A planet of mass m is in an elliptical orbit about the sun (m

Question

A planet of mass m is in an elliptical orbit about the sun (m < < M textsun) with an orbital period T . If A be the area of orbit, then its angular momentum would be (A) (2 m A/T) (B) mAT (C) (m A/2 T) (D) 2mAT

Tardigrade Admin · Accepted Answer

using Kepler's IInd law ; areal velocity = constant = (L/2 m) &rArr; (d A/d t) = (L/2 m) &rArr; L=2m(d A/d t) L=(2 m A/T)

Q. A planet of mass $m$ is in an elliptical orbit about the sun $(m << M_{sun})$ with an orbital period $T$ . If $A$ be the area of orbit, then its angular momentum would be

$\frac{2 m A}{T}$

$m A T$

$\frac{m A}{2 T}$

$2 m A T$

using Kepler's II^ndlaw ; areal velocity = constant = $\frac{L}{2 m}$
⇒ $\frac{d A}{d t}$ = $\frac{L}{2 m}$
⇒ $L = 2 m \frac{d A}{d t}$
$L = \frac{2 m A}{T}$

Q. A planet of mass m is in an elliptical orbit about the sun (m<<Msun​) with an orbital period T . If A be the area of orbit, then its angular momentum would be

T2mA​

mAT

2TmA​

2mAT