Lesson7b_Jupiter and its moons Galilean Moons of Jupiter

Jupiter formed an accretion disk

The disk would have formed directly above the equator of Jupiter. As material accumulated in the disk, it was possible to form moons in the debris found in the disk. This is like how the Galilean moons formed. They could not hold on to hydrogen and helium but were able to accumulate rocky material and water ice.

Galilean Moon Data Moon Orbital Radius (km) Radius (km) Mass (in Earth masses) Density (g/cm3) Orbital Period (Earth days) Relative surface age Io 422,000 1,815 0.0145 3.53 1.77 Youngest Europa 671,000 1,569 0.0080 3.03 3.55 Young Ganymede 1,070,000 2,631 0.0242 1.93 7.16 Older Callisto 1,883,000 2,400 0.0176 1.79 16.69 Oldest

Correlations with surface age Unlike the terrestrial planets, no correlation with mass or radius of the moon There are correlations between orbital radius, orbital period, and density. The sense of the correlation is: Closer to Jupiter the younger the surface Shorter the orbital period the younger the surface More dense the moon, the younger the surface

For objects orbiting another body, is there a relationship between orbital radius and orbital period?

We learned earlier in this class that the bigger the orbital radius the slower the object moves in its orbit. Also the larger the radius the bigger the circumference of the orbit (C = 2πR). So the bigger the orbit, the longer the time it takes an object to orbit. (Orbital Period) So Orbital Period depends on the radius of the orbit. We can eliminate the orbital period in our correlation. It is the same as saying the orbital radius is bigger.

Now let’s consider the density of the Moons. What can you conclude about the reason why Io has a much higher, mean density than Ganymede and Callisto?

. Io is smaller so it has a smaller volume. That makes it more dense Io is closer to Jupiter so it has a different chemical composition Io doesn’t have water Io must have been captured by Jupiter

Io is more dense because it doesn’t have large amounts of water ice covering its rocky surface like Europa, Ganymede and Callisto do. We know that Io is very geologically active. If it was once covered with ice, the ice probably evaporated and was lost.

Io may have been close to the same composition as Ganymede and Callisto originally. Because of its volcanic activity, the icy surface was evaporated. Since Io has no atmosphere, the pressure is too low for liquid water to be possible. The water vapor was lost and eventually Io became a much denser moon on average.

How big was Io? If we assume it had the same average density as Callisto, originally, then is had to have the equivalent of 0.006 Earth masses in water in order to drop its density to Callisto’s density. That would give Io a mass of 0.0145 + 0.006(in water) = 0.0205 Earth masses. That’s actually bigger than the current day Callisto.

Galilean Moon Data Moon Orbital Radius (km) Radius (km) Mass (in Earth masses) Density (g/cm3) Orbital Period (Earth days) Relative surface age Io 422,000 1,815 0.0145 (0.0205) 3.53 (1.79) 1.77 Youngest Europa 671,000 1,569 0.0080 3.03 3.55 Young Ganymede 1,070,000 2,631 0.0242 1.93 7.16 Older Callisto 1,883,000 2,400 0.0176 1.79 16.69 Oldest

Io may have formed this way The other possibility is that Io formed this way. Jupiter was probably much hotter at the time it formed. It is possible that Jupiter was hot enough that water was in a gas phase at the distance of Io. Io would have therefore formed without any water ice on its surface. Today Jupiter is much cooler than in the past.

Jupiter formed an accretion disk

How active is Io? It is estimated that Io resurfaces its self to a depth of about 1 cm/year. This rate of resurfacing is estimated using the amount of time it takes to fill in a crater. On the moon there is a relation between the size of a crater and its depth. In general the depth to diameter ratio is 1.3:10. In other words, a 10 km wide crater is about 1.3 km deep.

There are no 20 km craters on Io There are no 20 km craters on Io. A typical depth for a crater is about 10% of the diameter. 20 km 2 km

There are no 20 km craters on Io There are no 20 km craters on Io. This means that about 2 km of material had to be deposited to fill the crater in. How can this be used to estimate the global resurfacing rate? 20 km 2 km

There are no 20 km craters on Io There are no 20 km craters on Io. This means that about 2 km of magma material had to be deposited to fill the crater in. By estimating how frequently a 20 km impact crater is formed on Io, it is possible to estimate the how long it took to fill that last 20 km crater in. These types of analysis give about 1 cm/yr added to the global surface.

This is a phenomenal rate This is a phenomenal rate. If this rate were constant back to the formation of Io 4.5 billion years ago, then Io added: (1 cm/yr)(4.5 x 109 yrs) = 4.5 x 109 cm. That is 450,000 km. Io only has a radius of 1815 km (450,000 km)/(1815 km) = 248 !! This means Io turned itself, inside out, 248 times. Or it completely turns itself inside out every 18 million years.

Cavaets… Io may not have always been as active as it is today. Magma from inside Io, likely comes from its lithosphere, which is closer to the surface. So it doesn’t actually “turn-itself inside out.” If the lithosphere on Io is 100 km thick, then the lithosphere has recycled, 4500 times, or about once every 1 million years.

Why so active??? The correlation appears to show that the closer a Moon is to Jupiter, the more active it is, or the younger the surface. This means that the physical mechanism that is causing all of this activity decreases as a function of distance from Jupiter. Gravity does exactly that. But how does Jupiter’s gravity cause Io to be active?

