How do you calculate. How many years would it take the planet to orbit the sun. All I have is, that the planet is 97 times farther from sun than earth or 97 Astronomical units
Use Kepler's Third Law. If you have never heard of it, read
http://csep10.phys.utk.edu/astr161/lect/history/kepler.html
To calculate the number of years it would take for a planet to orbit the sun, you can use Kepler's Third Law of Planetary Motion. This law states that the square of a planet's orbital period is proportional to the cube of its average distance from the sun.
In this case, you mentioned that the planet is 97 times farther from the sun than the Earth, or 97 Astronomical Units (AU). The average distance between Earth and the sun is about 1 AU.
So, using Kepler's Third Law, we can set up the following equation:
(T_planet^2) / (T_earth^2) = (D_planet^3) / (D_earth^3)
where T_planet is the orbital period of the planet (in years), T_earth is the orbital period of Earth (approximately 1 year), D_planet is the average distance of the planet from the sun in AU (97 AU), and D_earth is the average distance of Earth from the sun in AU (1 AU).
Let's plug in the values into the equation:
(T_planet^2) / (1^2) = (97^3) / (1^3)
Simplifying the equation, we have:
(T_planet^2) = 912,673
Now, to solve for T_planet, we take the square root of both sides of the equation:
T_planet = sqrt(912,673)
Calculating the square root, we find that T_planet is approximately 955.72 years.
Therefore, it would take approximately 955.72 years for the planet to complete one orbit around the sun.