For the purpose of collecting 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 toward its 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 simplification purpose. We will modal 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 the 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 the work-energy theorem.

The initial separation of the probe and the Sun is the radius of the Earth’s orbit, 1.50 × 10 11 m. The final separation is the radius of the sun 7 × 10 8 m. The amount of work done by the gravitational force of the sun on the probe can be found using

W =

As the force is in radial direction, equation is applied in radial direction.

Further

W = = –

= GM sun m probe dr

where G is universal gravitational constant

= 6.7 × 10 –11 Nm 2 /kg 2 , mass of the Sun

= 2 × 10 30 kg. Using work energy theorem

W = Δ K, final speed of the probe can be calculated.

(i) Using the data provided in the passage total work of the gravitational force of the Sun on the probe is nearly equal to–