Earth is moving around the Sun in elliptical orbit as show .The ratio of OB and OA is R .Then the ratio of Earth at A and B is

Question

Earth is moving around the Sun in elliptical orbit as show .The ratio of OB and OA is R .Then the ratio of Earth at A and B is (A) R-1 (B) √ R (C) R (D) R2/3

Tardigrade Admin · Accepted Answer

In central force motion, the angular momentum of body remains conserved.

i.e., Angular momentum,

L = r \times p = m v r

[at minor and major axis

v

and

r

are perpendicular]
So, if

v_{1}

and

v_{2}

be the speed of earth at

A

and

B

, respectively
Then,

m v_{1} r_{1} = m v_{2} r_{2}

\Rightarrow \frac{v _{1}}{v _{2}} = \frac{r _{2}}{r _{1}} = \frac{OB}{O A}

\Rightarrow \frac{v _{1}}{v _{2}} = R

Q. Earth is moving around the Sun in elliptical orbit as show .The ratio of $OB$ and $O A$ is $R$ .Then the ratio of Earth at $A$ and $B$ is

$R^{- 1}$

$R$

$R$

$R^{2/3}$

Q. Earth is moving around the Sun in elliptical orbit as show .The ratio of OB and OA is R .Then the ratio of Earth at A and B is

R−1

R​

R

R2/3

Q. Earth is moving around the Sun in elliptical orbit as show .The ratio of $OB$ and $O A$ is $R$ .Then the ratio of Earth at $A$ and $B$ is

$R^{- 1}$

$R$

$R$

$R^{2/3}$