how can we derive newtons law of gravitation on the basis of keplers law
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In 1619, Johannaes Kepler published a relationship between how long a planet takes to orbit the sun and the size of that orbit, something we call his "3rd law of planetary motion",or just "Kepler's third law". It states that
T² × a³
where 'T' is the period of the orbit and 'a' is the size of the orbit. Kepler also found that the planets orbit the sun elliptical orbits (his 1st law) and so the size 'a' that we refer to is actually something called the "semi - major action", 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
T² = ka³
where 'k' is our constant of proportionality.
T² × a³
where 'T' is the period of the orbit and 'a' is the size of the orbit. Kepler also found that the planets orbit the sun elliptical orbits (his 1st law) and so the size 'a' that we refer to is actually something called the "semi - major action", 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
T² = ka³
where 'k' is our constant of proportionality.
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