Question

Kepler’s third law. According to Kepler’s third law of
planetary motion, the ratio
t^2/r^3
has the same value for every planet in our solar system. R is the average radius of the
orbit of the planet measured in astronomical units (AU),
and T is the number of years it takes for one complete
orbit of the sun. Jupiter orbits the sun in 11.86 years with
an average radius of 5.2 AU, whereas Saturn orbits the
sun in 29.46 years

If the average radius of the orbit of Venus
is 0.723 AU, then how many years does it take for Venus
to complete one orbit of the sun?

Answer 1

t^2 / r^3 = (11.86)^2 / (5.2)^3 = 140.66 / 140.61 = 1.00 For all planets in the solar system.

t^2 / (0.723)^3 = 1.00,
Solve for t:

t^2 = (0.723)^3,
t^2 = 0.3779,
Take sqrt of both sides:
t = 0.615 years.