Gravitational Fields Flashcards
What is a gravitational field?
A special type of field in which any object with mass experiences a gravitational force
What are gravitational fields set up around?
Any objects with a mass
What are gravitational fields always?
Attractive
Where are the lines of a gravitational field always directed?
Towards the centre of mass of the body
What do gravitational fields map?
How a gravitational force would be exerted on a mass
Where do all gravitational fields extend to?
Infinity
What can a uniform sphere be considered as?
A point mass
What are the field lines like around a point mass?
Radial
Are radial fields uniform or non-uniform fields?
Non-uniform; the GF strength is different depending on how far object is from the centre of mass
What is a uniform gravitational field?
Where the field strength is the same at all points
How is a uniform field represented?
Equally spaced parallel gravitational field lines
What are the factors of GF lines?
- They do not cross
- The arrows on them show the direction of the field
- They always point to the centre of mass
- A stronger field is represented by field lines that are closer together
What is gravitational field strength?
The force per unit mass at a given point
What is the unit of gravitational field strength?
N kg^-1
What is the equation for gravitational field strength?
g = F/ m
g = gravitational field strength, N kg^-1
F = force, N
m = mass, kg
What are the factors that affect GF strength on the surface of a planet?
- Radius of the planet
- The mass or density of the planet
What is the value of g on earth?
9.81 N kg^-1
What do gravitational fields give a rise to?
(Gravitational) force - it acts on any object with a mass
What is Newtons Law of Gravitation?
The gravitational force between 2 masses, M & m, is proportional to the product of their masses and inversely proportional to the square of their separation
What are the proportionality equations of the gravitational force?
F ∝ Mm
F ∝ 1/ r^2
so F ∝ Mm/ r^2
What is Newtons Law of Gravitation equation?
F = -GMm/ r^2
F = gravitational forces between the 2 masses, N
G = Newtons gravitational constant
M = mass 1, kg
m = mass 2, kg
r = seperation, m
What does the negative sign in Newtons Law of Gravitation equation represent?
That the force is attractive
What happens to the GF lines in a radial field?
They get further apart from each other
What is the equation for GF strength in a radial field?
g = -GM/ r^2
g = GF strength, N kg^-2
G = Newtons gravitational constant
M = mass of an object, kg
r = distance from the centre of mass, m
What is the value of Newtons Gravitational constant?
6.67 x 10^-11 Nm^2 kg^-1
What is the graph for g against r?
What can the GF field near the earths surface be described to be?
Uniform; meaning the GF strength is constant at every point near the earths surface
What is Kepler’s First Law?
The orbit of a planet is an ellipse; with the sun at one of 2 foci
What is an ellipse?
An elongated circle with 2 foci
What is eccentricity?
A measure of how elongated the circle is
What is aphelion?
Furthest point from the sun
What is perihelion?
Closest point to the sun
What is Kepler’s Second Law?
A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time
What does this show?
Area x = area y when time AB = time CD
When does the sun move faster?
When it is closer to the sun
When does the sun move fastest?
Perihelion
When does the sun move slowest?
Aphelion
What is Kepler’s Third Law?
The square of the orbital time period of a planet is directly proportional to the cube of the orbital radius
T^2 ∝ r^3
How do you relate the gravitational force equation and the centripetal force equation?
Typically, most planets and satellites have a near circular orbit. Therefore, the gravitational force between the sun and another planet provides the centripetal force needed to stay in orbit
F = F centripetal
Gmm/ r^2 = mv^2/ r
v^2 = GM/ r
v = sqr (GM/ r)
What does equation, v = sqr (GM/ r), indicate?
All satellites, whatever their mass, will travel at the same speed in a particular orbital radius
Assuming a planet or satellite is travelling in circular motion when in orbit, what equations can be used?
v = 2πr/ T
v^2 = GM/ r
so T^2 = (4π^2 / GM) r^3
What can Kepler’s Third Law be applied to?
Any body is orbit about some larger body ; this means it can be applied to other systems not just the planets in out solar system orbiting the sun
What is a geostationary satellite?
A satellite which:
- Remains directly above the equator
- Is in the plane of the equator
- Always orbits at the same point above the Earths surface
- Moves from west to east
- Has an orbital time period equal to the earths rotational period of 24 hours
What are the uses of satellites?
- Telecommunications transmissions eg. radio
- Television broadcast
- Military surveillance
- Scientific research and analysis
- Weather and climate analysis
- Global positioning
What is gravitational potential?
The work done per unit of mass in bringing a mass from infinity to a defined point
What is infinity?
A point so far from the object producing the field that its strength equals 0
When is gravitational potential at a maximum?
At infinity, where its value is 0 J kg^-1
Why are gravitational potential values negative?
Because all masses are attracted to each other, and gravitational potential considers the energy for 1 mass to move to another
When would gravitational potential be positive?
When work done is needed to move a point towards infinity
What does the gravitational potential at any point is a radial field depend on?
- Distance r from point mass producing the field
- The mass M of the point mass
What is gravitational potential proportional to?
Mass of the point mass
What is gravitational potential inversely proportional to?
The distance from the point mass
What is the equation for gravitational potential?
Vg = -GM/ r
Vg = gravitational potential
G = gravitational constant
M = mass of body causing field
r = distance from centre of mass to point in the field
What is the equation for change in potential?
ΔVg =.GM ((1/ initial r) - (1/ final r) )
What does a gravitational force-distance graph look like?
What does the area under a gravitational force-distance graph equal?
Work done
What are the equation for GPE and work done?
E = mVg
E = -GMm/ r
ΔW = mΔVg
ΔGPE = GMm ((1/ initial r) - (1/ final r))
ΔW = work done/energy transferred
What is gravitational potential energy?
The work done to move the mass from infinity to a point in a gravitational field
What happens when an object moves away from the surface of the earth?
It gains GPE because it gains gravitational potential
What is escape velocity?
The minimum speed that will allow an object to escape a gravitational field with no further energy input
What is the key feature of escape velocity??
It is the same for all masses in the same gravitational field
What is the equation for escape velocity?
v = sqr( 2GM/ r)
