Question
in our solar system, which is the only variable that is used to calculate the time it takes for planetary body to complete its orbit? The mass of the sun; the gravitational constant; the radius of the orbit; or the mass of the planetary body.
Answers
GPT-4o mini
In our solar system, the primary variable used to calculate the time it takes for a planetary body to complete its orbit is the **radius of the orbit**. According to Kepler's Third Law of Planetary Motion, the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. The law can be described mathematically as:
\[
T^2 \propto r^3
\]
While the mass of the Sun and the gravitational constant are important for understanding the gravitational forces involved, the specific calculation for the orbital period focuses on the radius of the orbit. The mass of the planetary body has a negligible effect on the orbital period in the case of planets orbiting the Sun, since the Sun's mass is so large in comparison.
\[
T^2 \propto r^3
\]
While the mass of the Sun and the gravitational constant are important for understanding the gravitational forces involved, the specific calculation for the orbital period focuses on the radius of the orbit. The mass of the planetary body has a negligible effect on the orbital period in the case of planets orbiting the Sun, since the Sun's mass is so large in comparison.