18 - Gravitational Fields Flashcards
What objects create gravitational fields around them?
All objects with mass
How far does a gravitational field extend?
To infinity
Becomes infinitely small at long distances
What will happen to any object with mass that is placed inside a gravitational field?
It will experience an attractive force towards the centre of mass of the object creating the field.
Define GRAVITATIONAL FIELD STRENGTH at a point within a gravitational field.
The gravitational force exerted per unit mass on a small object placed at that point within the field.
g = F / m
F = Gravitational force m = mass of object in field
What is the symbol for gravitational field strength?
g
Is gravitational field strength a vector?
Yes
Where does gravitational field strength always point?
Towards the centre of mass of the object creating the field.
Can gravitational field lines cross?
NO
Where do the arrows on gravitational field lines always point/
Towards the centre of mass of the object.
In the direction of the field.
How is the strength of a gravitational field represented by field lines?
Their density.
What do close gravitational field lines represent?
A strong gravitational field
What do far apart gravitational field lines represent?
A weak gravitational field.
What do we model every object which is creating a gravitational field as?
A point mass
What does it mean if a gravitational field is uniform?
The field strength does not change.
How do we represent a uniform gravitational field using field lines?
Parallel and equally spaced lines.
What does Newton’s law of gravitation state (in words)?
A point mass will attract another point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers
What is Newton’s law of gravitation?
F = -(GMm) / r²
What is G?
The gravitational constant.
Why does Newton’s law of gravitation use a minus sign?
To show that the force is an attractive force.
It acts towards the object creating the field.
What is the separation, r, between?
The centre of the masses.
How do we calculate the force between multiple objects that are in the same plane?
Add and subtract the forces
How do we calculate the force between multiple objects that are in different planes?
Use pythagoras / trigonometry to find the resultant force.
What is the gravitational field strength of the Earth equal to, close to the surface of the earth?
The acceleration of free fall
9.81 ms-2 / Nkg-1
What is the relationship between the gravitational field strength at a point and the mass of the object creating the field?
Directly proportional
g ∝ M
What is the relationship between the gravitational field strength at a point and the distance between the centre of mass and the object?
Inverse square
g ∝ 1 / r²
How do we calculate the gravitational field strength at a point?
g = -GM / r²
Use definition for gravitational field strength and Newton’s law of gravitation
What is Kepler’s first law?
The orbit of a planet is an ellipse with the Sun as one of its two foci.
Why do we often model the orbit of a planet as a circle if it is actually an ellipse?
Because there is such as small difference between the length of the sides. The longer side is very similiar to the shorter side.
Low eccentricity.
What is Kepler’s second law?
A line segment joining the sun and the orbiting planet sweeps out equal areas in equal time intervals.
Do orbiting planets move at a constant speed?
NO
Where does an orbiting planet move the fastest?
When it is closest to the sun
When does an orbiting planet move the slowest?
When it is farthest from the Sun
What is Kepler’s third law?
The square of the orbital period, T, is directly proportional to the cube of its average distance, r, from the Sun.
T² ∝ r³
What provides the centripetal force required to keep a planet in orbit?
The gravitational force between it and the Sun
What can Kepler’s laws be applied to?
Any object in orbit of another in the solar system
What two equations do we use to calculate the orbital speed of a satellite?
Centripetal force = Gravitational force
Rearrange to find v
What can satellites be used for?
Global positioning
Mapping
Reconaissance
What is a geostationary satellite?
A satellite that never changes its position relative to the rotation of the Earth.
Orbits the equator with a period of 24 hours.
What three criteria must a satellite fulfill in order to be a geostationary satellite?
- Period of 24 hours
- Orbit equator
- Orbit in same direction as Earth’s rotation
Define gravitational potential at a point in a gravitational field.
The work done per unit mass to bring an object from infinity to that point.
What is the value of gravitational potential at infinity?
0
What is the unit for gravitational potential?
J kg⁻¹
What is the relationship between gravitational potential at a point in a gravitational field and the distance between the object creating the field and the point?
Inversely proportional
V ∝ 1 / r
What is the relationship between gravitational potential at a point in a gravitational field and mass of the object creating the field?
Directly proportional
V ∝ M
What will a graph of V against r show as r approaches infinity?
The graph will tend towards 0.
What will the graph of V against 1/r look like?
Straight line through 0/
What will the gradient of a graph of V against 1/r be?
-GM
How does the gravitational potential change as you approach a point mass creating a field?
It decreases.
Negative number to more negative number
(e.g. -40 to -80)
How does the gravitational potential change as you move away from a point mass creating a field?
It increases
Negative number to less negative number
(e.g. -40 to -20)
Define gravitational potential energy.
The work done to move a mass from infinity to a point in a field.
How do we calculate gravitational potential energy?
E = mV
= mass x gravitational potential
On a graph of gravitational force against distance, r, what does the area under the graph represent?
The work done to move the object that distance.
W = Fx
How does an object escape a planet’s orbit?
It must have enough kinetic energy to overcome the gravitational energy to move an object out of the field.
What is escape velocity?
The minimum velocity that any object must be travelling at to have enough kinetic energy to overcome the gravitational force and break orbit.
