher KE
Lower GPE
Shorter orbital time period, T
At orbit Y, where the radius of orbit r is larger, the satellite has a:
Smaller gravitational force on it
Smaller speed
Lower KE
Higher GPE
Longer orbital time period, T
Definition for escape velocity
Escape velocity is defined as:
The minimum speed that will allow an object to escape a gravitational field
with no further energy input.
How to derive escape velocity
Make kinetic energy equivalent to Gravitational potential energy
Equation for escape velocity
v^2 = 2GM/R
Why do you not need to achieve escape velocity to reach orbit?
v = escape velocity of the object (m s-1)
G = Newton’s Gravitational Constant
M = mass of the object to be escaped from (ie. a planet) (kg)
R = distance from the centre of mass M (m)
What is synchronous and geosynchronous orbit?
A synchronous orbit is:
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.
When the plane of the orbit is directly above the equator, it is known as a
geosynchronous orbit.
What is a geostationery orbit?
This is a specific type of orbit in which the satellite:
Remains directly above the equator
Is in the plane of the equator
Always orbits at the same point above the Earth’s surface
Moves from west to east (same direction as the Earth spins)
Has an orbital time period equal to Earth’s rotational period of 24 hours
What are geostationery orbits used for?
Geostationary satellites are used for telecommunication transmissions (e.g. radio) and
television broadcast
A base station on Earth sends the TV signal up to the satellite where it is amplified and
broadcast back to the ground to the desired locations
The satellite receiver dishes on the surface must point towards the same point in the sky
Since the geostationary orbits of the satellites are fixed, the receiver dishes can be fixed too
What is a low orbit, an example and uses for it?
Some satellites are in low orbits, which means their altitude is closer to the Earth’s surface
One example of this is a polar orbit, where the satellite orbits around the north and south
pole of the Earth
Low orbits are useful for taking high-quality photographs of the Earth’s surface. This could be
used for:
Weather
Military applications
What is a force field?
A region of space where an object will experience a non-contact force
What is gravitational potential energy?
The energy possessed by an obejct due to its position within a gravitational field.
What do you need to be careful of when calculating Kepler’s law?
The radius being used is the orbital radius and the radius of the object it is orbiting together. Since you are calculating it as point mass, the radius of the planet can also be seen as ‘extra space’.
What is gravity?
A universal attractive force that acts between all matter
What is a point mass?
A mass in which it behaviours like all the mass is concentrated at the centre
What can be classed as a low orbit?
Distance wise
Satellites orbiting the earth below 2000km in terms of orbital radius.
