Question

According to Kepler's second law, the line joining the planet to the sun sweeps out equal to the areas in equal time intervals. This suggests that for the planet:
A) Radial acceleration is zero.
B) Tangential acceleration is zero.
C) Transverse acceleration is zero.
D) All.

Answer 1

Hint: Kepler's law states that the line that joins from the sun and planet sweeps an area at an interval of time and that area that the planet sweeps is equal for an equal interval of time in different positions at the elliptical orbit around the sun.

Complete step by step answer:
It is given in the problem that the line joining the planet to the sun sweeps out equal areas in equal time intervals which is Kepler’s second law and we need to tell about the acceleration of the planet earth.
According to Kepler’s law,
$\dfrac{{dA}}{{dt}} = \dfrac{L}{{2m}}$
Here the area swept by the earth is constant with respect to the time.
Where angular momentum is $L$ mass is $m$ area is $A$.
Here the angular momentum is constant as the radius changes so it leads to a change in the velocity therefore the tangential accelerations come into play but the transverse acceleration will be zero as the motion is planar.

So the transverse acceleration of the planet earth while orbiting earth is zero. The correct is option C.

Note:
The orbit at which the planet earth moves is elliptical and as the elliptical orbit has sun at one of its centre and nothing at its second centre so the planet earth is sometimes very close to the sun and at other times it is very far from the sun. The planet earth has very high speed when earth is close to the sun and its speed is very slow when it is far away from the sun.