Would it be possible for an earth-sized planet to have two moons, with the smaller inside the orbit of the larger, and each moon have sufficient apparent diameter to eclipse the parent star and the smaller, inner moon have sufficient apparent diameter to eclipse the larger moon?

For the sake of argument, I presume a sunlike (G or F) star with the planet positioned in the 'habitable' zone (so that there could be an observer to see the apparent diameter and be awed).

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"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.

BTW - I'd be perfectly happy to work this out on my own if anyone could give me the formulae - or tips on where to find the info.

Thanks

__________________
Talent develops in quiet places, character in the full current of human life.
- Goethe

Jump in with both feet!
- Me, indulging my inner eight-year-old

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"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.

Formula? Use trig.

BTW, do you need totality, such that the umbra extends to the surface of the planet for some unit of area?

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"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

Well, see that's my problem. I never took trig. In fact, were it not for a "business calc" course in college I'd have no maths past HS Algebra II. 20 years later, I'm suddenly interested...

This question came after I read about Mars' moons and about an upcoming eclipse the same day.

I guess I'd say (for the sake of argument, and if I understand your question) an umbra similar to the moon's on earth. (Never thought about the umbra: Just learned something from your question, thanks!).

__________________
Talent develops in quiet places, character in the full current of human life.
- Goethe

Jump in with both feet!
- Me, indulging my inner eight-year-old

*** *** ***

"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.

The problem is probably in checking the stability of the resultant system. One could for instance, get the effect you want by placing an object half the size of the moon at half the distance from Earth, but I doubt if it would be stable under the perturbing force of the "original" moon.
So maybe a tenth the size of the moon at a tenth of the distance? That would have a period shorter than a day, I reckon, so would evolve inwards tidally.
So maybe something between those extremes would be best.

To a first approximation, our new satellite would raise tides the same height as the moon's: the tide-raising force varies as the inverse cube of the distance, but the mass varies as the cube of the radius (assuming constant density). Since we require distance and radius to retain lunar proportions (so that we can have eclipses), the tides should therefore stay the same, unless our new moon is considerably different in density from the original.

Grant Hutchison

By the way:Heh. All these years I was hoping to get into a sig because of something I said.

Grant Hutchison

Okay, take the diameter of the object and divide it by the distance to the object, then take your trig calculator (you can use the scientific calculator that comes with Windows) hit inverse then hit tan (tangent) and you'll get the angular diameter (disc size) in degrees. It may not be the actual or most precise formula, but it will give you a close approximation.

I never got beyond algebra II either, but there was trig in that algebra.

__________________
"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

Well your response
was apt and amusing. However, it would require some context for others to appreciate the humor (and restraint).



---Thanks AP & GH for your responses: I'll take some time at my lunch hour to see if I can figure this out.

__________________
Talent develops in quiet places, character in the full current of human life.
- Goethe

Jump in with both feet!
- Me, indulging my inner eight-year-old

*** *** ***

"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.

Am I correct in assuming that if I want to have a stable system I need to determine the Roche limit to find the minimum distance of the inner moon?



...



Although, considering Mars' inner moon is not 'stable' does stability really matter? If the inner moon were in an instable orbit under which it would eventually spiral in - but take say, a billion years or more to do so, am I correct in presuming an observer on my ficticious planet coulde evolve to see the double eclipse?

Either way, I still need to know the Roche limit of the parent satellite for the moon to maintain cohesion, correct?

__________________
Talent develops in quiet places, character in the full current of human life.
- Goethe

Jump in with both feet!
- Me, indulging my inner eight-year-old

*** *** ***

"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.

Well, that wasn't what I meant about stability, though obviously you wouldn't want to have your inner moon within the parent's Roche limit.
I was thinking that our moon is a fairly massive perturbing influence, and could be expected to disrupt the orbits of objects in nearby orbits. There are some rules of thumb to work out the stable zones, though, which I should be able to dig out.

