Keplars laws of planetary motion

Recent Developments

Keplars laws of planetary motion
Location: Surat
Description of the Exhibit/ working Principle
Historical Background: Around 1600, Kepler was assigned as assistant in Tycho Brahe’s observatory to reconcile Tycho’s extraordinary accurate astronomical observations with Tychonic theory. However, Kepler applied Copernican theory and his own intuitions and after six years of calculation and recalculations, he enunciated that planets move in elliptical orbit.  Kepler reached these conclusions entirely on the basis of astronomical observations and geometrical modelling without providing a convincing physical explanation for why the planets move as they do Around 1619 he issued his Harmonic mundi or Harmonies of the world which contained Kepler’s three famous laws as follows: 
  • The planets orbit in ellipses with the Sun at one of the foci.
  • Planets sweep out equal areas in equal interval of time.
  • The square of the time of period of a planet equals the cube of the mean distance from the Sun or t^2 ∞ r^3
Working principle: Among these three laws the second law has an observable consequence. As the law states planets sweep out equal areas in equal interval of time, mathematical calculation shows that if the planet has minimum velocity in apehelion (furthest point from the selected focus of the ellipse) and maximum velocity in perihelion (nearest point from the selected focus of the ellipse) only then it will sweep out equal area in equal time. 

Mode of Display
Cometarium: This machine demonstrates the observable consequence of Kepler’s second law.  The device was originally constructed in 1732 to show the changes of velocity of a planet or a comet from perihelion to aphelion during its course of motion around the sun. It was indeed a machine ahead of its time.

Kepler’s laws are completely a manifestation of universal theory of gravity. From the engineering perspective, it was very hard to illustrate the second law (Change in angular velocity) mechanically before this device was discovered. Following the original drawing, it has been designed by using one pair of elliptical gear, of which the rotating axis lies on one of the focus, which is essential to obtain the peripheral velocity of the planet rotating on an elliptical path.