What is Newton’s law of gravitation?
Newton’s law of gravitation states that the gravitational force between two point masses is directly proportional to the product of the masses and inversely proportional to the square of their separation.
What is the relationship between gravitational force and distance?
The relationship between gravitational force and distance is an inverse square law.
This means that when the distance between two point masses doubles, the gravitational force between them falls by 1/4
What is the significance of a test mass?
Test masses are used to define the strength of a field at a point and the direction a mass will move in the field.
This is because gravitational field strength is a vector quantity.
Which two quantities does the strength of a gravitational field at the surface of a planet depend on?
The strength of a gravitational field at the surface of a planet depends on:
the radius of the planet
the mass of the planet
Inside the planet gravitational field strength…
Inside the planet, the gravitational field strength decreases linearly from a maximum value (at the surface) to zero at the centre.
State Kepler’s first law.
Kepler’s first law states that the orbit of a planet is an ellipse, with the Sun at one of the two foci.
Define gravitational potential at a point.
The gravitational potential at a point is the work done per unit mass in bringing a small test mass from infinity to a defined point.
State Kepler’s second law.
The imaginary line joining the sun to the moving planet sweeps out equal areas in equal times. This means that for eliptical orbits the speed of the planet changes (faster nearer the sun).
State Kepler’s third law.
Kepler’s third law states that 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 orbital radius.
Gravitational potential is always…
negative
At what point in a comet’s orbit does it travel fastest?
Comets travel fastest when they are at the closest point to the Sun in their elliptical orbit.
What happens to gravitational potential as r approaches infinity?
As r approaches infinity, gravitational potential approaches zero.
Define gravitational potential energy of a system.
The gravitational potential energy of a system is the work done when bringing all the masses in a system to their positions from infinity.
Define gravitational potential difference.
Gravitational potential difference is the difference in gravitational potential between two points.
It is equal to the work done when a mass of 1 kg is moved between the points.
What does the area under a force-distance graph represent?
The area under a force-distance graph represents the change in gravitational potential energy or the work done in moving the mass from one point to another.
Define the potential gradient of a gravitational field.
Gravitational gradient is the rate of change of gravitational potential with respect to displacement in the direction of the field.
What does the gradient of a V minus r graph represent?
The gradient of a potential-distance (V-r) graph represents the gravitational field strength at that point.
What does the area under a g-r graph represent?
The area under a field-distance (g-r) graph represents the potential difference between the two points.
True or False?
The curve of a field-distance ,g-r, graph is steeper than its corresponding potential-distance, V-r, graph
True
The curve of a g-r graph is steeper than its corresponding V-r graph.
This is because g-r follows a 1/r^2 relation whereas V-r graphs follow a -1/r relation.
True or False?
Work is done when a mass moves along an equipotential surface.
False.
No work is done when a mass moves along an equipotential surface.
What are the key features of the equipotential lines in a radial gravitational field?
The key features of the equipotential lines in a radial gravitational field are:
concentric circles
become further apart with distance
What are the key features of the equipotential lines in a uniform gravitational field?
The key features of the equipotential lines in a uniform gravitational field are:
horizontal straight lines
parallel
equally spaced
Define escape speed.
Escape speed is the minimum speed that will allow an object to escape a gravitational field with no further energy input. Escape speed is the same for all masses in the gravitational field.
How does the mass of the planet affect escape speed?
The greater the mass of the planet, the greater the escape speed.
escape velocity is proportional to the square root of the mass of the planet.