Gravitational Fields

What do close together gravitational field lines mean?

Stronger force

How do field lines appear in a uniform field?

Parallel

Define gravitational field strength

Gravitational force experienced per unit mass by an object in the field

State the formula for gravitational field strength

g = F/m

What is Newton’s Law of Gravitation?

Two point masses attract each other with a force directly proportional to the product of their masses, and inversely proportional to their distance squared

Define the formula for gravitational force

F = -GMm/r²

State the formula for gravitational field strength of a point mass

g = GM/r²

What is Kepler’s first law?

the orbit of a planet is an ellipse, with the sun at one focus

What is Kepler’s second law?

a line segment joining a planet and the sun sweeps out equal area during intervals of equal time

What is Kepler’s third law?

the square of the orbital period is proportional to the cube of the distance r from the sun

How to derive Kepler’s third law

F = mω²r = GMm/r²

(2π/T)²r = GM/r²

4π²r³/T²=GM

4π²r³/GM = T²

What is a satellite?

an object which orbits other larger objects

What is a geostationary satellite?

a satellite which has an orbital period of one day, orbiting along the equator (above the same point on the earth’s surface)

Define gravitational potential

work done per unit mass to move an object from that point to infinity (at infinity V_g = 0, its max)

What is the formula for gravitational potential?

V_g = -GM/r

Define gravitational potential energy

work done to move an object of mass m from infinity to that point in the field

State the formula for gravitational potential

(E = mV_g)

E = -GMm/r

What is escape velocity

the speed needed to escape a gravitational field (kinetic energy must be equal or greateer to gravitational potential energy)

Derive the equation for escape velocity

1/2mv² = GMm/r

v = sqrt(2GM/r)

What is the area under a force distance graph for a point/spherical mass?

work done