Question

Kepler's work revealed that the sun was _____. at the center of the circular orbits of the planets at the center of the elliptical orbits of the planets located between the two focus points of the elliptical orbits of the planets at one focus of the elliptical orbits of the planets

Answer 1

Kepler's work revealed that the orbit of each planet is an ellipse,
with the sun at one focus.

Newton's work revealed that if his law of universal gravitation is
correct, then the orbit of each planet MUST be an ellipse with the
sun at one focus.

Answer 2

The correct answer of this question is :  At one of the focus of the elliptical orbits of the planet.

EXPLANATION :

Before going to answer this question, first we have to understand Kepler's first law on planetary motion.

As per Kepler's first law on planetary motion, every planet moves in elliptical orbits around the sun, and the sun is situated at one of its foci.

It is so because the eccentricity of the orbit traced by the planet is less than 1.

The eccentricity of the orbits traced by any object is calculated as -

                       $e=\ \sqrt{1+\frac{2EJ^2}{mk^2}}$

Here, E is the total energy of the planet when  it moves around the sun.

         J is the angular momentum of the planet.

         m is the mass of the planet, and k = $GMm$ where M and m are masses of sun and planet respectively.

G is universal gravitational force constant.

Putting the above values in the equation, the eccentricity e is found to be less than 1.

Hence, path of planet is elliptical.

Hence, the correct answer will be that the sun is situated at one focus of the elliptical orbits.