Kepler 3rd law for circular orbits

In summary, Kepler's third law states that for two bodies of different masses orbiting in circular motion around their center of mass, they must have the same period and radius of orbit. However, this may seem contradictory as the masses are different. This is because the law applies to the system as a whole, with the distance between the objects as the radius. Looking at each individual body separately does not constitute a Kepler problem.
  • #1
Silviu
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Hello! I am a bit confused about Kepler 3rd law for circular orbits. So assume you have 2 bodies of masses M>m orbiting in circles around their center of mass. As the center of mass passes through the line connecting them, they must have the same period. But according to Kepler's 3rd law, this means that, as they rotate around the same center, they must also have the same radius of the orbits. But this is not possible as they have different masses. So how does this work? Thank you!
 
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  • #2
Kepler's third law holds for the system as a whole with the distance between the objects as the radius.

If you only look at each individual body, you do not have a Kepler problem.
 

What is Kepler's 3rd law for circular orbits?

Kepler's 3rd law states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. In other words, the farther a planet is from the sun, the longer it takes to complete one orbit.

How is Kepler's 3rd law used in astronomy?

Kepler's 3rd law is used to calculate the orbital periods of planets and other objects in our solar system. It also helps astronomers determine the distance between planets and their parent star.

What is the significance of Kepler's 3rd law?

Kepler's 3rd law provides a mathematical relationship between a planet's orbital period and its distance from the sun. This helped scientists better understand the structure and dynamics of our solar system and paved the way for future discoveries in astronomy.

Can Kepler's 3rd law be applied to all types of orbits?

No, Kepler's 3rd law only applies to circular orbits. For elliptical orbits, a modified version of the law known as Kepler's 3rd law for elliptical orbits is used.

How was Kepler's 3rd law developed?

Kepler's 3rd law was developed by German astronomer Johannes Kepler in the early 17th century. He studied the observations of his mentor, Tycho Brahe, and used them to formulate his three laws of planetary motion.

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