Chapter 8.2, Problem 57E

Solution

A conclusion about for orbits of the sungrazers.

It has been determined that the required conclusion is

Given:

The diameter of the Sun is Gm.

One comet group, known as the sungrazers, passes within a Sun’s diameter.

Concept used:

The perihelion distance from the Sun is

Calculation:

As discussed, the perihelion distance is given by

This is the closest distance between the object and the Sun.

Now, it is given that the diameter of the Sun is Gm.

It is also given that the comet group, known as the sungrazers, passes within a Sun’s diameter.

Then, the closest distance between the sungrazers and the Sun is less than the Sun’s diameter.

Equivalently, the closest distance between the sungrazers and the Sun is less than Gm.

That is, the perihelion distance for the sungrazers from the Sun is less than Gm.

This implies that

This is the required conclusion.

Conclusion:

It has been determined that the required conclusion is