Question

How does Keplers third law compare the periods and orbital radii of two planets with a solar system?


-the square of the ratio of the periods equals the cube of the ratio of the radii

-the square of the ratio of the periods equals the ration of the radii

-the ratio of the periods equals the square of the ratio of the radii

-the cube of the ratio of the periods equals the square of the ratio of the radii

Answer 1

Answer:

The square of the ratio of the periods equals the cube of the ratio of radii.

Explanation:

German astronomer Johannes Kepler who lived from 1571-1630, gave the three descriptive laws called Kepler's law. He derived this law after he had study and make observations of planetary motion done by Tycho Brahe.

The Kepler's third laws state that the square ratios of the period equals the cube ratio of the distance or radii.

Answer 2

From Kepler's third law, the square of the ratio of the periods equals the cube of the ratio of the radii.

Kepler's third law states that the ratio of the square of an object's orbital period with the cube of the semi-major axis of its orbit is the same for all objects orbiting the same primary.

The law is simplified using mathematical formula as follows;

T² ∝ R³

$(\frac{T_2}{T_1})^2 = (\frac{R_2}{R_1} )^3$

where;

• T is the orbital period of the planet
• R is the radius of the planet

Thus, we can conclude that from the Kepler's third law, the square of the ratio of the periods equals the cube of the ratio of the radii.

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