The four largest moons of Jupiter are Io, Europa, Ganymede, and Callisto. First seen by Galileo Galilei in December 1609 or January 1610, he described them as satellites in orbit of Jupiter in March 1610. They are easily seen near the planet using a simple telescope or a steadied pair of binoculars. They are currently well placed with Jupiter in the evening sky to the southeast soon after sunset.
Imagine being high above Jupiter looking down at the planet and the four moons. Desktop planetarium software is very helpful here. In this view, Jupiter is centered. The Sun is far to the left off-screen. The moons are labeled in each of their orbits. The fastest is Io closest to Jupiter. Callisto is the slowest. Three of the moon have shadow lines drawn in orange. Play the video and watch their movements. The shadows cast by each of those three moons are intercepted by Jupiter. The software speeded up the rate many times.
What would this event look like for viewers on Earth? Earth would be located far off-screen to the left toward the Sun. Could we see the shadows cast by the moons upon the cloud tops of Jupiter? Again, software can simulate the view accurately. The answer is yes. Earthlings with powerful amateur telescopes are capable of seeing the shadows.
Play the video and watch for several things in this simulation. The first is Callisto casting its shadow on Jupiter. Over the course of several hours, it moves across the entire face of the planet. Next, Ganymede and Europa approach from the left. At 24 sec in the video, both of their shadows are cast. Also, Callisto’s shadow moves off the planet and the moon Io disappears into the shadow of Jupiter just off the right limb of the planet.
Watch at the 30 sec time how Europa is occulted by Ganymede. Both shadows are still visible but they become one briefly at the 32 sec mark. Finally, at 38 sec, both moons and their shadows are off to the right. Did you notice how Io emerged to the left of Jupiter in the distance? You might need to view both of these videos a few times.
On 15 August 2021, the moons were actually positioned as in my simulation above for viewers in the western Pacific region. Christopher Go of Cebu City, Philippines, captured images that night. He was fortunate to enjoy clear sky conditions for the duration of these events. His images are posted on his site. Scroll down his page until you reach August 15, 2021. The Astronomy Picture of the Day APOD highlighted his work.