Section 7.2: Gravitational Fields Flashcards
State Newton’s law of gravitation
The magnitude of the gravitational force between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centres.
Define gravitational field strength
The force per unit mass exerted by a gravitational field on an object, symbol g.
Compare gravitational field strength in a uniform field and a radial field
In a uniform field, gravitational field strength is constant, while in a radial field it varies.
Define gravitational potential at a point
The work done per unit mass to move an object from infinity to that point, symbol V.
Why is gravitational potential always negative?
Because it is zero at infinity and gravity is always attractive, so moving and object from infinity releases energy, meaning the potential will be less than zero.
Define gravitational potential difference
The energy needed to move a unit mass between two points.
This means you can find the work done when moving an object in a gravitational field by multiplying the gravitational potential difference by the mass of the object.
How do you find gravitational field strength at a given point graphically?
Draw a tangent to a potential-distance graph at the given distance, calculate its gradient, then multiply it by -1
How do you find gravitational potential difference between two points graphically?
Find the area underneath the graph of gravitational field strength over distance (between those two distances).
What is Kepler’s third law?
The square of the orbital period is directly proportional to the cube of the radius.
How do you derive Kepler’s third law?
Set centripetal force equal to gravitational force and rearrange to make v^2 the subject.
Velocity is the rate of change of displacement, so v = 2π r / T.
Substitute this value for v into the previous equation, then rearrange to make T^2 the subject, and the other side will have r^3 x a constant.
What is the total energy of an orbiting satellite?
A constant, made up of the sum of the satellite’s kinetic and potential energy.
How and why does the height of an orbiting satellite affect its speed?
Decreasing the height of a satellite decreases the gravitational potential energy, and since the total energy must be constant, the kinetic energy will need to increase, thereby increasing the satellite’s speed. The opposite is true for an increase in height.
What is escape velocity?
The minimum velocity an object must travel at in order to escape the gravitational field, from the surface of a mass.
It is the velocity at which an object’s kinetic energy is equal to the magnitude of its gravitational potential energy.
Define synchronous orbit
Where the orbit of a satellite is equal to the rotational period of the object that it is orbiting.
What is a geostationary satellite?
A satellite with an orbital period of 24 hours that is situated directly above the equator, meaning it stays at the same point above Earth at all times.
