Which form of Kepler's third law can you use to relate the period T and radius r of a planet in our solar system as long as the unit year is used for the period and astronomical unit is used for the radius? (= means proportional to in this case)
O T ^ 2 = r
O T = r ^ 2;
O T ^ 2 = r ^ 3;
O T ^ 3 = r ^ 2
The correct form of Kepler's third law that relates the period T and radius r of a planet in our solar system when using years for the period and astronomical units for the radius is:
O T ^ 2 = r ^ 3
The correct form of Kepler's third law that can relate the period T and radius r of a planet in our solar system, when using the unit year for the period and astronomical unit for the radius, is:
O T ^ 2 = r ^ 3
To relate the period T and radius r of a planet using Kepler's third law, we can use the formula:
T^2 = r^3
In this equation, T represents the period of the planet (in years) and r represents the radius of its orbit (in astronomical units).
To understand why this formula is used, let's break it down:
- Kepler's third law states that the square of the period of revolution of a planet is proportional to the cube of the semi-major axis of its orbit.
- The period T is the time it takes for a planet to complete one full orbit around the sun.
- The radius r, in this case, represents the semi-major axis of the planet's orbit, which is the average distance between the planet and the sun.
- By taking the square of the period (T^2) and comparing it to the cube of the radius (r^3), we establish a relationship that holds true for planets in our solar system.
So, in summary, the correct form of Kepler's third law to relate the period T and radius r of a planet using the unit year for the period and astronomical unit for the radius is:
T^2 = r^3