Enter any two of the three variables in Kepler’s third law; mass, orbital radius, and time. The calculator will solve for the missing variable.
Kepler’s Third Law Formula
The following formula is created through Kepler’s third law of orbital motion.
G · m · t² = 4 · π² · r³
- Where G is the gravitational constant
- m is mass
- t is time
- and r is orbital radius
This equation can be further simplified into the following equations to solve for individual variables.
M= 4 · π² · r³ /t²*G
T = square root (4 · π² · r³ /m*G)
r = cube root (G · m · t²/4*π²)
Kepler’s Third Law Definition
Kepler’s third law defines the relationship between mass, time, and orbital radius between two bodies of mass.
Kepler’s Third Law Example
How to calculate Kepler’s third law?
- First, determine the variable you are solving for.
Determine which of the 3 variables you want to find.
- Next, find the known variable.
Determine the values of the 2 known variables.
- Finally, calculate the missing variable.
Using the formulas above, calculate the missing variable.
FAQ
How does Kepler’s Third Law apply to planetary motion?
Kepler’s Third Law is fundamental in understanding planetary motion, as it describes how the period of orbit (time) is related to the distance of a planet from the sun (orbital radius). Specifically, it implies that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Can Kepler’s Third Law be used for moons orbiting planets?
Yes, Kepler’s Third Law can also be applied to moons orbiting planets or any other types of satellites, whether natural or artificial, orbiting around larger bodies. The law is universal for any two objects in orbit around each other under their mutual gravitational attraction.
What is the significance of the gravitational constant (G) in the formula?
The gravitational constant (G) is a key factor in the formula that represents the force of gravity between two objects. It is a universal constant used in calculating gravitational forces in the law of universal gravitation, and its value helps determine the strength of the gravitational pull between the mass of the objects and their distance apart.
How can Kepler’s Third Law be used in astronomy today?
In modern astronomy, Kepler’s Third Law is used to determine the masses of celestial bodies, calculate the distances of planets and stars from each other, and understand the dynamics of exoplanetary systems. It’s also essential in space mission planning, where it helps in calculating orbital paths and speeds for satellites and space probes.
