Kepler's Laws

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Second Law

The connecting line from the sun to the planet traces out equal areas in qual times.

Explanation: Keplers 2nd law meets thus a statement about the speed, with which a heavenly body on its ellipse moves. The more near it at the Zentralgestirn is, the faster is the slower it, the further removes.

Perhaps you already know that comets are to be seen in each case a certain, relatively short time, before you disappear again for relatively long time in the dark widths of the solar system.

Mental impetus: Explain this circumstances, how you may proceed with the comet courses from extremely eccentric ellipses!

The physical cause of the 2nd law follows from the principle for conservation of angular momentum . Think of an ice princess, who bends the arms with a Pirouette, or of a stone, which rolls the cord up at a cord around a peg rotary during itself. Both become faster thereby!

With the 2nd kg the speed is everywhere on the course well-known, comfortably calculably however unfortunately only in the two extreme places Perihel and aphelion:

A4. Speed extrema

Show that: The speed in the Perihel behaves to in the aphelion in reverse like the Perihelentfernung for aphelion distance.

A5. Seasons

The Earth's orbit ellipse is nearly circular, since their eccentricity \ varepsilon = 0,0167 is very small!

  • a) Compute aphelion and Perihelentfernung (in astronomical units AE), as well as their difference!
  • b) Around like much per cent the aphelion distance is larger than the Perihelentfernung?
  • c) In the Perihel the earth has a speed of 30,29 km/s. calculation you the aphelion speed!
  • d) The radiation intensity I of the sun decreases in reverse proportionally to the square of the distance. Assumed, it amounts to in the Perihel 100%, it is how large then in the aphelion?
  • e) Take to the assumption position that in the Perihel on earth summer is and in the aphelion winter.
  • f) Explain the occurrence of the seasons in the northern hemisphere.