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How is Kepler's Law used to find the period of orbit for earth?

Answer 1

#T^2=(4pi^2)/(GM)R^3#

According to Kepler's Third Law of Planetary Motion, the cube of the semi-major axis R of the orbit is directly proportional to the square of the period T of revolution for any planet (mass M) around the sun.

We may then make the period T the subject of the formula to obtain if one applies the fundamentals of physics to derive the equation and fill in the pertinent constants of proportionality.

#T^2=(4pi^2)/(GM)R^3#

If you would like a precise physics-based derivation of this formula, let me know and I will upload it for you as well.

G is Newton's Universal Gravitational constant and has value #6,67 xx 10^(-11)N.m^2//kg^2#

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Answer 2

Asher Cohen

The period of Earth's orbit around the Sun can be calculated by applying Kepler's Law, specifically his Third Law, which states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. Given the semi-major axis, or average distance from Earth to the Sun, this calculation yields the fact that an orbit around the Sun takes Earth approximately 365.25 days to complete.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.