Expert: Jayendra Upadhye - 4/14/2004

Question
hi,
  my question about the orbits of planets of our solar system,you know very well that all the planets revolving around the sun in eliptical orbit,so i would like to ask you that why are they (planets)revolveing in eliptical orbits,i means why are not they revolving in circular orbits.tell me the reason.


ok bye

Answer
Hello Asif,
The reason is very simple.
Nature hates particularities and likes variation and generalities.
The only cases where it cannot do away with particulars are those of the "universal constants" such as
G - The universal constant for Gravitation.
Epsilon - The dielectric constant of absolute vacuum
C - The speed of light in vacuum
Mu - The constant for magnetic fields and so on
k - Boltzmann's constant relating to temperature of gases.
etc etc.
Coming back to orbits, the circle is only a particular case of the general "ellipse". It is an ellipse with eccentricity 0.
Looking at it from the "physics" side, one has to satisfy the equation :-
v*v/r = G*M/(r*r) ...equation 1
[meaning the centripetal acceleration equals that due to gravity..here M is the attracting parent mass]. clearly,
linear velocity v = sqrt{G*M/r}
It is very tough with all the randomness that predominates in the formative period of planets, for an orbit to evolve with such "exactness"!
Any inequality leads to eccentricity.
I have submitted interesting graphic orbital simulations on
http://www.qb4all.com there under "downloads" ..then under "graphics"...go to page 2 and download the orbit7.zip
as well as orbit3.zip. play around and learn the why part of orbital eccentricity.
Alternatively just give the string "orbit7 upadhye" in google to go there.
If you need any more clarification do send in another question on the same lines.
Jayen