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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
Note
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