# Question #c668f

##### 1 Answer

Final calculations are left for the reader.

#### Explanation:

In the instant case I could not find applicability of [Kepler's In the instant case I could not find applicability of Kepler's Laws of motion. As such expressions applicable to satellites have been used and Law of Conservation of energy is used.

Let a body of mass

Gravitational PE of this body

where

Total initial energy

Let the body be at a distance

Total energy

Using law of conservation of energy we get

Rearranging we get

where

If the body takes time

Using (3) we get

Time taken to reach the sun's surface is time integral of LHS from

Which is

and total distance traveled by the body is distance integral of RHS from

we have

Using online integral calculator we get

-.-.-.-.-.-.-.-.-.-.-.

Choose the appropriate root as time can't be negative.

Insert value of

Velocity as the body reaches surface of the sun, i.e., at

Inserting values we get

Even though we know that velocity increases steeply, lets find rough average velocity

Hence time taken

Actual time would be much less.

Most of the bodies would have evaporated much earlier due to temperature at sun's surface estimated as 5,778 K.

Compare this temperature with highest bp - Tungsten 5,555 °C

and bp - Uranium 4,131 °C