I was recently asked the following question:
Which of the Kepler Laws change if the Universal Constant Of Gravitation is changed? And why?
I list the 3 laws of Kepler below:
The Law of Orbits: All planets move in elliptical orbits, with the sun at one focus.
The Law of Areas: A line that connects a planet to the sun sweeps out equal areas in equal times.
The Law of Periods: The square of the period of any planet is proportional to the cube of the semi-major axis of its orbit.
Intuitively I don't expect first and the third laws to change.
Writing the equation of Time period even if the G changes, the square of the period is still proportional to cube of semi major axis.
So I don't expect any of the laws to change.
However the answer provided to me by some professor was that the second and third laws both would change slightly.