Question

A small body starts falling onto the Sun from a distance equal to the radius of the Earth orbit. The initial velocity of the body is equal to zero in the heliocentric reference frame. Making use of Kepler s laws, find how long the body will be falling.

Answer 1

Solution

Here according to question semi major axis a=R/2

Hence $\tau$ is the time of fall then

$(\frac{2\tau}{T}) ^2=(\frac{R/2}{R}) ^3$

By using kepler third law. 

So it's become

$\tau^2=\frac{T}{32}$

$\tau=\frac{365}{4\sqrt{2}}=64.5$ days