Question

Why does a planet follow an elliptical orbit and not circular??

I know keplers laws and i know the laws of gravitation.. but I wanna know if there is some reason why the planets follow an ellipse and not a perfect circle

Answer 1

I think when you do the derivation using mathematics for a central force which varies 1 over r square... the result turns out to be an ellipse.. is there any intuitive way to come to this conclusion qualitatively?

Answer 2

note: physics isn't intuitive. example: try to use intuition to understand special relativity.
if you want the derivation for the ellipse form, you might want to try Exercise 11.9.32 from "Calculus" by James Stewart. nothing about forces though.

Answer 3

physics isn't intuitive? :P.. what is wrong with you!!.. special relativity is not intuitive TO US cause.. we are not travelling at sub luminal speeds... it was intuitive to EINSTIEN.. if it wasn't.. we wouldn't have the theory in the first place.... Infact.. all the theories are intially laid down by making use of intuitions!!.. sometimes mathematics helps to derive stuff which are totally non intuitive... but at certain level intuition can always be made!!.. PHYSICS IS INTUITIVE mate!

Answer 4

lol i'm meaning intuitive as in straightforward.

Answer 5

the above question "is there any intuitive way to come to this conclusion qualitatively", if you count mathematics as intuition (like 1+1=2, duh, thing),then yes...

Answer 6

lol obviously need not be straightforward.. but we can always generate some sort of intuition.. but i agree.. in this case. its not all that straight forward :P

Answer 7

but i think.. its better to understand why the planets DO NOT REVOLVE in a circular orbit.. and thats because.. the initial speed does not satisfy the condition!

Answer 8

if you want, i could give you some equations where you do a step-by-step derivation and develop your own intuition?
technically....the initial speed doesn't really matter? lol how did you arrive to that conclusion?

Answer 9

the initial speed matters.. if mv^2/r is not equal to the force of gravity.. then the object will not give a perfect circle..!!!

Answer 10

"Uniform circular motion
Every central force can produce uniform circular motion, provided that the initial radius r and speed v satisfy the equation for the centripetal force

If this equation is satisfied at the initial moments, it will be satisfied at all later times; the particle will continue to move in a circle of radius r at speed v forever."

form wiki :P

http://en.wikipedia.org/wiki/Classical_central-force_problem

Answer 11

but it's always equal to \(F_G\). if initial speed just affect the altitude of orbit.

Answer 12

NOOOOO!!!.. initial speed decides whether it ll be a circular orbit or not!

Answer 13

otherwise the velocity will not be perpendicular to the force!!.. it ll have some tangential component

Answer 14

i mean.. NON TANGENTIAL component :P

Answer 15

ah. I saw it. though that might be why most planets are just almost circles.

Answer 16

*orbits

Answer 17

almost circles cause their eccentricities are too small!

Answer 18

so the deviation from the required speed must be have been very small!!

Answer 19

hmm,...which brings us to the problem....why? lol

Answer 20

and how?!

Answer 21

why they are not doing CIRCULAR ORBITTING :P..

Answer 22

wait.. what why??? that depends upon the initial conditions.. when the planet was formed... why should the exact speed be matched!!?

Answer 23

so basically those planets are just...lucky that they managed to do so? lol :P

Answer 24

i dunno. .. you tell me :P..

Answer 25

lol let's leave that to the NASA boys

Answer 26

http://www.physicsforums.com/showthread.php?t=297095

this says.. drag forces must have reduced the velocity somehow.. !!

Answer 27

i can't i am a teacher.. i need answers :P