Question

Using two of those moons, calculate the mass of Jupiter. Are the

masses about the same and close to the published mass of Jupiter
that is 1.892 x 10^27 kg? Include your calculations in your
answers.

Answer 1

To calculate Jupiter's mass from its moon Io's orbital data, we can use Kepler's Third Law, converting the radius and period to SI units and solving for Jupiter's mass. This method allows us to compare the calculation to the known mass of Jupiter, which is 1.9 × 10^27 kg.

Step-by-step explanation:

To calculate the mass of Jupiter using the data from one of its moons, 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 directly proportional to the cube of the semi-major axis (r) of its orbit, and this proposition allows us to determine the mass of the planet around which the moon orbits.

For example, if we take the moon Io and its given average orbital radius of 421,700 km and a period of 1.77 days, we can convert these to SI units (meters and seconds) and then apply the formula derived from Kepler's Third Law for moons:
T^2 = (4π^2/GM_Jupiter)*r^3. Where G is the gravitational constant.

By rearranging the formula to solve for M_Jupiter, we can calculate the estimated mass. Comparing this to the known mass of Jupiter, 1.9 × 10^27 kg, provides a way to assess the accuracy of our calculation.