As for tidal evolution, IIRC, this goes a bit faster around Earth than it does around Mars, because of all that water sloshing around. Again, there are OOM calculations that I should be able to find in the files.

I'm not going to have access to the info until tomorrow, though.

Grant Hutchison

Should I determine the diameter of the sunlike star* and the distance of the planet first to give me the conic section the moons will need to fit?


*I'm probably going to try to set the equations up in Excel <if I can> - because I like to play around with the variables and see what happens under different conditions*

__________________
Talent develops in quiet places, character in the full current of human life.
- Goethe

Jump in with both feet!
- Me, indulging my inner eight-year-old

*** *** ***

"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.

It's all simple ratios: the diameter and distance of the moon(s) need to be in the same ratio as the diameter and distance of the star. For instance, with reference to Earth, the moon is 400 times closer and 400 times smaller than the sun: hence the neat match in apparent diameters.

Grant Hutchison

There's probably a way to work backwards with trig, but I forget how. It's been a long time. I had to look up that other trig formula when I was inventing a fictional planetary system a couple weeks ago for a story I'm writing.

__________________
"What you think you thought you saw you did not see." Agent J, MiB - Manhatten Bureau

This was my pretty much my thoughts as well. (Although, it turns out 1/10 puts you just above geostationary orbit, which I presume is stable, but not very satisfying for a technological society that can't have geostationary communications satellites.)

But I was sufficiently interested to check the details, and for the sake of giving DyerWolf as complete an answer as we can manage, so I've hacked my N-body code into a crude Earth-satellite(s) model. It's not going to win any prizes for accuracy, but it's good enough to give a yes/no answer to the question 'is it stable?'. I'll see how long I can run it and then post the results, if anyone's interested.

I'm thinking that you may be mixing geosynchronous altitude with geosynchronous radius.
A tenth of the lunar distance is 38440km. Geosynchronous radius is 42160km. So a tenth of lunar distance is inside geosynchronous radius, meaning that tidal evolution will be directed inwards.
Such an orbital radius is "stable" for low-mass objects over the lifespan of civilizations. But put something one thousandth the mass of the moon there, and it can evolve inwards pretty quickly, in geological terms, because the tidal evolution time scale is inversely proportional to the satellite mass (which is of course what drives the tides in the parent body). Plugging in a thousandth lunar mass at a tenth lunar distance, I get impact with the surface of Earth on the timescale of a million years.

Looking forward to the results of your simulation!

Grant Hutchison

Geez, you're right, I can't believe I did that. (Well, actually, I can...) Thanks! Serves me right for not doing it properly.

(Oh, 's worth noting I really did mean geostationary, rather than geosynchronous, though - I couldn't be bothered messing around with significant inclinations, and the question was Earth-like, not our actual system.)

Fair enough. I just use "geosynchronous" out of force of habit, unless I specifically want to talk about a stationary orbit, for some reason.

Grant Hutchison

Sure. Happens on Jupiter all the time.

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Thanks. I know that Jupiter's moons occult one another, but I meant eclipse in the sense that all three 'celestial' objects have the same apparent diameter.

The next part questioned whether an earth-sized planet could sustain such a lunar system within the star's habitable zone. At Jupiter's distance from a G- or F-type star, the apparent stellar-diameter allows for fairly small moons that meet the criteria. Within the habitable zone, the moons would have to be fairly large (I'm presuming).

So while I can imagine the system easily, I didn't/don't know enough to determine whether the system is possible/stable. If it is, I think it would be fun to know how large & massive the moons would be, and what effect there would be on the tides (i.e. would the surf be better there, or here?).

Cress - I'm very interested in what your simulation shows. Thanks!

__________________
Talent develops in quiet places, character in the full current of human life.
- Goethe

Jump in with both feet!
- Me, indulging my inner eight-year-old

*** *** ***

"Are you a mad-hatter that just types what he wishes, or have you actually any physics training?"
Occam's Ghost to Grant Hutchison.