1. Extrasolar planets and Kepler’s Third Law
AF. May 2015

2. Nose lost in 1566 following a sword duel with third cousin Manderup Parsberg over the legitimacy of a mathematical formula!
Nicolaus Copernicus
Tycho Brahe
Johannes Kepler
Isaac Newton

3. Johannes Kepler 1571-1630 Polar equation of ellipse This is a constant
Equal areas swept out in equal times
Eccentricity of ellipse
Orbital period P
Johannes Kepler

4. Radii of planets not to scale!
Neptune
Kepler’s Third Law
Johannes Kepler
Orbital period P /years
Uranus
Mercury, Venus, Earth, Mars
Saturn
Jupiter
Semi-major axis of orbit a / AU

5. Planet and Solar masses
Isaac Newton
( ) developed
a mathematical model of Gravity which predicted the elliptical orbits proposed by Kepler
Planet and Solar masses
Force of gravity
Semi-major
axis
Polar equation of ellipse
Semi-minor axis
Eccentricity of ellipse
Orbital period P

6. Kepler’s Third Law
semi-major axis of elliptical orbit

8. Vertical intercept is very
close to ln(365) = 5.90
Gradient is 1.49, not far
off the Kepler #3
prediction of 3/2

12. Earth-like candidates?