The following table shows the period of revolution of some unknown planets of equal mass.
Planet Period of Revolution
W 1.9 years
X 11.8 years
Which of the following best explains which planet is farther from the sun?
Planet W, because gravity is inversely proportional to the square of distance
Planet X, because gravity is inversely proportional to the square of distance
Planet X, because the sun exerts a greater gravitational force on it than on planet W
Planet W, because the sun exerts a greater gravitational force on it than on planet X
The correct explanation is:
Planet X, because gravity is inversely proportional to the square of distance.
According to Newton's Law of Universal Gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Therefore, if two planets have the same mass, the planet that is farther from the sun will experience a weaker gravitational force. In this case, since planet X has a longer period of revolution, it means that it is farther from the sun compared to planet W.
The period of revolution of a planet is the time it takes for the planet to complete one orbit around the sun. In this question, we are given the period of revolution for two unknown planets, W and X.
To determine which planet is farther from the sun, we need to understand the relationship between gravity and distance. According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Now, let's analyze the answer choices:
1. Planet W, because gravity is inversely proportional to the square of distance.
This statement is correct. According to Newton's law of universal gravitation, gravity is indeed inversely proportional to the square of the distance. However, this does not directly answer the question of which planet is farther from the sun.
2. Planet X, because gravity is inversely proportional to the square of distance.
This statement is incorrect. Gravity being inversely proportional to the square of distance does not directly imply that Planet X is farther from the sun. It is an incomplete explanation.
3. Planet X, because the sun exerts a greater gravitational force on it than on planet W.
This statement is also incorrect. The period of revolution is not directly linked to the gravitational force exerted by the sun on the planets. The period of revolution depends on the distance and mass of the planet, not just the gravitational force.
4. Planet W, because the sun exerts a greater gravitational force on it than on planet X.
This statement is also incorrect. Similar to the previous choice, the period of revolution does not depend solely on the gravitational force exerted by the sun.
In conclusion, none of the answer choices accurately explains which planet is farther from the sun based on the given information. To determine which planet is farther, we would need additional information such as their distances from the sun or their masses.