Step-by-step explanation:
To find the orbital period of an object without knowing its orbital speed and mass, but knowing 4 different radii, you can use Kepler's third law.
Kepler's third law states that the square of the orbital period (T) of a planet or satellite is proportional to the cube of the semi-major axis (a) of its orbit. The semi-major axis is half of the longest diameter of the elliptical orbit.
The formula for Kepler's third law is:
T^2 = (4π^2 / GM) * a^3
Where T is the orbital period, G is the gravitational constant, M is the mass of the central body around which the object is orbiting, and a is the semi-major axis.
To use this formula, you need to know the semi-major axis of the orbit. If you have 4 different radii, you can calculate the semi-major axis by taking the average of the maximum and minimum radii.
Once you have the semi-major axis, you can plug it into the formula along with the other known values and solve for T. Keep in mind that the units of T will depend on the units used for G, M, and a.