Define weight:
The force due to gravity acting on a mass
Define gravitational field:
A region of space where a mass experiences a force
In what direction does a gravitational field act?
It is always directed towards the centre of the mass; it is always attractive
What do gravitational field lines represent?
They show the direction and magnitude of a gravitational field
What are the two types of gravitational fields?
Uniform and non-uniform
What are radial gravitational fields?
- The field strength decreases with distance from the centre of the object
- The field lines around a point mass are directed radially inwards
What are uniform gravitational fields?
- The field strength is the same throughout the field
- Hence, it is represented by equally spaced parallel lines
What type of gravitational field is near the Earth’s surface?
The Earth’s gravitational field near the surface is almost uniform
What is a point mass?
An object with an even mass distribution and the distance being considered is larger than its size
What is Newton’s law of gravitation?
The gravitational force between two bodies outside a uniform field is defined by Newton’s law of gravitation: The gravitational force between two point masses is proportional to the product of the masses and inversely proportional to the square of their separation
Inverse square law: F is inversely proportional to 1/r^2 - as r increases, F decreases and the rate of decrease follows a square relationship with distance
What is the equation for Newton’s law of gravitation?
F = Gm1m2 / r^2
What is the value of G?
G or Newton’s gravitational constant is equal to 6.67x10^-11 Nm^2kg^-2
What is a geostationary satellite?
- It remains directly above the equator, always orbiting the same point above the Earth
- Moves from West to East, the same direction as the Earth spins
- Has a orbital period of 24 hours, equal to the Earth’s rotational period
What are geostationary satellites used for?
Telecommunication transmissions (radios) and television broadcasts
How do you calculate gravitational field strength at a point?
The gravitational field strength at a point describes how strong or weak a gravitational field is at that point: g = F / m
How do you calculate the gravitational field strength due to a point mass within a gravitational field?
g = GM / r^2
M = mass of the body producing the gravitational field
r = distance between the point source and position in field
Define gravitational potential (φ):
The work done per unit mass in bringing a small test mass from infinity to the point
Why does gravitational potential always have a negative value?
- It is defined as having a value of zero at infinity
- Since the gravitational force is attractive, work must be done on a mass to reach infinity
How do you calculate gravitational potential?
φ = - GM / r
r = distance from the centre of the mass to the point mass
How do calculate change in gravitational potential?
Δφ = (- GM / r2) - (-GM / r1), for Δφ, the negative design does not need to be included as you are finding a difference in values
Define gravitational potential energy between two point masses:
For a radial field, it is the work done to assemble the system from the infinite separation of the components of the system
How do you calculate the gravitational potential energy between two point masses?
EP = - Gm1m2 / r
r = the distance between the centres of m1 and m2
How do you calculate change in gravitational potential energy between two point masses?
ΔEP = mΔV = Gm1m2 * (1 / r2 - 1 / r1)
What is the difference between EP and GPE?
GPE is only relevant for an object lifted in a uniform gravitational field while EP is used for radial fields with different values of g for different planets
