ASTR Spring 2008 Joel E. Tohline, Alumni Professor 247 Nicholson Hall [Slides from Lecture14]

Scientific utility of the Copernican Heliocentric Model Can deduce the true “sidereal” (as opposed to readily measured “synodic”) orbital periods of each of the planets [see textbook BOX 4-1 and Table 4-1] Can deduce the distance that each planet is from the Sun, relative to the Earth’s distance from the Sun (1 AU); [see textbook discussion associated with Table 4-2]

Scientific utility of the Copernican Heliocentric Model Can deduce the true “sidereal” (as opposed to readily measured “synodic”) orbital periods of each of the planets [see textbook BOX 4-1 and Table 4-1] Can deduce the distance that each planet is from the Sun, relative to the Earth’s distance from the Sun (1 AU); [see textbook discussion associated with Table 4-2]

Determining the size of the orbit of Mars Suppose that at sunrise, Mars is on the western horizon; does Mars lie in Direction #1 or direction #2? Suppose that at sunrise, Mars is seen directly overhead; does Mars lie in Direction #1 or direction #2?

Determining the size of the orbit of Mars At sunrise, if Mars is on the western horizon, Mars must lie in Direction #1. At sunrise, if Mars is seen directly overhead, Mars must lie in Direction #2.

Determining the size of the orbit of Mars But until we know the size of the orbit of Mars, we don’t know precisely where it resides along either line of sight. Consider the three possible orbits shown on the next few slides …

Determining the size of the orbit of Mars But until we know the size of the orbit of Mars, we don’t know precisely where it resides along either line of sight. Consider the three possible orbits shown on the next few slides …

Determining the size of the orbit of Mars

So, by measuring the amount of time it takes Mars to travel from point “A” to point “B” each orbit, Copernicus was able to determine the size of the orbit of Mars (and of Jupiter, Saturn, Mercury, and Venus).

Determining the size of the orbit of Mars So, by measuring the amount of time it takes Mars to travel from point “A” to point “B” each orbit, Copernicus was able to determine the size of the orbit of Mars (and of Jupiter, Saturn, Mercury, and Venus).

Scientific utility of the Copernican Heliocentric Model Can deduce the true “sidereal” (as opposed to readily measured “synodic”) orbital periods of each of the planets [see textbook BOX 4-1 and Table 4-1] Can deduce the distance that each planet is from the Sun, relative to the Earth’s distance from the Sun (1 AU); [see textbook discussion associated with Table 4-2]

Summary Results (deduced by Copernicus) PlanetP (years) D (AU) P2P2 D3D3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune ,200.

Summary Results (all 8 planets) PlanetP (years) D (AU) P2P2 D3D3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune ,200.

Notice … There is a strong correlation between a planet’s orbital period and its distance from the Sun … Planets that are farther and farther from the Sun exhibit longer and longer orbital periods

Summary Results (all 8 planets) PlanetP (years) D (AU) P2P2 D3D3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune ,200.

Additional Realization … (first noticed by Kepler) PlanetP (years) D (AU) P2P2 D3D3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune ,200.

Additional Realization … (first noticed by Kepler) PlanetP (years) D (AU) P2P2 D3D3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune ,200. P 2 = D 3 !!

P 2 = D 3 (works for all 8 planets) PlanetP (years) D (AU) P2P2 D3D3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune ,200.

Kepler’s Observed Laws of Planetary Motion …