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Exploring the Moons of Jupiter

 
 
 
 List of Solar System objects by size

 List of gravitationally rounded objects of the Solar System

The remaining Galilean moons are Ganymede and Callisto, and both of them have lots of impact craters. Ganymede also has thick light-colored splotches on its surface, though Callisto doesn't.

The two moons have mean densities consistent with much of them being water, whether ice or liquid water. The lower parts of this water may be high-pressure ice and/or mixed with rock. Like Europa, Ganymede and Callisto may also have subsurface oceans. But they don't have nearly at much tidal heating as Io or Europa, at least at present.
 
I estimated how much tidal distortion each big moon gets: (M/m)*r^4/a^3 * e -- 12.7 m -- 3.3 m -- 0.55 m -- 0.66 m

I then checked on which instruments might be able to observe those distortion of those moons.

JUICE:
  • RIME - radar - 30 m
  • GALA - lidar - 10 cm
Europa Clipper:
  • REASON - radar - (I couldn't find resolution numbers)

ESA's Juice mission (@ESA_JUICE) / Twitter

JUICE's instruments are steadily being deployed and tested.

But there was trouble with RIME's antenna. ESA - Juice’s RIME antenna breaks free - 12/05/2023 (European date order; American order: 05/12/2023)
During the first attempt to extend the folded-up antenna, only the first segments of each half were deployed. Flight controllers suspected that a tiny stuck pin jammed the other segments in place.

Fortunately, the flight control teams at ESA’s mission control centre in Darmstadt had lots of ideas up their sleeves.

To try to shift the pin, they shook Juice using its thrusters, then they warmed Juice with sunlight. Every day the RIME antenna was showing signs of movement, but no full release.

On 12 May RIME was finally jolted into life when the flight control team fired a mechanical device called a ‘non-explosive actuator’ (NEA), located in the jammed bracket. This delivered a shock that moved the pin by a matter of millimetres and allowed the antenna to unfold.
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The article includes a graph of how the spacecraft oscillated from that part going into action.
But a final part of the antenna remained folded. Confirmation that the RIME antenna was successfully deployed came only when the flight control team fired another actuator in the bracket, causing RIME to fully stretch itself out after months spent folded up for launch.
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How far can these antennas see through the icy moons' crusts?
RIME + REASON ~ "without rhyme or reason"
 
Now for a collection of gravity-field data -- how much nonsphericity? How good are the measurements?
 
I must add one more: Gravity field and solar component of the precession rate and nutation coefficients of Comet 67P/Churyumov–Gerasimenko | Monthly Notices of the Royal Astronomical Society | Oxford Academic -- about 0.1

So we have a big collection of numbers for the shapes of celestial bodies' gravitational fields. What can one do with them? One can find a constant-potential shape, the "geoid", and then try to intrepret it. How do its shape features correlate with other shape features?

One can also test for departures from hydrostatic equilibrium, like from rigidity of material. One does that by finding what shape-coefficient values that one expects from that equilibrium.

For an essentially isolated body, like a planet, h-e implies axial symmetry combined with equatorial reflection symmetry. This is from rotation, and no rotation would mean spherical symmetry, with all coefficients zero unless one counts the body's mass as a coefficient.

The zonal or axially-symmetric gravity coefficients are J(n) = - C(n,0) for positive integers n and the non-axisymmetric ones are C(n,m) and S(n,m) for positive integers m <= n.

So for hydrostatic equilibrium under rotation, the only nonzero ones are J(2n) with J(2n+1) = C(n,m) = S(n,m) = 0 (m > 0)

Also, for rotation, J(2n) ~ (-1)n+1 * (J2)n + (higher powers of J2), though the exact multipliers are very complicated functions. The most analytically tractable case is for constant density, and even that is rather complicated. Next in line is a material equation of state with pressure proportional to the square of the density, and that is even more complicated.
 
