zeion said:I'm being asked to find K for each individual moons; each of which has a different period and radius. I was given both the T and r for the first four so I could find K easily, but for the last four I'm only given either r or T, which I think would require me to use
GM/4(pi)^2 = K = r^3 / T^2
But since I wasn't given mass of Uranus (M), I can't :/
The formula IS K = r^3 / T^2 right?
Kepler's constant, also known as the third law of planetary motion, is a mathematical relationship between the orbital period and the average distance of a planet from the sun. It states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the sun.
Yes, Kepler's constant can be calculated with only the radius or period given. However, it requires an additional constant known as the gravitational constant, which relates the gravitational force between two objects to their masses and distance. With this constant, Kepler's constant can be calculated using the formula K = 4π²/G, where G is the gravitational constant.
Kepler's constant is used to study the motion of celestial bodies, such as planets and moons, in our solar system and beyond. It allows scientists to accurately predict the orbital periods and distances of these objects, and has been instrumental in discovering exoplanets and understanding the dynamics of our solar system.
The units of measurement for Kepler's constant depend on the units used for the radius and period. If the radius is measured in meters and the period in seconds, then Kepler's constant will have units of meters cubed per second squared.
While Kepler's constant has been proven to be accurate in predicting the motion of celestial bodies, it does have some limitations. It assumes that the orbiting objects are in circular orbits and that there are no other significant gravitational forces acting on them. In reality, orbits can be elliptical and there may be other objects or forces affecting the motion of the orbiting body.