Chapter 9.5, Problem 4CYP

To determine

To find the diameter of the sun would appear on Earth as on Jupiter.

Answer to Problem 4CYP

The value of $d_e\text{ is 5}{\text{.2d}}_j$

Explanation of Solution

Given information:

The apparent length of an object is inversely proportional to one’s distance from the object. Earth is about 93 million miles from the sun. Jupiter is about 483.6 million miles from the Sun.

Calculation:

The diameter of the sun would appear on Earth as on Jupiter can be obtained as

Let,

  $\begin{array}{l}{l}_e\propto \frac{1}{d_e}\left[\begin{array}{l}{l}_e=\text{apparent lenght of earth}\\ {\text{d}}_e=\text{earth diameter}\end{array}\right]\\ l_j\propto \frac{1}{d_j}\left[\begin{array}{l}{l}_j=\text{apparent length of jupiter}\\ {\text{d}}_j=\text{jupiter diameter}\end{array}\right]\\ l_e{d}_e=l_j{d}_j\\ \frac{d_e}{d_j}=\frac{l_j}{l_e}\end{array}$

Put the values of $l_j=483.6\text{ and }{l}_e=93$ in above equation

  $\begin{array}{l}\frac{d_e}{d_j}=\frac{483.6}{93}\\ \frac{d_e}{d_j}=5.2\left[\text{divide numerator and denominator by 93}\right]\\ d_e=5.2d_j\end{array}$

Hence,

The value of $d_e\text{ is 5}{\text{.2d}}_j$