Jupiter's four big moons have a complication. Their rotation is tidally locked, with one side facing toward their planets, and one side facing away. The Earth's Moon shows a familiar example of that effect, and most other big moons have that effect. The largest counterexample that I know of is Saturn's moon Hyperion, which rotates chaotically. Hyperion is in a 4:3 orbital resonance with Titan, and that moon forces an orbital eccentricity of 0.123. Adding to that is the moon's irregular shape: approximately a triaxial ellipsoid with axis diameters 360.2 km × 266.0 km × 205.4 km (223.8 mi × 165.3 mi × 127.6 mi) (Wikipedia). These two effects combine to make that chaotic rotation.

In addition to the rotational flattening, a tidally locked moon is distorted into an American football shape by its planet's gravity. The effects combine to make a sort of flattened American football.

The distortion proportions are 7/3 : -2/3 : -5/3 with rotation making 1/3 : 1/3 : -2/3 and tides making 2 : -1 : -1

From hydrostatic equilibrium, one can deduce constraints on the gravity coefficients. As with rotation, only even J's are nonzero, and of the C's and S's, C(n,m) is nonzero only for n and m both even, and S(n,m) is zero, using a coordinate system aligned with the moon's planet.

The lowest-order nonzero coefficients are thus J2 and C22, and unnormalized and to lowest order, they are related by

C22/J2 = 3/10
 
For the Earth, the gravity coefficients are the  Geopotential model -- and it calls the axially-symmetric parts the zonal parts and the others the tesseral parts.

J2 stands out as 1.08*10-3, and the others are around 10-6 -- giving heights of around 10 meters. J2 is mostly from the Earth's equatorial bulge, and that in turn is from the Earth's rotation.

The Relativity of Wrong by Isaac Asimov
The correction in going from spherical to oblate spheroidal is much smaller than going from flat to spherical. Therefore, although the notion of the Earth as sphere is wrong, strictly speaking, it is not as wrong as the notion of the Earth as flat.

Even the oblate-spheroidal notion of the Earth is wrong, strictly speaking. In 1958, when the satellite Vanguard 1 was put into orbit about the Earth, it was able to measure the local gravitational pull of the Earth—and therefore its shape—with unprecedented precision. It turned out that the equatorial bulge south of the equator was slightly bulgier than the bulge north of the equator, and that the South Pole sea level was slightly nearer the center of the Earth than the North Pole sea level was.

There seemed no other way of describing this than by saying the Earth was pearshaped and at once many people decided that the Earth was nothing like a sphere but was shaped like a Bartlett pear dangling in space. Actually, the pearlike deviation from oblate-spheroid perfect was a matter of yards rather than miles and the adjustment of curvature was in the millionths of an inch per mile.
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Vanguard 1's observers thus measured the J3 part of Earth's gravity, what makes that pear-shaped effect, and J3 is about 2.54*10-6.
 
Looking at the other planets, Mercury has J2 and C22 around 10-5 and the largest others at around 10-6.

Venus has J2 and C22 around 10-3 and the largest others around 10-4 - 10-5.

Mars has J2 around 10-3 and the largest others around 10-4.

Vesta has J2 around 3*10-2 and the largest others around 3*10-3

Ceres has J2 around 10-2 and the largest others around 10-4. For Ceres, J2 and J4 are close to their hydrostatic-equilibrium estimates.

Jupiter has J2 around 10-2 and the largest asymmetric others around 10-7

Saturn has J2 around 10-2 and the largest asymmetric others around 10-6

-

Turning to the large moons,

The Earth's Moon has J2 and C22 around 10-4 with C22/J2 = 0.382, and the largest others around 10-5.

Io has J2 and C22 around 10-3 but was assumed to be in hydrostatic equilibrium, and the rest of its gravity coefficients were not calculated.

Europa has J2 and C22 around 3*10-4 with C22/J2 around 0.32, and with the largest others around 10-5, though with comparably-sized error bars.

Ganymede has J2 and C22 around 10-4 and Callisto around 3*10-5, and the other coefficients are within their error bars.

Enceladus has J2 and C22 around 3*10-3 with C22/J2 around 0.30, and the largest others are around 10-4

Dione has J2 and C22 around 10-3 with C22/J2 around 0.24, a departure from hydrostatic equilibrium, and the largest others are around 10-5.

