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Kepler’s Laws: Orbits are ellipses Planetary Velocity Varies P 2 = A 3

Kepler’s Laws: Orbits are ellipses Planetary Velocity Varies P 2 = A 3. The Orbit of Mars. Observational Consequences of Elliptical Orbit in terms of apparent brightness and apparent size of mars. Used Tycho’s Positional Data for Mars. Important Notes. This is Good Data – 10 orbital periods

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Kepler’s Laws: Orbits are ellipses Planetary Velocity Varies P 2 = A 3

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  1. Kepler’s Laws:Orbits are ellipsesPlanetary Velocity VariesP2 = A3

  2. The Orbit of Mars

  3. Observational Consequences of Elliptical Orbit in terms of apparent brightness and apparent size of mars

  4. Used Tycho’s Positional Data for Mars

  5. Important Notes • This is Good Data – 10 orbital periods • The Y-axis (basically the position of Mars) has a large amplitude • In real life, the “eccentricity” of Mars orbit is 9% - after 10 orbital periods the difference between a perfect circle and an ellipse is pretty clear

  6. The recognition of Error • Kepler writes: And from this such small difference of eight minutes [of arc] it is clear why Ptolemy , since he was working with bisection [of the linear eccentricity], accepted a fixed equant point. ... For Ptolemy set out that he actually did not get below ten minutes [of arc], that is a sixth of a degree, in making observations. To us, on whom Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy's in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it. So let us work upon it so as to at last track down the real form of celestial motions (these arguments giving support to our belief that the assumptions are incorrect). This is the path I shall, in my own way, strike out in what follows. For if I thought the eight minutes in [ecliptic] longitude were unimportant, I could make a sufficient correction (by bisecting the [linear] eccentricity) to the hypothesis found in Chapter 16. Now, because they could not be disregarded, these eight minutes alone will lead us along a path to the reform of the whole of Astronomy, and they are the matter for a great part of this work. • Kepler's Self Written Epitaph: • Mensus eram coelos, nunc Terrae metior umbras. Mens coelestis erat, corporis umbra jacet.

  7. Kepler Discovers the Physics but Doesn’t realize this

  8. Period2 a A(distance)3The Harmonic Universe This sets the Relative Scale of the Solar System (e.g. Jupiter is 5 times further from the Sun than Earth)

  9. Kepler’s Laws are a purely empirical and precise description of the orbits of the planets But, he has no dynamical basis for understanding why these laws exist.

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