A newly discovered planet is found to have a circular orbit, with a radius equal to 11 times the radius of Earth's orbit. How long does this planet take to complete one orbit around the Sun?
Physics
What is Kepler's third law?
http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion
To determine the time it takes for the newly discovered planet to complete one orbit around the Sun, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period (T) of a planet is proportional to the cube of the average distance from the Sun (r).
Mathematically, we can express this relationship as:
T^2 = K * r^3
where T is the orbital period, r is the average distance from the Sun, and K is a constant.
In this case, we know that the radius of the newly discovered planet's orbit (r) is 11 times the radius of Earth's orbit. The radius of Earth's orbit is approximately 149.6 million kilometers (or 93 million miles), so the radius of the newly discovered planet's orbit is 11 times that, giving us:
r = 11 * 149.6 million km
We can substitute this value into the equation to solve for T:
T^2 = K * (11 * 149.6 million km)^3
To simplify the calculations, we can convert the distance into meters, so:
T^2 = K * (11 * 149,600,000,000 m)^3
Now, we just need to solve for T. But since we do not know the value of the constant K, we cannot determine the exact length of the newly discovered planet's orbital period.