Circular, Elliptic or Parabolic orbit for any Planet/Heavenly body around Sun (Boundary conditions), Engineer Mir akter Hussain, Toronto
In the equations of ellipse , equation no : 1 describe path of a planate around Sun & equation no : 2 is the equation of eccentricity of ellipse where “a’ is the length of semi major axis , “b” is the length of semi minor axis & “e” is eccentricity . When “a” = “b”, then “e” =0 according to equation “2”, which means planet will move in circular orbit . When “a” >>> than “b “ then value of” b/a” ratio will reduce gradually , which will cause increase of value “e” continuously & the orbit will be more & more elliptic till the value of “e” is very near to or close to “1”. When “e” =1, the curve will be a parabola instead of circle or ellipse & if in this situation , the planet or heavenly body attains a velocity more than 617 Km /sec, which is escape velocity from the gravitation pull of Sun , then it will go permanently out of solar System .
There are three options for a heavenly body/planet moving around Sun
- It will follow circular orbit if the value of eccentricity “e” = 0 , when b/a =1 (close curve )
- It will follow elliptic orbit if the value of eccentricity 0 < e < 1 , or 0 < b/a < 1 ( close curve )
- It will follow parabolic path if “ e “ = 1 & it may go out of Solar System if it attains a velocity more than 617 km /Sec , which is escape velocity from gravitation pull of Sun . (open curve , when b/a = 0 )