It is a simple relation

Classical Mechanics Level 2

Suppose a planet of Mass M M is moving around a star in elliptical orbit. Let its closest distance from star be R 1 R_1 and linear velocity at that point be V 1 V_1 & its furthest distance from star be R 2 R_2 and linear velocity at that point be V 2 V_2 . What is the ratio of velocities V 1 / V 2 V_1/V_2 in terms of radius R 1 R_1 and R 2 R_2 ?

(R1/R2)^2 (R2/R1)^2 R2/R1 R1/R2

Rushi Panmand by rushi panmand , 23, India

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2 solutions

Rushi Panmand
Jan 12, 2016

We know that whenever a particle rotates, its angular momentun is conserved. So using relation of angular momentum i.e., M V1 R1=M V2 R2 we get that V1/V2=R2/R1

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Manas Wadhwa
Jan 24, 2016

we know that V1 will be inversely proportional to R1 and V2 will be inversely proportional to R2 thus V1/V2=R2/R1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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