Saturn makes one complete orbit of the Sun every 29.4 years. Calculate the radius of the orbit of Saturn. Hint: It is a very good approximation to assume this orbit is circular.
use the law: T^2 proportional to r^3
swag
To calculate the radius of the orbit of Saturn, we can use the formula for the circumference of a circle, which is 2π times the radius. Since we know that Saturn takes 29.4 years to complete one orbit around the Sun, we can use this information to find the circumference of Saturn's orbit.
First, we need to determine the length of time taken by Saturn to complete one full orbit. This is given as 29.4 years.
Next, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference and r is the radius.
Since we want to calculate the radius, we rearrange the formula to solve for r:
r = C / (2π)
To find the circumference, we can use the formula for the circumference of a circle, where C = 2πr:
C = 2π * r
Substituting the given time period for one orbit (29.4 years) into the equation, we have:
29.4 years = 2π * r
Finally, solve the equation for r:
r = 29.4 years / (2π)
Calculating the expression, we find:
r ≈ 4.667 years / π
So, the radius of Saturn's orbit is approximately 4.667 years divided by π.