Question
The following table shows the period of revolution of some unknown planets of equal mass.
Period of Revolution
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 the sun exerts less gravitational force as distance increases
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
Period of Revolution
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 the sun exerts less gravitational force as distance increases
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
Answers
GPT-4o mini
The best explanation for which planet is farther from the sun is:
**Planet X, because the sun exerts less gravitational force as distance increases.**
This conclusion is based on Kepler's Third Law of Planetary Motion, which states that the square of the period of revolution (T²) of a planet is directly proportional to the cube of the semi-major axis of its orbit (a³). This implies that planets with longer periods of revolution are farther from the sun.
Since Planet X has a longer period of revolution (11.8 years) compared to Planet W (1.9 years), it must be farther from the sun. Consequently, the gravitational force exerted by the sun on Planet X is less than that on Planet W, but Planet X's greater distance allows it to maintain its longer orbital period.
**Planet X, because the sun exerts less gravitational force as distance increases.**
This conclusion is based on Kepler's Third Law of Planetary Motion, which states that the square of the period of revolution (T²) of a planet is directly proportional to the cube of the semi-major axis of its orbit (a³). This implies that planets with longer periods of revolution are farther from the sun.
Since Planet X has a longer period of revolution (11.8 years) compared to Planet W (1.9 years), it must be farther from the sun. Consequently, the gravitational force exerted by the sun on Planet X is less than that on Planet W, but Planet X's greater distance allows it to maintain its longer orbital period.