Chapter 14, Problem 37A

If Pluto were somehow stopped short in its orbit, it would fall into the sun rather than around it. About how fast would it be moving when it hit the sun?

To determine

The speed of Pluto.

Answer to Problem 37A

Equal to escape velocity $620\text{km/s}$ .

Explanation of Solution

Introduction:

Escape velocity is the minimum speed needed to escape permanently from the gravitational attraction that holds it.

When an object at rest acquires the speed equals to escape velocity, it escapes from the gravitational pull. Similarly, when Pluto moving in its orbit, if stopped suddenly in its orbit then it will be attracted towards the gravitational field of Sun that binds all the planets and moons inside the system. When Pluto falls inside, it will impact the Sun with little less than the speed needed to escape from its gravitational pull i.e. little bit lesser than $620\text{km/s}$ because Pluto is at the extreme position from the Sun.

Conclusion: Thus, without any external force, Sun’s gravity will attract the object inside its gravitational field and hits surface with the same or a little bit lesser than $620km/s$ .