Question

A planet is revolving round the sun in elliptical orbit. Velocity at perigee position (nearest) is v₁ and at apogee position (farthest) is v₂ Both these velocities are perpendicular to the joining center of sun and planet r is the minimum distance and r₂ the maximum distance. 

(1) when the planet is at perigee position, it wants to revolve in a circular orbit by itself. For this value of G 

(A) Should increase 

(B) Should decrease 

(C) data is insufficient 

(D) will not depend on the value of G 

(2) At apogee position suppose speed of planer is slightly decreased from v₂, then what will happen to minimum distance r₁ in the subsequent motion 

(A) r₁ and r₂ both will decreases 

(B) r₁ and r₂ both will increases 

(C) r₂ will remain as it is while r₁ will increase 

(D) r₂ will remain as it is while r₁ will decrease

Answer 1

Correct option: 1 (A) Should increase, 

2 (D) r₂ will remain as it is while r₁ will decrease

Explanation:

1. At perigee position, V₁ > V₀ where V₀ is the orbital velocity for circular motion.

V₀ = √(GM / R)

V₀ ∝ √G

So value of G should increase for thus position and which will become equal to V₁.

2. Path will become more elliptical, keeping r₂ constant and r₁ to decreases.