Rhea has J2 and C22 around 10-3 with C22/J2 around 0.26, also a departure from hydrostatic equilibrium, and the largest others are around 10-5.

Titan has J2 and C22 around 3*10-5 with C22/J2 around 0.31, and the largest others are around 10-6.

-

JUICE and Europa Clipper should improve our knowledge of the gravitational fields of Europa, Ganymede, and Callisto, even if not necessarily Io.
 
For pure rotation, the lowest-order hydrostatic-equilibrium estimate for the flattening is

f = (3/2)*J2 + (1/2)*m

where m = w2 * R3 / (G*M)

and f = 1 - R(polar)/R(equatorial)

w = rotation angular velocity, R = radius, G = grav. const., M = mass

 Darwin–Radau equation - from the flattening, one can find an estimate of the moment of inertia:

I/(M*R2 = (2/3)*(1 - (2/5)*sqrt(1+x))

where x = (5*m)/(2*f) - 2

If one has J2, one calculates f from it, then x, and then I.

For a moon with tidally-locked rotation, one has to adjust J2 to give its pure-rotation value, by multiplying by (2/5).
 
ESA Operations on Twitter: "@ESA_JUICE @AirbusSpace BREAKING NEWS!
Well, deployment news ;) - @ESA_Juice boom deployments are complete!
With confirmation of the successful release of #ESAJuice's 4th Langmuir probe, here captured by one of the 🛰️'s onboard monitoring cameras, we declare Juice in full flight configuration 🏁🥳 (vid link)" / Twitter

Then,
ESA's Juice mission on Twitter: "🆕 With all deployments complete, Juice is fully stretched out and ready for cruising to Jupiter 🥳
Discover more details, GIFs and infographics, as well as science data from Juice's newly switched-on instruments 👉 (link)" / Twitter

ESA - Juice deployments complete: final form for Jupiter

The next big event will be flybys of the Moon and the Earth in August 2024. Yes, JUICE will fly close to the Moon for a gravity assist, about 1.5 days before flying by the Earth for another gravity assist.
 
Checking on the Darwin-Radau equation, I use some known solutions for a rotating object, working in lowest order in rotation effects.

First, m = w2*R3/(G*M) is (equator centrifugal force) / (gravitational force)

For constant density, f = (5/4)*m = 1.25 m, J2 = (1/2)*m = 0.5 m, and I = (2/5)*M*R2 -- it is exact.

For (pressure) ~ (density)2 -- a good approximation for Jupiter even if not its moons -- I find f = (15/(2*pi^2))*m ~ 0.760 m, J2 = ((15-pi^2)/(3*pi^2)*m ~ 0.173 m, and I/(M*R2) = (2*(pi^2-6)/(3*pi^2) )~ 0.261 (exact), 0.263 (Darwin-Radau)

For all the mass at the center, I find f = (1/2)*m = 0.5 m, J2 = 0, and I = 0 (exact), 2/15 ~ 0.133 (Darwin-Radau)


For constant density, one can find an exact solution to this problem to all orders, all powers of m. The body's shape is a triaxial ellipsoid, a full generalization of an ellipse to three dimensions. But the relative lengths of its axes are some rather complicated functions of m.

For pressure ~ density^2, one can find a solution as an infinite series in powers of m, but one has to find each coefficient from previously-found coefficients, and one either has to do a lot of computer algebra, or else one has to do the calculations numerically. If one uses computer algebra, one ends up with results that require a lot of cancellation when evaluated numerically.
 
Fortunately, others have used the Darwin-Radau formula on Jupiter's moons:  oment of inertia factor - C/(M*R2) - C = moment of inertia around the pole, M = mass, R = equatorial radius

For constant density, this is 2/5 = 0.4, and for pressure ~ density^2, (2/3)*(1-6/pi^2) ~ 0.261

Terrestrial planets:
Mercury 0.346(14), Venus 0.337(24), Earth 0.3307, Moon 0.3929(9), Mars 0.3644(5), Ceres 0.36(15)

Jovian planets:
Jupiter 0.2756(6), Saturn 0.22, Uranus 0.23, Neptune 0.23

Jupiter's moons:
Io 0.37824(22), Europa 0.346(5), Ganymede 0.3115(28), Callisto 0.3549(42)

Saturn's moons:
Enceladus 0.3305(25), Rhea 0.3911(45), Titan 0.341

From these numbers, Europa, Callisto, and especially Ganymede are largely rock underneath their ice, and those moons and Io may also have iron cores.
 
