A probe to the sun

For the purpose of collescting data related to the space near the sun ,a probe is to be prepared that would be sending solar data back to the earth as it rushes towards it's demise.The design plan for our probe is that we will release it from our spacecraft in such a way that it has zero velocity relative to the sun.the probe has a mass $200$ kg and no rocket engine ,so it simply falls into the sun from rest due to the gravitational force from the sun.All other gravitational forces on the probe from other planets are neglected (for simplyfication) We will model the probe as a system consisting of a single particle.The gravitational force from the sun acts as the interaction with the environment ,doing work on thr probe .The result of this work is the increasing kinetic energy of the probe as it falls towards the sun .Thus situation is suitable for application of work energy theorem.

The initial separation of the probe and the sun is the radius of earth's orbit , $1.50\times 10^{11}$ m .The final separation is the radius of the sun $7\times 10^8$.The amount of work done by the gravitational force of the sun on the probe can be found using

$\displaystyle\int_{r_i}^{r_f}$$F_r$ $dr$

As the force is in radial direction , further

$W=\displaystyle\int_{r_i}^{r_f}$$F_r$$dr$$= -\displaystyle\int_{r_i}^{r_f}$$\dfrac{G\times{M_{sun}}\times{m_{probe}}}{r^2}=$$G\times{M_{sun}}$$\times{m_{probe}}\dfrac{r_i-r_f}{r_f\times{r_i}}$

Where G is univerasl gravitational constant = $6.7\times{10^{-11}}$N$m^2$/$kg^2$

mass of sun = $2.8\times {10^30}$,using $W=\triangle {K}$ , final speed can be calculated.

This is part of the set A probe to Sun