Question

According to Kepler's Second Law the radius vector drawn from the Sun to a planet Multiple Choice is the same for all planets. sweeps out equal areas in equal times. sweeps out a larger area for a given time when the planet is moving faster. sweeps out a larger area for a given time when the distance to the Sun is greater.

Answer 1

Answer:

sweeps out equal areas in equal times.

Explanation:

As we know that there is no torque due to Sun on the planets revolving about the sun

so we will have

$\tau_{net} = 0$

now we have

$\frac{dL}{dt}= 0$

now we also know that

$Area = \frac{1}{2}r^2d\theta$

so rate of change in area is given as

$\frac{dA}{dt} = \frac{1}{2}r^2\frac{d\theta}{dt}$

so we will have

$\frac{dA}{dt} = \frac{1}{2}r^2\omega$

$\frac{dA}{dt} = \frac{L}{2m}$

since angular momentum and mass is constant here so

all planets sweeps out equal areas in equal times.