physics - gravitational fields (D.2)

gravitational field definition

a region of space in which an object experiences a force due to its mass

field lines

show the direction a particle will travel if placed into a gravitational field; always point towards the mass responsible for them

gravitational potential definition

work done per unit mass in moving a small test mass from a point of zero potential (infinity) to a point in the field

kinetic energy formula

(GMm)/(2r)

total energy formula

(-GMm)/(2r)

kepler’s first law

planetary orbits are elliptical with a star at the focus

kepler’s second law

the line connecting the orbiting object to the star sweeps out equal areas in equal times

kepler’s third law

the square of the periodic orbital time of an orbiting object is directly proportional to the cube of the semimajor axis (radius) of its orbit

gravitational potential difference definition

the work done in moving a mass between two points in a gravitational field

polar orbit

satellites orbit over the earth’s poles in one plane, intersecting the earth’s center, with earth rotating underneath

geosynchronous orbit

satellites stay in the same area of sky and typically follow a figure-of-eight orbit (orbit at a greater distance from earth than polar orbits)

geostationary orbit

satellites orbit above the plane of the equator and will not appear to move when viewed from the surface

a loss in the orbital energy -ΔE leads to a decrease in the orbital radius Δr that has two contributions:

• a loss of gravitational potential energy -2ΔE

• a gain in kinetic energy +ΔE