The moons are lovely...

So, you look up at the night sky and see the moon. Lovely, isn't it? As in uffish thought I stood, I started thinking about the Jovian moons.

If you were standing on the surface of Jupiter* and looking up, what would the Jovians look like? I would assume that Ganymede would have a familiar disk, being larger than Mercury. But looking up at Io, Europa, and Ganymede together*, would you see different disks? Would there be a notable difference between Io and Europa as Io is closer but they are similar in size?

I guess my real question is that is it at least plausible with physics that you can look up and see three different sizes of moon, or would it be an interesting happenstance that the moons because of their size and resultant distance that they happen to look mostly the same, disk-wise?

Posted here since it's actually a detail for a game, and not a wholly random musing.

* Not on the surface-surface; on the visible cloud cover, hovering, in my orbital platform with an unobstructed view of the heavens. Roll with it.

* Yes, I know you can't see the three of them at the same time. Keep rollin'.
 

Celebrim

Legend
There are mostly much further from Jupiter, than Luna is from Terra. Ganymede for example is three times further from Jupiter than our moon is from Earth. Also, it's a bit of an optical illusion how large the moon appears. The eye perceives it as larger than it is just because it is so bright. You get a good feel for the true size of the moon without any illusion during a lunar eclipse. As such, the crescents that they produce would appear much smaller than that of Luna.

I remember having seen pictures that simulated the view of the moons you are imagining, but I don't at all remember where I've seen them.
 
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ninjayeti

Explorer
Angular size is inversely proportional to distance. So pulling numbers off the this site and doing rough calculations:

Io would appear slightly smaller than the moon appears from Earth
Europa and Ganymede would both appear roughly half the size of our moon
Callisto would be about a quarter size our moon

As they all have different periods, I imagine there would be times when you could see all of them at once.
 

Umbran

Mod Squad
Staff member
So, you look up at the night sky and see the moon. Lovely, isn't it? As in uffish thought I stood, I started thinking about the Jovian moons.

If you were standing on the surface of Jupiter* and looking up, what would the Jovians look like? I would assume that Ganymede would have a familiar disk, being larger than Mercury.
So, quick calculation:

From Jupiter, Ganymede takes up about 0.3 degrees of arc in the sky.

The Moon, seen from Earth, takes up about 0.5 degrees of arc.

So, Ganymede is a disk, but smaller than the moon.

I guess my real question is that is it at least plausible with physics that you can look up and see three different sizes of moon, or would it be an interesting happenstance that the moons because of their size and resultant distance that they happen to look mostly the same, disk-wise?
It would be quite a coincidence that they all happen to look mostly the same. But, coincidences do happen. For example, we just happen to live at a time when the Sun and our own Moon just happen to be the same size in the sky.
 
Given the relatively large radius of Jupiter compared to the orbital radii of the innermost big moons (roughly 20%, I think?), I wonder if those moons would change appreciably in apparent size (and brightness) from moon-rise to zenith? Would Io appear to "fall" toward the observer as it rises in the sky, then recede back over the horizon? (On earth, we have the illusion of the Moon being huge when it's low near the horizon, and small when overhead. Would the visual effect be reversed on Jupiter?)

I also imagine the moons go in and out of Jupiter's shadow quite frequently, so lunar eclipses wouldn't be as special as they are for us. How often would "full" moons even occur compared to eclipses? Perhaps the full moons would be the special events?

Fun questions to think about....


(Also, the word "Io" is a compelling standalone argument in favor of serifed fonts, imho.)
 
Okay. So there isn't any particular correspondence or correlation between a moon's size, orbital distance, and apparent size from the planet's perspective. Good to know.

If the moon is 0.5 degrees of arc, I gather that 0.05-0.1 would be getting close to the point of seeing a disk rather than a star-like point.

Actually, due to the 1:2:4 harmony with the inner three moons, you can only see two of them at a time, as I understand it. When two would be above you, the third is at least a quarter orbit away. Callisto isn't in orbital resonance with the other moons, so she's doing her own thing. So, you could see three out of four at a time.

I take it that any such equations to determine disk size are readily found... Now, to repair the 3D printer!
 

Umbran

Mod Squad
Staff member
Okay. So there isn't any particular correspondence or correlation between a moon's size, orbital distance, and apparent size from the planet's perspective. Good to know.
Um... the apparent size is determined by the actual size and the orbital distance.

Other than the Roche Limit there is no particular correspondence between the moon's size and its orbital distance.

The Roche limit is a limit on the orbital radius of large smoons - if a large satellite gets too close to its parent body, the satellite will be ripped apart by tidal forces. You will not find very large moons very close to the planet, as they get ripped apart.

If the moon is 0.5 degrees of arc, I gather that 0.05-0.1 would be getting close to the point of seeing a disk rather than a star-like point.
Human visual acuity can't generally make out any shape at under about 0.02 degrees - roughly the size of hte Intenational Space Station seen from the ground. Anything smaller than that is just a point. Larger than that, you go from a point to a dot, to a spot, to a disk. I don't know if there's an agreed upon limit when something gets called a "disk".

I take it that any such equations to determine disk size are readily found...
To quote WIkipedia on Angular Diameter:

1581352243125.png



delta = 2arctan(d/2D)
 
Um... the apparent size is determined by the actual size and the orbital distance.
Right. I meant that it's individual, and moons of different masses won't arrange themselves so that they look the same. Smaller ones aren't necessarily going to move closer and large move farther away.

Thanks for the further details!
 

