GATE-2018 (24) :Wyllie – Time average equation

Orbital eccentricity:-

The orbital eccentricity of an astronomical object is a parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptical orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola.

The eccentricity may take the following values:

circular orbit: e=0

elliptic orbit: 0<e<1

parabolic trajectory: e=1

hyperbolic trajectory: e>1

 

Eccentricity of a Planet’s orbit

Derive : Eccentricity = c/a

The aphelion is the point in the orbit of an object where it is farthest from the Sun. The point in orbit where an object is nearest to the sun is called the perihelion.

Perihelion R_P =147,098,000km

Aphelion R_A =152,098,000km

Eccentricity (e) = (R_A-R_P) / (R_A+R_P)

= ( 152,098,000- 147,098,000) / ( 152,098,000+ 147,098,000)

= 0.0167

R_P+R_A = 2*a

R_P = a- c

R_A = a+ c

e = (R_A-R_P) / (R_A+R_P)

   = {(a+c)- (a-c) / (a+c) +(a-c) }

   = 2c/ 2a

   = c/a

 

Reference

1.http://www.askiitians.com/iit-jee-mathematics/coordinate-geometry/conic-sections/

2. https://www.youtube.com/watch?v=X1XrtqubGPE