Europa is one of Jupiter's moons. This moon is in a circular orbit of 6.71x10^8 meters within a period of 3.55 days. What is the mass of Jupiter?

Nevermind, I found the answer by myself. In case anyone was wondering (which i doubt it), the mass of Jupiter by these calculations is 1.9x10^27 kg.

To find the mass of Jupiter based on the given information, we can use Kepler's Third Law of planetary motion.

Kepler's Third Law states that the square of a planet's orbital period is directly proportional to the cube of its average distance from the Sun (or in this case, its average distance from Jupiter for one of its moons).

The formula for Kepler's Third Law is:

(T^2) / (R^3) = (4π^2) / (G * M)

Where:
T is the orbital period of the moon (in seconds)
R is the average distance between the moon and Jupiter (in meters)
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
M is the mass of Jupiter (in kg)

First, we need to convert the given orbital period from days to seconds:
3.55 days = 3.55 * 24 * 60 * 60 seconds ≈ 306,720 seconds

Now, we can substitute the values into the formula:
(306,720^2) / (6.71 x 10^8)^3 = (4π^2) / (6.67430 x 10^-11 * M)

Simplifying the equation:
94,065,702,400 / (6.71 x 10^8)^3 = (4π^2) / (6.67430 x 10^-11 * M)

Calculate the cube of the average distance:
6.71 x 10^8)^3 = 3.717651 x 10^26

94,065,702,400 / 3.717651 x 10^26 = (4π^2) / (6.67430 x 10^-11 * M)

Multiply both sides by (6.67430 x 10^-11 * M):
M = (4π^2 * 3.717651 x 10^26) / 94,065,702,400

Now we can evaluate the expression on the right-hand side using a calculator:

M ≈ 1.901 x 10^27 kg

Therefore, the mass of Jupiter is approximately 1.901 x 10^27 kg.

Note: In calculations like this, it is important to use consistent units to get accurate results. Ensure that all values are expressed in the same unit system (e.g., meters, kilograms, seconds) before performing the calculations.