gravitational fields

what is a field

A region in which a mass/charge feels a gravitational/electric/magnetic force

what is gravitational field strength

• The gravitational force per unit mass acting on a point mass

• g = F/m = GM/r²

Newtons 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

• F = GMm/r²

what is gravitational potential energy

• The work done to bring a pair of masses together from infinite separation

• Ep = -GMm/rwhat

what is gravitational potential

• The work done per unit mass in bringing an object from infinity to a given point in a gravitational field

• Vg = Ep/m = -GM/r

why is gravitational potential always negative

• Gravitational potential is defined as 0 at infinite distance

• Work is done by the field to bring it closer, so potential gets more negative

feature of a graphs of gravitational potential against radius

• Gradient of a graph of Vg against r is the gravitational field strength, g

features of a graphs of gravitational field strength against radius

• The area under a graph of g against r is change in Vg

what are equipotential lines

• Lines which have equal potential

• drawn perpendicular to the field

how to derive the equation for orbital speed

The gravitational force on an orbiting object provides the centripetal force, so we can equate the equations:

GMm/r² = mv²/r

Orbital speed = sqrt(GM/r) = sqrt(gr)

Kepler’s third law

• The square of a planets orbital period, T, is proportional to the cube of its average orbital radius, R

• T² = constant * R³

what is escape velocity

• The minimum speed that will allow an object to escape a gravitational field with no further energy input

• Vesc = sqrt(2GM/r)

• this comes from equating equation for KE with equation for gravitational potential energy