It's  Moment of inertia factor

The  Europa Clipper spacecraft is on its way. Its launch was delayed for a few days by Hurricane Milton, but was successfully launched atop a Falcon Heavy rocket.

NASA's Europa Clipper Launch - YouTube - from an hour before to an hour and a half later, ending at the acquisition of the first signal from the spacecraft after its separation from the second stage of its booster rocket.

So there are now two spacecraft on their way to Jupiter and its big moons: JUICE and Europa Clipper.

ESA - Juice - JUICE is doing well. It returned pictures of the Earth and the Moon from its recent flybys of those two celestial bodies.
Both spacecraft will be doing several gravity-assist flybys, like JUICE's recent one of the Earth.
  •  Jupiter Icy Moons Explorer 14 April 2023 -- Moon 19 August 2024 -- Earth 20 August 2024 -- Venus 31 August 2025 -- Earth 29 September 2026 -- Earth 18 January 2029 -- Jupiter orbit July 2031 -- Ganymede orbit December 2034
  •  Europa Clipper October 14, 2024 -- Mars March 1, 2025 - Earth December 3, 2026 -- Jupiter orbit April 11, 2030
 
Europa Clipper Solar Arrays Arrive at NASA for Jupiter Moon Mission – NASA's Europa Clipper Mission - February 21, 2024
Workers unloaded the five-panel solar arrays at the Payload Hazardous Servicing Facility. The solar arrays will attach to the spacecraft to power it on the 1.8-billion-mile journey to Europa. Strong evidence shows an ocean beneath Europa’s crust that is twice the volume of all the Earth’s oceans combined, and scientists want to determine if any areas can support life.

The solar array travelled by air from Leiden, Netherlands, where Airbus workers assembled them over the last year. Once at the Port of Miami in Florida, a truck transported the arrays to Kennedy.
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NASA’s Europa Clipper Mission Advances with Solar Array Deployment – NASA's Europa Clipper Mission - March 12, 2024
When both solar arrays are installed and deployed on Europa Clipper – the agency’s largest spacecraft ever developed for a planetary mission – the spacecraft will span a total length of more than 100 feet and weigh 7,145 pounds without the inclusion of propellants. The spacecraft needs the large solar arrays to collect enough light to power it as it operates in the Jupiter system, which is more than five times as far from the Sun as Earth.
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NASA’s Europa Clipper Makes Cross Country Flight to Florida – NASA's Europa Clipper Mission - May 24, 2024
It traveled aboard a US Air Force C-17 Globemaster III.
NASA Examines Electrical Switches on Europa Clipper Spacecraft – NASA's Europa Clipper Mission - May 31, 2024
After noting the radiation hardening of the spacecraft's power transistors (100 - 300 kilorads),
However, the mission team at NASA’s Jet Propulsion Laboratory in Southern California, which manages the mission, is assessing test data that indicates some transistors could be affected by significantly lower radiation levels in some conditions.
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NASA Installs High Gain Antenna for Mission to Study Icy Moon of Jupiter – NASA's Europa Clipper Mission - June 20, 2024
It is 3 m / 10 ft across
NASA Continues Assessing Electrical Switches on Europa Clipper – NASA's Europa Clipper Mission - July 11, 2024
NASA’s Europa Clipper Mission Moving Toward October Launch Date – NASA's Europa Clipper Mission - August 28, 2024
NASA’s Europa Clipper Continues Path to Launch – NASA's Europa Clipper Mission - September 9, 2024
NASA’s Europa Clipper mission passed a mission planning milestone, known as Key Decision Point E, on Monday. It now is approved to continue to proceed toward launch, with a launch period that opens Thursday, Oct. 10.
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Fueling Complete on NASA’s Europa Clipper Spacecraft – NASA's Europa Clipper Mission - September 25, 2024
Housed in the largest spacecraft NASA has ever built for a planetary mission, Europa Clipper’s propulsion module is an aluminum cylinder 10 feet (3 meters) long and 5 feet (1.5 meters) wide, and it holds the spacecraft’s array of 24 engines and 6067.6 pounds (2,752.2 kilograms) of propellant in two propulsion tanks, as well as the spacecraft’s helium pressurant tanks.
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The spacecraft's propellants are monomethylhydrazine, CH3HN-NH2 and nitrogen tetroxide, N2O4. These are common propellants for spacecraft, because they don't have to be kept very cold to stay liquid.
So one does not need to refrigerate these propellants, as one does for O2 and H2, and if they become too cold to be liquid, they can be heated, a much simpler operation.

