Question

derive gravitatational force using keplers 3rd law.T^2 directly proportional to r^3.

Answer 1

Johannes Kepler published a relationship between how long a planet takes to orbit the Sun and the size of that orbit, something we now call his 3rd law of planetary motion, or just “Kepler’s 3rd law”. It states that





where  is the period of the orbit and  is the size of the orbit. Kepler also found that the planets orbit the Sun in elliptical orbits (his 1st law), and so the size of the orbit  that we refer to is actually something called the “semi-major axis”, half the length of the long axis of an ellipse.

Any proportionality can be written as an equality if we introduce a constant, so we can write




Answer 2

Johannes Kepler published a relationship between how long a planet takes to orbit the Sun and the size of that orbit, something we now call his 3rd law of planetary motion, or just “Kepler’s 3rd law”. It states that



where  is the period of the orbit and  is the size of the orbit. Kepler also found that the planets orbit the Sun in elliptical orbits (his 1st law), and so the size of the orbit  that we refer to is actually something called the “semi-major axis”, half the length of the long axis of an ellipse.
Any proportionality can be written as an equality if we introduce a constant, so we can write