Chapter 33, Problem 11P

To determine

The average density of the Sun if it expands to the orbit of the Earth.

Answer to Problem 11P

The average density of the Sun when it expands to the orbit of the Earth, is $1.4\times {10}^{-4}{\text{kg/m}}^3$

Explanation of Solution

Given:

The radius of Earth’s orbit from the Sun is $R=1.5\times {10}^{11}m$ .

Consider the mass of the Sun is $M=2\times {10}^{30}\text{kg}$ .

Formula used:

Assume the planet is spherical in shape.

The expression for the volume ( V ) of the Planet (spherical shape) is,

  $V=\frac{4}{3}\pi R^3$

Here, R is the radius of the sphere.

The expression for the density ( D ) of the planet is,

  $D=\frac{M}{V}$

Here, M is the mass of the planet

Calculation:

The volume of the Sun is,

  $\begin{array}{l}V=\frac{4}{3}\pi R^3\\ V=\frac{4}{3}\pi {\left(1.5\times {10}^{11}\right)}^3\\ V=14.13\times {10}^{33}{\text{m}}^3\end{array}$

The average density of the Sun when it expands to the orbit of the Earth is,

  $\begin{array}{c}D=\frac{M}{V}\\ =\left(\frac{2\times {10}^{30}\text{kg}}{14.13\times {10}^{33}{\text{m}}^3}\right)\\ =1.4\times {10}^{-4}{\text{kg/m}}^3\end{array}$

Conclusion:

Thus, the average density of the Sun when it expands to the orbit of the Earth, is $1.4\times {10}^{-4}{\text{kg/m}}^3$ .