Download Orbital Geometry Notes

Orbital
Geometry
Johann Kepler
• In 1600, Johann Kepler
developed his “Laws of
Planetary Motion.” He
observed that the planets
traveled in closed curves
(ellipses), rather than
circular paths.
Ellipses
• The center of an ellipse differs from a
circle in that there are two fixed
points (foci) rather than one.
• Kepler's first law: the orbits of the
planets around the sun are ellipses,
with the Sun at one of the foci.
• The eccentricity of an ellipse can be
thought of as the degree of nonroundness, or ovalness, of the orbit.
Eccentricity = distance between
foci/length of major axis
• e = d/L
• The smaller the
eccentricity, the
more circular the
orbit.
The Solar System
• Looking at the Solar System Data table, most
of the planets have fairly circular orbits (low
eccentricities) with the exception of Mercury.
The Earth’s Orbit
• The earth actually receives 7% less radiation in the
summer of the northern hemisphere than the winter!
Why is it warmer here in the summer?
Other Solar Systems
Comet Eccentricities
Kepler’s Second Law
• An imaginary line joining a
planet to the Sun will
sweep over equal areas in
equal periods of time.
• The consequence of this:
planets travel faster when
they are closest to the sun,
and slower when they are
farther away.
• Closest point: perihelion (Jan 3) Farthest
point: aphelion (July 4)
• At the perihelion, kinetic energy is at a
maximum, potential energy a minimum. At
the aphelion, the opposite is true.
Kepler's Third Law
• The square of any planets period of
revolution (orbital period) T2 is
proportional to the cube of the
mean radius (R3)
• In other words, farther the planet is
from the sun, the larger the orbit
and the longer its period.
• The mean radius is expressed in
astronomical units (AU)
• 1 AU equals 150,000,000 km, or 1
earth-sun radius
• This is a function of Newton’s Law
of gravitation.
Find the eccentricity of each of the
following ellipses:
Lab 4 Ellipses