If you’ve been watching these past few days, you know the waxing gibbous moon has been moving past the glorious planet Jupiter in our night sky. These shining beauties beam in front of the constellation Gemini the Twins. Despite the moonlit glare, you are likely also to see Gemini’s two brightest stars, Castor and Pollux, near Jupiter and the moon.
Do you have a telescope? Wait until Earth’s moon moves away, then try to view Jupiter’s four major moons through your ‘scope. Or try tonight, because you can often see these moons in a moonlit sky. In their outward order from Jupiter, the moons are Io, Europa, Ganymede and Callisto. But, as viewed from Earth on successive evenings, their order will be seen to change. As darkness falls over North America on March 10, 2014, Io and Callisto will appear on one side of Jupiter, while Europa and Ganymede will be on the other. Follow Jupiter’s moons with this chart from skyandtelescope.com.
The inner three moons – Io, Europa and Ganymede – have a 4:2:1 orbital resonance. For every four times that Io orbits Jupiter, Europa orbits twice and Ganymede orbits once. Callisto is expected to join in several hundred million years from now, to create a 8:4:2:1 orbital resonance.
Given that Io’s mean distance from Jupiter is 262,000 miles, we can figure out Europa’s distance by using Kepler’s third law of orbital motion, D3 = P2, where D = distance and P = orbital period. We know Europa’s orbital period (P) is twice that of Io. So we can plug the number 2 into Kepler’s equation below to find out Europa’s distance relative to Io:
D3 = P2
D x D x D = 2 x 2
D x D x D = 4
D = 1.5874 times Io’s distance from Jupiter
Distance of Europa = 1.5874 x 262,000 = 415,898.8 miles
Bottom line: Whether you enjoy the simple beauty of Kepler’s third law or the visual beauty of the heavens – or both – let the waxing gibbous moon be your guide to the planet Jupiter tonight!