The period of revolution of a planet around the sun is the time it takes for the planet to complete one orbit of the sun. The period, P years, is give by Kepler's third law P^2=D^3, where D is the average distance from the sun in astronomical units (AU). One AU is the average distance f the Earth fromt he sun. Use the average distance formt he sun to find the period of revolution for Jupiter; 5.20 AU to the nearest tenth of a year.
I don't get that, the teacher said the answer was 11.9 I think. Anyone care to explain how?
Thanks
Easy.
5.20 AU is the distance so:
P^2=D^3 is equivalent to:
P^2=5.20^3
5.20^3 is 140.608, 140.608 is the period.
So the new equation would be:
P^2=140.608
Since you now know that 140.608 is the period squared, the opposite of squaring is square rooting. So this is how you would write it.
�ã140.608=11.85782442
It asked for the nearest tenth of the year so rounding up would make the answer 11.9
So the period of revolution for Jupiter is 11.9 years.
-Don
Well, let's do the calculation and see if we can get close to the answer of 11.9 years. According to Kepler's third law, P^2 = D^3, where P is the period of revolution in years and D is the average distance from the Sun in AU.
In this case, the average distance from the Sun for Jupiter is 5.20 AU. So, let's plug that into the equation:
P^2 = (5.20)^3
P^2 = 140.608
To find P, we need to take the square root of both sides:
P = √140.608
P ≈ 11.86
So, it looks like the period of revolution for Jupiter is around 11.86 years, which is quite close to the teacher's answer of 11.9 years. It's possible that the teacher used more precise values or rounded differently, but this should give you a good approximation.
To find the period of revolution for Jupiter, we can use Kepler's third law equation: P^2 = D^3.
First, we need to substitute the average distance from the sun for Jupiter, which is given as 5.20 AU.
P^2 = (5.20)^3
Next, we solve for P by taking the square root of both sides of the equation:
P = sqrt((5.20)^3)
Using a calculator, this evaluates to approximately 11.9 years when rounded to the nearest tenth.
So, based on Kepler's third law, the period of revolution for Jupiter is approximately 11.9 years.