Gravitational Fields Flashcards
What is the magnitude and direction of the gravitational force between two point masses?
F = - GMm/r2
How is gravitational field strength defined and what is its magnitude in a radial field caused by a point mass M?
- g is the force per unit mass: g = F/m
- g = GM/r2
What type of quantity are gravitational attraction and field strength?
Vectors
What is gravitational potential?
The gravitational potential at a point is the gravitational potential energy that a unit mass at that point would have (potential energy per unit mass).
It is given by:
V = -GM/r
How does gravitational potential vary as r increases?
V becomes less negative as r increases, and is zero at infinity.
How are fields strength and gravitational potential related?
g = -(delta) V/ (delta) r
What is the formula for gravitational potential energy?
GPE = GMm/r
(Gravitational potential multiplied by mass)
How can you calulate escape velocity?
If the kinetic energy of a particle is equal in magnitude to its gravitational potential energy at the launch point, it can escape the atmosphere:
KE = (1/2)mv2 = GMm/r = GPE
⇒ v = sqrt(2GM/r)
where r is the radius of the earth (+ height of launch point(
What is gravitational potential difference?
The difference in gravitational potential between two points, _delta V
Work done to move an object of mass m between two points with a potential difference _delta V is given by:
_delta W = m * _delta V
but g = - _delta V / _delta r
therefore:
_delta W = m * g * _delta r (or _delta h)
Derive Kepler’s Third Law
Describe how the energy of a satellite in circular orbit changes.
As the satellites speed and altitude are constant, its kinetic and pravitational potential energy are both constant.
Describe how the orbit of a satellite in elliptical orbit changes.
In elliptical orbit, the satellites altitude changes. As its height decreases, its gravitational potential energy becomes more negative, so its kinetic energy and therefore speed must increase to conserve energy.
What is a synchronous orbit?
Orbital period = rotational period of orbited object
How is the plane of orbit of geosynchronous satellites defined?
By the equator
What is the orbital radius of geosynchronous satellites and what are they used for?
42,000 km (36,000 km altitude)
Used to send telephone and TV signals as the satellite is stationary relative to any point on Earth, so the angle of the reciever doesn’t have to be altered.
