Question
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?
Answers
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?
The time it takes a satellite to orbit a central body, its orbital period, can be calculated from
T = 2(Pi)sqrt[a^3/µ]
where T is the orbital period in seconds, Pi = 3.1416, a = the semi-major axis of an elliptical orbit = (rp+ra)/2 where rp = the perigee (closest) radius and ra = the apogee (farthest) radius from the center of the earth, µ = the central bodies gravitational constant = GM, the gravitational constant times the mass of the central body. In the case of a circular orbit, a = r, the radius of the orbit.
You have T, r, and G = 6.67259x10^-11m^3/kg.sec.^2. Solve for M.
The time it takes a satellite to orbit a central body, its orbital period, can be calculated from
T = 2(Pi)sqrt[a^3/µ]
where T is the orbital period in seconds, Pi = 3.1416, a = the semi-major axis of an elliptical orbit = (rp+ra)/2 where rp = the perigee (closest) radius and ra = the apogee (farthest) radius from the center of the earth, µ = the central bodies gravitational constant = GM, the gravitational constant times the mass of the central body. In the case of a circular orbit, a = r, the radius of the orbit.
You have T, r, and G = 6.67259x10^-11m^3/kg.sec.^2. Solve for M.
Related Questions
Io, one of the moons of Jupiter, circles Jupiter once every 1.77 days. The radius of its orbit is 4...
Io and Europa are two of Jupiter's many moons. The mean distance of Europa from Jupiter is about twi...
Io and Europa are two of Jupiter's many moons. The mean distance of Europa from Jupiter is about twi...