Question

Jupiter's four large moons -- Io, Europa, Ganymede, and Callisto -- were discovered by Galileo in 1610. Jupiter also has dozens of smaller moons. Callisto has a radius of about 2.40 106 m, and the mean distance between Callisto and Jupiter is 1.88 109 m. (a) If Callisto's orbit were circular, how many days would it take Callisto to complete one full revolution around Jupiter

Answer 1

If Callisto's orbit were circular, it would take approximately 16.7 days for Callisto to complete one full revolution around Jupiter.

Step-by-step explanation:

The orbital period (T) of a moon in a circular orbit around a planet can be calculated using Kepler's Third Law:

T^2 = (4π²r³) / GM

Where:

T is the orbital period,

r is the mean distance between the moon and the planet,

G is the gravitational constant,

M is the mass of the planet.

For Callisto:

r = 1.88 x 10^9 m (mean distance),

G is a constant,

M is the mass of Jupiter.

By solving for T, we find that T is approximately 16.7 days.

Answer 2

You would use

P^2 = (2π)^2(D^3)/((G)(M))

where P is the orbital period in seconds, D is the distance in meters, M is the mass in kilograms of Jupiter, and G is the 6.67 x 10^ -11 m^3/ kg sec^2

M Jupiter = 1.9 x 10^27 kg, D = 1.88 x10^9 meters

P^2 = 39.5*(6.65 x 10^27)/(( 6.67 x 10^ -11)(1.9 x 10^27)) = 2.07 x 10^12

P = 1,440,000 seconds = 16.66 days