. Since Jupiter has a large gravity it pulls harder on the side of Io nearer to it, causing stretching Jupiter pulls on one side of Io and the other moons pull in the opposite direction, stretching Io. Io is in an elliptical orbit and Jupiter twists it, trying to bring it back into alignment.

Here’s what we know… Io’s rotation is synchronously locked to Jupiter. (It keeps the same side facing Jupiter at all times) Io is in a slightly elliptical orbit. Io bulges in the direction of Jupiter. (These are tidal bulges)

The Moon’s rotational period (spin on its axis) is always the same. This means that the Moon turns a little too much when it is moving the slowest in its orbit, and it doesn’t turn quite fast enough when it is moving the fastest in its orbit. This causes the Moon to appear to wobble as it orbits the Earth. We can actually see 59% of the Moon’s surface instead of 50%.

Io does the same thing. It over turns and under turns as its orbital speed increases and decreases. This causes the tidal bulge to be out of alignment with Jupiter.

Jupiter attempting to re-align Io causes a torque that twists Io as it orbits. The result is the heating of the interior of Io from the strong gravity of Jupiter. Would this happen if Io were in a circular orbit?

Jupiter attempting to re-align Io causes a torque that twists Io as it orbits. The result is the heating of the interior of Io from the strong gravity of Jupiter. Would this happen if Io were in a circular orbit? No

No, if Io were in a circular orbit, then it would be truly synchronous, and there would be no torque acting to bring it back in line.

Io’s orbit should be circular It turns out that Jupiter is large enough that Io should have been forced into a circular orbit very long ago. So Io shouldn’t have activity. But it obviously does. And its orbit is not circular. Let’s think about why.

What do you notice about the orbital periods of the Galilean moons? Orbital Radius (km) Radius (km) Mass (in Earth masses) Density (g/cm3) Orbital Period (Earth days) Relative surface age Io 422,000 1,815 0.0145 3.53 1.77 Youngest Europa 671,000 1,569 0.0080 3.03 3.55 Young Ganymede 1,070,000 2,631 0.0242 1.93 7.16 Older Callisto 1,883,000 2,400 0.0176 1.79 16.69 Oldest

. The close in moons have shorter periods than the ones farther away from Jupiter. The orbital period is related to the density of the moon The moon-to-moon relation is related by a factor of 2

From moon-to-moon the orbital period changes by a factor of 2. PEuropa /PIo = 3.55/1.77 = 2 PGanymede/PIo = 7.16/1.77 = 4 PCallisto/Pio = 16.69/1.77 = 9.24 (not 8 but close) What are the chances that Io, Europa, Ganymede should have this relationship?

. It is not very likely It’s 100% It seems likely, there isn’t really any reason they shouldn’t have these orbital periods.

In a given, random system, with four moons it would seem that such an alignment is highly unlikely. Just as it is highly unlikely that most of the big moons in the solar system are in synchronous orbits about their planets. When something unlikely occurs we need to think more deeply as to what mechanism would cause this. What do you think? Why the factor of 2 in the periods?

. The pull of gravity from Jupiter drops off like the distance squared. That makes the moons move to a factor of two distance. There are four moons so the number has to be a multiple of four The moons exchanged angular momentum and this is the lowest energy state.

Notice: Orbital radius is NOT a factor of 2. Only the period. Moon Orbital Radius (km) Radius (km) Mass (in Earth masses) Density (g/cm3) Orbital Period (Earth days) Relative surface age Io 422,000 1,815 0.0145 3.53 1.77 Youngest Europa 671,000 1,569 0.0080 3.03 3.55 Young Ganymede 1,070,000 2,631 0.0242 1.93 7.16 Older Callisto 1,883,000 2,400 0.0176 1.79 16.69 Oldest

It is caused by the exchange of orbital angular momentum between the moons. Io, Europa and Ganymede pass each other very frequently. When they do so, the faster orbiting moon tries to pull the slower moon ahead in its orbit, while the more slowly moving moon tries to pull the fast one back. This causes an exchange of angular momentum between the moons, until they reach a resonance orbit. This takes a long time… Callisto still isn’t there yet.

Here is why Io is in an elliptical orbit The moons’ gravities are very weak. They can perturb each other only very slightly. If Io passed by the other moons at random places in its orbit, the effect would average out and Io would be in a circular orbit.

Ganymede Io Europa

Ganymede Io Europa

Ganymede Io Europa

If Io just randomly passed the other moons at various positions, the net result would be virtually no effect on Io’s orbit. But the resonance orbits of the three mean that they pass at the same location each time. Here is an example.

Initial orientation of the Moons Europa Ganymede

Io completes one orbit Io Europa Ganymede

Io completes two orbits

Io completes three orbits

Io completes four orbits

The effect of gravity is the strongest when the moons are close together. This happens at the same location all the time. It’s like a game of knuckles This allows the little perturbing effects of Europa and Ganymede to add up as time goes by. The result is that Io’s orbit becomes slightly elliptical.

So Europa and Ganymede force Io into a slightly elliptical orbit. This orbit causes Io’s tidal bulges to advance and lag the direction to the center of Jupiter, slightly. Jupiter exerts a torque, trying to bring Io back into alignment. This torque heats up the interior of Io. Without the other moons, Io would be a dead world today.