Beleriphon

Totally Awesome Pirate Brain
Not that this is relevant to Jovian moons, but it is relevant to D&D:


First graphic shows our Moon to the actual described sizes of Eberron's moons. Later on there is a graphic of their apparent size compared to our Moon. Zanatyr for example is roughtly half the size of Earth's moon, but would appear to be 9 times larger in comparison.
 

Umbran

Mod Squad
Staff member
First graphic shows our Moon to the actual described sizes of Eberron's moons. Later on there is a graphic of their apparent size compared to our Moon. Zanatyr for example is roughtly half the size of Earth's moon, but would appear to be 9 times larger in comparison.
I think there's an issue in the calculations.

The radius of an orbit is typically given from center of the parent body to the center of the satellite.

The apparent size of the satellite is determined by the distance from the viewer, to the center of the satellite.

The "D" in the equations above, then, is the radius of the orbit minus the radius of the PARENT body.

So, we note that in the discussion of Zarantyr, we'd need to know the radius of Eberron, not the radius of Zarantyr.

Mind you, usually, in the real world, the orbital distance is very large compared to the radius of the Parent body. For example, the radius of the Moon's orbit is something like 60 times the radius of the Earth - if you just neglected the Radius of the Earth, your D would be off by less than 2%.

If you are looking for a ballpark - just use the Orbital radius, and never mind the rest.
 

Beleriphon

Totally Awesome Pirate Brain
Mind you, usually, in the real world, the orbital distance is very large compared to the radius of the Parent body. For example, the radius of the Moon's orbit is something like 60 times the radius of the Earth - if you just neglected the Radius of the Earth, your D would be off by less than 2%.

If you are looking for a ballpark - just use the Orbital radius, and never mind the rest.
I recall correctly, the same blog has another post about the planet and just assumes it is more or less the same size as Earth.
 

Umbran

Mod Squad
Staff member
I recall correctly, the same blog has another post about the planet and just assumes it is more or less the same size as Earth.
Yes, but if you review the actual numbers above, they are pretty clearly using the satellite's radius.
 

Umbran

Mod Squad
Staff member
I'll have to take your word on it, I'm no astronomer.
It isn't a matter of astronomy. It is a matter of arithmetic.

Zarantyr, the first of Eberron’s moons, has a diameter of 1250 miles, or 2.0117x10^6 meters, while it has a mean distance from Eberron of 14,300 miles, or 2.3014x10^7 meters. The distance to the center of Zarantyr is then the mean distance plus half the diameter, which is 2.4019x10^7 meters. We can then plug our values into the equation.
He gives the diameter of Zarantyr. He gives a mean distance to Eberron.

If you take half the diameter of Zarantyr he gives, and add it to the mean distance to Eberron, you get the 2.4019x10^7 meters. That... includes a rounding error on his part as well.

Now, when I review these numbers in detail... woof!

So Zarantyr has a diameter of 1250 miles. Earth's Moon has a diameter of about 2160 miles. The Moon is on the order of twice as big across as Zarantyr.

Zarantyr is 14,300 miles from Eberron. That is absurdly close. Earth's Moon is 239,000 miles away. So, our Moon is nearly 20 times farther away from Earth as Zarantyr is from Eberron.

If I have much numbers right.... If we assume Eberron is Earth-mass, and Zarantyr has a density like our Moon...... Zarantyr is inside the Roche limit for the pair... and by normal physics would be ripped apart by tidal forces.

So, there's that....

 

Beleriphon

Totally Awesome Pirate Brain
Zarantyr is 14,300 miles from Eberron. That is absurdly close. Earth's Moon is 239,000 miles away. So, our Moon is nearly 20 times farther away from Earth as Zarantyr is from Eberron.

If I have much numbers right.... If we assume Eberron is Earth-mass, and Zarantyr has a density like our Moon...... Zarantyr is inside the Roche limit for the pair... and by normal physics would be ripped apart by tidal forces.

So, there's that....
I know the numbers are straight from an article about Eberron's moons from WotC, so take that as you will. I think it's safe to assume that Eberron's moons are not the same density as our own.
 

Umbran

Mod Squad
Staff member
I know the numbers are straight from an article about Eberron's moons from WotC, so take that as you will. I think it's safe to assume that Eberron's moons are not the same density as our own.
Yeah, but it is several thousand miles inside the limit. 14,000 miles is really close. It is less than the circumference of the Earth! You have three basic optiosn for composition - ice, rock, or rock and iron. Even if the thing is made out of even ice... aside fromteh out-gassing from heating in the sun.... I think the tidal action on Eberron is apt to be devastating. No coastal cities for you!

It is less about density at that point, and more about how our laws of physics don't apply at all. Which is okay.
 

Raduin711

Explorer
So what kind of effect would having multiple moons... or no moons... have on the ocean?

Would we even have tides without a moon?

And having multiple moons would make the tides unpredictable (or at least, less predictable) which would probably have some negative effects on maritime travel...

But this is all based on common wisdom which isn't always that trustworthy.
 

doctorbadwolf

Heretic of The Seventh Circle
Yeah, but it is several thousand miles inside the limit. 14,000 miles is really close. It is less than the circumference of the Earth! You have three basic optiosn for composition - ice, rock, or rock and iron. Even if the thing is made out of even ice... aside fromteh out-gassing from heating in the sun.... I think the tidal action on Eberron is apt to be devastating. No coastal cities for you!

It is less about density at that point, and more about how our laws of physics don't apply at all. Which is okay.
Clearly, it just needs the same treatment as Eberron’s population numbers. Add one or more zeros.
 

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