What new quantity is introduced into the equation of kepler's 3rd law??

Question

relating periods and sizes of orbits..

Answer 1

The third law : "The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits." Thus, not only does the length of the orbit increase with distance, the orbital speed decreases, so that the increase of the orbital period is more than proportional.

Answer 2

See the ref. The new quantity is the constant that relates the semimajor axis of the orbit a to the orbital period P, in the expression
P^2 = a^3 * const
In an expanded version
P^2 = a^3 * 4pi^2/(k^2*(m1+m2))
the constant k is called the Gaussian constant. It is, of course, related to the universal gravitational constant G.

Answer 3

a million. no longer something modifications 2. no longer something modifications. Kepler's 0.33 regulation is era squared (in earth years) = semi-significant axis cubed. Mass isn't coated. as immediately as you're making the main significant of Newton's version, the hundreds cancel out, as immediately as you do the math genuine. particularly some human beings shrink back decrease back to rubble on the instruments on an same time as utilizing Kepler's regulation the 1st few circumstances. I did that lots on an same time as i grew to become into in a junior element introductory astrophysics direction on the college of Arizona. That direction taught me to continuously save song of the instruments, and to double and triple be taught each element on an same time with the aid of fact the instruments are no longer to any extent further optimum recommendations-blowing, AND to double and triple be taught the unit conversion too.