Extrasolar planets and Kepler’s Third Law

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Presentation transcript:

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

Nose lost in 1566 following a sword duel with third cousin Manderup Parsberg over the legitimacy of a mathematical formula! Nicolaus Copernicus 1473-1543 Tycho Brahe 1546-1601 Johannes Kepler 1571-1630 Isaac Newton 1642-1727

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 1571-1630

Radii of planets not to scale! Neptune Kepler’s Third Law Johannes Kepler 1571-1630 Orbital period P /years Uranus Mercury, Venus, Earth, Mars Saturn Jupiter Semi-major axis of orbit a / AU

Planet and Solar masses Isaac Newton (1642-1727) 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

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

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

Earth-like candidates?

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