NASA’s Europa Clipper Mated to Payload Adapter, Encapsulated – NASA's Europa Clipper Mission - October 4, 2024
Teams Hold Flight Readiness Review for NASA’s Europa Clipper – NASA's Europa Clipper Mission - October 4, 2024
NASA’s Europa Clipper Spacecraft Transported to Hangar – NASA's Europa Clipper Mission - October 4, 2024
NASA, SpaceX Secure Europa Clipper Ahead of Hurricane – NASA's Europa Clipper Mission - October 6, 2024
While Europa Clipper’s launch period opens Oct. 10, the window provides launch opportunities until Wednesday, Nov. 6.
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NASA Begins Post-Hurricane Milton Assessments at Kennedy – NASA's Europa Clipper Mission - October 10, 2024
NASA, SpaceX Targeting NET Oct. 14 for Europa Clipper Launch – NASA's Europa Clipper Mission - October 11, 2024
NASA, SpaceX Set Launch Readiness Review for Europa Clipper Mission – NASA's Europa Clipper Mission - October 12, 2024
Teams stood down from a potential launch opportunity on Oct. 13, to double-check technical readiness of the Falcon Heavy rocket, as well as continued assessments for launch readiness following Hurricane Milton.
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NASA, SpaceX Complete Europa Clipper Mission’s Launch Readiness Review – NASA's Europa Clipper Mission - October 13, 2024
 
Live Coverage for NASA’s Europa Clipper Begins – NASA's Europa Clipper Mission - October 14, 2024
Weather Extremely Favorable for Today’s Launch – NASA's Europa Clipper Mission
NASA’s Europa Clipper Mission: Investigating an ‘Ocean World’ – NASA's Europa Clipper Mission
I once found a paper that discussed estimates of the thickness of Europa's crust -- a wide range of them, a result of different assumptions and different methods.
Key Milestones for Today’s Europa Clipper Launch – NASA's Europa Clipper Mission - with the schedule of events
Meet NASA’s Europa Clipper Spacecraft – NASA's Europa Clipper Mission
Europa Clipper’s electronics are enclosed in a vault with walls made of 1/3-inch-thick (9.2-mm) sheets of aluminum-zinc alloy to protect the electronics from Jupiter’s intense radiation. These electronics include computers (or the “brains” of the spacecraft), flight software, and more.

The vault plate, made of tantalum metal about 1 millimeter thick and about 7 by 11 inches (18 by 28 centimeters), is part of the structure that will protect Europa Clipper’s electronics from Jupiter’s harmful radiation. It is engraved with poetry, artwork, and other messages that pay tribute to the connection between Europa’s ocean world and our own. It also carries a dime-size microchip stenciled with more than 2.6 million names submitted by the public.

...
Europa Clipper carries pumps that circulate fluids through pipes to all the spacecraft’s sensitive electronics, carrying heat from hot spots to cold spots. Europa Clipper also has temperature sensors, heaters, blanketing, and a radiator with louvers that can be opened to shed heat to help regulate the spacecraft’s temperature.
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NASA’s Europa Clipper Science Instruments – NASA's Europa Clipper Mission

Both JUCE and EC have a variety of instruments. Both of them have infrared, visible-light, and ultraviolet cameras and spectrometers, some of them combined, both have magnetometers and plasma-environment sensors, both have radars, and both of them will do radio science for probing the moons' gravity. EC will additionally analyze dust and gases.

