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

[tex]\[
\begin{tabular}{|l|l|}
\hline
Planet & Distance from Sun \\
\hline
W & [tex]$1.5 \, AU$[/tex] \\
\hline
X & [tex]$0.723 \, AU$[/tex] \\
\hline
\end{tabular}
\][/tex]

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

A. Planet X, because the gravitational force is strengthened by distance.
B. Planet W, because the gravitational force is weakened by distance.
C. Planet X, because the sun pulls it with a greater force.
D. Planet W, because the sun pulls it with a greater force.



Answer :

GinnyAnswer
To solve this problem, we need to understand the relationship between the distance of a planet from the sun and its orbital speed. According to Kepler's laws of planetary motion and the principles of gravitation, the closer a planet is to the sun, the stronger the gravitational force exerted on it by the sun. This stronger force results in a higher orbital speed.

Given the distances:
- Planet W is 1.5 AU from the sun
- Planet X is 0.723 AU from the sun

Among the given multiple-choice answers:
1. "Planet X, because the sun pulls it with a greater force": This statement is correct. Since Planet X is closer to the sun, it experiences a greater gravitational pull, which results in a faster orbital speed.
2. "Planet W, because the sun pulls it with a greater force": This statement is incorrect. Planet W is farther from the sun and therefore experiences a weaker gravitational pull.
3. "Planet W, because the gravitational force is weakened by distance": This is true but irrelevant to the question of which planet revolves faster.
4. "Planet X, because the gravitational force is strengthened by distance": This is a correct explanation. Planet X being closer to the sun experiences a stronger gravitational force, causing it to revolve faster.

Therefore, the best explanation is:
Planet [tex]\( X \)[/tex], because the gravitational force is strengthened by distance.

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