Can a Planet Have a Moon that Never Casts a Shadow?

[mincam]

TL;DR Summary

Can the shadow of a moon never touch it's planet?

I am a newbie, and really uninformed (read stupid.)

Here is my question: Would it be possible for the Earth (or any planet,) to have a moon whose orbit was such that it never came between the sun and the Earth?

In other words, could we have a moon that never cast a shadow on the Earth? Or is it inevitable that sometime during a year a moon must cast at least a partial shadow on its planet?

Here is what I am thinking: "If the moon's orbital plane rotates along with the planet, the moon will always cast a shadow on the planet some time or other; however, if the moon's orbital plane is stationary and does not rotate along with the planet, it is quite possible that the moon will never cast a shadow on the planet. (For example say the moon's orbital plane always faces the sun, then no shadow on planet. Impossible?) But darned if I know which case is true, although my Earthly experience should make the answer obvious - so I'm goin' with always a shadow. But I'd like to be wrong."

I have no clue about terminology, so I may be using the wrong words. And I am not talking about eclipses, any part of the shadow touching the planet will do (or not.)

In other words, I guess, "Can a planet have a moon that never comes between it and the sun?"

 

[DrStupid]

That could be possible if the orbit of the moon has a high inclination and is in resonance with the orbit of the planet. However, I do not know how stable such an orbit would be in the long term.

 

[PeroK]

I have no clue about terminology, so I may be using the wrong words. And I am not talking about eclipses, any part of the shadow touching the planet will do (or not.)

In other words, I guess, "Can a planet have a moon that never comes between it and the sun?"

Here's something on the terminology re the moons of Jupiter:

https://en.wikipedia.org/wiki/Solar_eclipses_on_Jupiter

It says the transits of some moons are rare, but it suggests they all must transit at some point.

 

[Halc]

Due to tidal interactions, any resonance is temporary and shadow must eventually cross its planet.

Would it be possible for the Earth (or any planet,) to have a moon whose orbit was such that it never came between the sun and the Earth?

In other words, could we have a moon that never cast a shadow on the Earth?

The wording of this question suggests a shadow cast on Earth, not one cast on the planet around which it orbits. That of course can never occur for anybody further from the sun than is Earth.

As for the two known objects within that radius (Mercury and Venus), those are both too small to fully eclipse the sun from this distance and thus do not cast distinct shadows on Earth at all just like the shadow of Earth never falls on anything except the moon and perhaps Mars which is small enough and close enough.

 

[256bits]

Summary:: Can the shadow of a moon never touch it's planet?

I have no clue about terminology, so I may be using the wrong words.

Some terminology - look up Umbra, Penumbra
https://en.wikipedia.org/wiki/Umbra,_penumbra_and_antumbra

 

[Andy Resnick]

Summary:: Can the shadow of a moon never touch it's planet?

I am a newbie, and really uninformed (read stupid.)

Here is my question: Would it be possible for the Earth (or any planet,) to have a moon whose orbit was such that it never came between the sun and the Earth?

The orbits of several moons of Uranus are nearly 90 degrees with respect to the orbital motion- Uranus's equator is oriented nearly 90 degrees relative to the orbital motion- and so those shadows never touch the planet, AFAIK.

 

[Halc]

The orbits of several moons of Uranus are nearly 90 degrees with respect to the orbital motion- Uranus's equator is oriented nearly 90 degrees relative to the orbital motion- and so those shadows never touch the planet, AFAIK.

But twice per the Uranian* year the plane of the orbit of those moons must cross the sun, and at that time, if the moon is in the correct place in its orbit, a shadow will be cast.

* Had to look that word up. What sprung immediately to mind was 'Urinal year'.

 

[Andy Resnick]

But twice per the Uranian* year the plane of the orbit of those moons must cross the sun, and at that time, if the moon is in the correct place in its orbit, a shadow will be cast.

* Had to look that word up. What sprung immediately to mind was 'Urinal year'.

Good point. However, if such a planet was tidally locked to its sun (Uranus is not), then the sun always illuminates one pole and the orbiting moons will never cast a shadow on the planet's surface.

 

[hutchphd]

This is intrinsically a three body problem, assuming the sun (light source) has mass. I do not think the "polar locked orbit" is a known stable solution to the three body problem. If you expect me to know more, you will be disappointed!

 

[Halc]

Good point. However, if such a planet was tidally locked to its sun (Uranus is not), then the sun always illuminates one pole and the orbiting moons will never cast a shadow on the planet's surface.

If it was tidally locked, its spin axis would match its orbital axis and one side (not the pole) would be permanently illuminated. What shadows are thrown on it have nothing to do with the planet spin and everything to do with the orbital plane of the moon throwing the shadow, and that plane must cross the sun twice each year regardless of the inclination of that orbit or whether the moon is spinning relative to the planet or if the orbital axis of the moon happens to be close to the spin axis of the planet.

