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?(1 point)
T=r2
cap t is equal to r squared
T3=r2
cap t cubed is equal to r squared
T2=r
cap t squared is equal to r
T2=r3
cap t squared is equal to r cubed
The correct form of Kepler's third law that can be used to relate the period T and radius r of a planet in our solar system is:
T2 = r3
This means that the square of the period is equal to the cube of the radius.
The correct form of Kepler's third law that relates the period (T) and radius (r) of a planet in our solar system, using the unit year for the period and astronomical unit (AU) for the radius, is:
T^2 = r^3
Explanation:
Kepler's third law states that the square of the period of revolution of a planet around the Sun is directly proportional to the cube of its average distance from the Sun. In mathematical terms, this relationship is expressed as T^2 = r^3.
To obtain this relationship, Kepler used observational data from various planets in our solar system. The period (T) of a planet refers to the time it takes for the planet to complete one full revolution around the Sun, while the radius (r) represents the average distance of the planet from the Sun.
By squaring the period (T^2) and cubing the radius (r^3), we establish a proportional relationship between the two. This form of Kepler's third law is consistent when the unit year is used for the period and astronomical unit (AU) is used for the radius, as it reflects the observations made in our solar system.