The following table shows the distance from the sun of some unknown planets of equal mass.

Distance from Sun
\begin{tabular}{|c|c|}
\hline Planet & Distance from Sun \\
\hline [tex]$Y$[/tex] & [tex]$1 \, \text{AU}$[/tex] \\
\hline [tex]$Z$[/tex] & [tex]$0.39 \, \text{AU}$[/tex] \\
\hline
\end{tabular}

Which of the following best explains which planet revolves at a slower speed?

A. Planet [tex]$Y$[/tex], because the sun pulls it with a greater force.
B. Planet [tex]$Z$[/tex], because the sun pulls it with a greater force.
C. Planet [tex]$Y$[/tex], because the gravitational force is weakened by distance.
D. Planet [tex]$Z$[/tex], because the gravitational force is strengthened by distance.



Answer :

To determine which planet revolves at a higher speed around the sun, we need to consider the gravitational force acting on each planet. The force of gravity is given by the equation \( F = \frac{G \cdot m_1 \cdot m_2}{r^2} \), where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between them. Because gravitational force is inversely proportional to the square of the distance \( r \), the closer a planet is to the Sun, the stronger the gravitational pull it experiences.

For Planet Y, which is at a distance of 1 AU from the Sun:
[tex]\[ F_Y = \frac{1}{(1)^2} = 1.0 \text{ (arbitrary units)} \][/tex]

For Planet Z, which is at a distance of 0.39 AU from the Sun:
[tex]\[ F_Z = \frac{1}{(0.39)^2} \approx 6.575 \text{ (arbitrary units)} \][/tex]

From these calculations:
1. The gravitational force experienced by Planet Y is \( 1.0 \) arbitrary units.
2. The gravitational force experienced by Planet Z is approximately \( 6.575 \) arbitrary units.

Since Planet Z is closer to the Sun, it experiences a stronger gravitational force compared to Planet Y. The stronger gravitational force on Planet Z means it must travel at a higher speed to maintain its orbit. Thus, Planet Z revolves at a higher speed around the Sun.

Therefore, the statement that best explains which planet revolves at a higher speed is:

Planet Z, because the gravitational force is strengthened by distance.