Ellipses
7 Orbital Elements
1. Semimajor axis of the ellipse (a)
2. eccentricity of the orbit ellipse (e)
3. Inclination of the plane of the Orbit ellipse
relative to the ecliptic (I)
4. Longitude (in the plane of the ecliptic) where the
orbit plane crosses (the node) (Ω)
5. Periapsis Latitude relative to the ecliptic (ω)
6. Time of Periapsis
7. Orbital Period (P)
7 Orbital Elements
Gravity
• Force = (Mass) x (acceleration)
• Newton’s Law of Gravitation
F = GMm/r2
™ Proportional to Distance!!
G = Gravitational Constant
G = 6.67 x 10-11 m3/kgs2
Kepler’s Laws
• Describe motions of a
small body revolving
around a massive
body
– Planets
– Comets
Kepler’s 1st Law
• The orbit of a planet/comet about the sun
is an ellipse with the sun’s center at one
focus
•r
=
a(1-e2)
(1 + ecos(Θ))
Kepler’s 2nd Law
• The line joining the planet to the sun sweeps out
equal areas in equal times.
Kepler’s 3rd Law
P12
P22
=
a13
a23
a3/P2 is constant =
G (M+m)
4 π2
This means the period for a planet to orbit
the sun increases rapidly with the radius of
the orbit.