NASA Begins Live Broadcast of Europa Clipper Mission – NASA's Europa Clipper Mission
First Stage Fueling Started – NASA's Europa Clipper Mission
The first stage has a central part and two side parts; the side boosters helped launch the Psyche spacecraft last year.
NASA’s Europa Clipper Mission: By the Numbers – NASA's Europa Clipper Mission
Second Stage Fueling Started – NASA's Europa Clipper Mission
‘In Praise of Mystery: A Poem for Europa’ – NASA's Europa Clipper Mission
Noting In Praise of Mystery: A Poem for Europa | Poet Laureate Projects | Poet Laureate | Poetry & Literature | Programs | Library of Congress
Arching under the night sky inky
with black expansiveness, we point
to the planets we know, we

pin quick wishes on stars. From earth,
we read the sky as if it is an unerring book
of the universe, expert and evident.

...
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It would be nice to compose such a poem in some rhythmic style -- rhyme, alliteration, poetic meter (patterns of stressed and unstressed syllables), parallelism. Like this, from Friedrich Schiller's  Song of the Bell - both the original Latin and my revision of that article's English translation:
Vîvôs vocô
Mortuôs plangô
Fulgura frangô

I call the living
I mourn the dead
I break the lightning
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Parallelism in both content and grammar.
 
Weather Remains Favorable – NASA's Europa Clipper Mission
NASA Launch Manager Gives ‘Go’ for Launch – NASA's Europa Clipper Mission
Because Europa Clipper needs a lot of energy to start it on its interplanetary trajectory to Jupiter, the rocket for this launch will be fully expendable, with the exception of a recoverable fairing. This means that there will be no return of first-stage boosters for this launch.

...
In addition to not recovering any boosters, technicians removed components only needed for reuse to increase the performance of the rocket, to launch the largest planetary spacecraft NASA has ever developed and give it the power it needs to travel to Jupiter.
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Liftoff of NASA’s Europa Clipper! – NASA's Europa Clipper Mission
Rocket Reaches Max Q, Booster Engines Cutoff, First Stage Separation – NASA's Europa Clipper Mission
Second Stage Engine Cutoff Reached – NASA's Europa Clipper Mission
BECO = Booster Engine Cutoff, MECO = Main ..., SECO = Second-stage ..., TECO = Third-stage ...
Orbit Departure Burn Coming Up – NASA's Europa Clipper Mission
NASA’s Europa Clipper Spacecraft Separates From Falcon Heavy Second Stage – NASA's Europa Clipper Mission
Signal Acquired – NASA’s Europa Clipper Begins Journey to Jovian System – NASA's Europa Clipper Mission
Solar Arrays on NASA’s Europa Clipper Fully Deployed in Space – NASA's Europa Clipper Mission
Successfully unfolded.

Also Liftoff! NASA’s Europa Clipper Sails Toward Ocean Moon of Jupiter - NASA
 
lpetrich said:
The spacecraft's propellants are monomethylhydrazine, CH3HN-NH2 and nitrogen tetroxide, N2O4. These are common propellants for spacecraft, because they don't have to be kept very cold to stay liquid.
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And because they are hypergolic - they ignite spontaneously when mixed, so you don't need an igniter.

They are horribly toxic, as are their combustion products (which include Nitric Acid), but in space that's not a big deal, because anyone who is trying to breathe in or above low Earth orbit has bigger problems than a few toxic fumes. The guys who fuel up the spacecraft have to be very careful, of course.
 
  • 2023 Apr 14 - JUICE launch
  • 2024 Aug 19, 20 - JUICE Moon, Earth flybys
  • 2024 Oct 14 - EC launch
  • 2025 Mar 1 - EC Mars flyby
  • 2025 Aug 31 - JUICE Venus flyby
  • 2026 Sep 29 - JUICE Earth flyby
  • 2026 Dec 13 - EC Earth flyby
  • 2029 Jan 18 - JUICE Earth flyby
  • 2030 Apr 11 - EC Jupiter orbit
  • 2031 Jul - JUICE Jupiter orbit
  • 2034 Dec - JUICE Ganymede orbit
 
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