This is intrinsically a three body problem, assuming the sun (light source) has mass. I do not think the "polar locked orbit" is a known stable solution to the three body problem. If you expect me to know more, you will be disappointed!

3 body problem assumes point masses and the spin of anything doesn't really play a role. So the 3 body problem, dealing with unstable arrangements of point masses, has no concept of stable orbits or spin. All the bodies in the solar system can be approximated as 2-body simplifications and thus has long term stability that a true 3-body system does not. For instance, the Earth/moon system can be treated as one body as far as the rest of the solar system is concerned. In the long run, this doesn't work since the mass all do effect each other a little, so predicting the position of the bodies 10 million years from now isn't just a matter of dividing by their periods and measured recession rates.

I don't think it is possible for an orbiting thing to be tide locked and have a spin axis that differs from its orbital axis. I could be wrong... Is a wobble possible? It seems not since any wobble on a different axis would set up a gyroscopic resistance to keeping one face towards the primary. The apparent wobble of our moon is due to the eccentricity of its orbit and not due to its spin axis being different than its orbital axis. The moon's spin/orbital axis does not align with Earth's spin axis nor Earth own orbital axis.

Mercury is in a wonderfully resonant tide-locked relationship with the sun where its spin is exactly 1.5 times its orbital period and will stay that way until the sun manages to bleed away the energy of its eccentricity until the tide-lock is broken and it can resume slowing its spin.

Venus is another gem, which is scheduled to stop spinning altogether eventually, and then start spinning again back up to approximately the rate is has now, but in the other direction. It will likely be swallowed before the latter happens, but maybe not. I didn't check.

 

[DaveC426913]

...that plane must cross the sun twice each year

The plane must - that doesn't mean the moon must be there when it does.

 

[jim mcnamara]

Hubble answers the Uranus question with a picture. The answer is Ariel does cast a shadow, see cool picture.:
https://hubblesite.org/contents/media/images/2006/42/1984-Image.html?news=true

 

[Halc]

The plane must - that doesn't mean the moon must be there when it does.

Per my reply in post 4, it must eventually be there. Our own moon does now and then, but most (~2/3) of the time the shadow misses the Earth. The chance of it hitting on a given instance of the orbital plane crossing is a function the orbital period of the moon and the duration needed for the 'shadow' of the moon's orbital path to cross the planet which is pretty dang slow for something as far out as Uranus. Resonance might keep the moon from being in the right place for millennia at a time, but the orbital period will eventually change, so said resonance is temporary. The shadow must eventually hit the planet.

 

[DaveC426913]

The shadow must eventually hit the planet.

But you're betting that. It's not fait accomplii that it "must" physically happen. It's just highly likely as time passes.

This is not me being pedantic: it depends on how literally the OP means the terms "never" and "is it possible" in his opening question.I'd say the appropriate answer to the OP is "the probability it won't cast a shadow approaches zero as time passes".

 

[Halc]

It's not fait accomplii that it "must" physically happen.

It isn't a random process. If it was, I'd agree with you.

 

[DaveC426913]

It isn't a random process. If it was, I'd agree with you.

I'm not suggesting it is.

I just think it's not true until it's true.

The OP doesn't seem to be looking for an answer with "likely".

 

[Halc]

It's like a roll of 5000 sheet toilet paper. Draw one line from the center to the edge. The odds of one of the perforations getting within a mm of that line is a certainty, not a high probability, especially if the paper is very thin, but not infinitely thin.
If the paper is resonant with the radius, then all the perforations line up for a while, but as the radius changes, they very slowly start moving left or right at a regular interval that is far less than the mm, so some perforation must end up at the selected line (which represents the direction of the sun).
If the paper is not resonant, then the perforation lines will fill space evenly, never in a place where some previous perforation was. That also must leave no significant gaps.
The perforations are the position of the moon at each successive crossing of sun and the orbital plane.
Infinitely thin paper represents zero tidal effect, and a moon that causes zero tidal drag and is in perfect resonance is very capable of never throwing a shadow, but it must be zero tidal effect, which is impossible even for locked orbits such as between Pluto and Charon.

 

[DaveC426913]

It's like a roll of 5000 sheet toilet paper. Draw one line from the center to the edge.

It took me six reads to get what you were describing.

This is what I got from your description:

But of course, you meant this:

If the paper is resonant with the radius, then all the perforations line up for a while, but as the radius changes, they very slowly start moving left or right at a regular interval that is far less than the mm, so some perforation must end up at the selected line (which represents the direction of the sun).
If the paper is not resonant, then the perforation lines will fill space evenly, never in a place where some previous perforation was. That also must leave no significant gaps.
The perforations are the position of the moon at each successive crossing of sun and the orbital plane.
Infinitely thin paper represents zero tidal effect, and a moon that causes zero tidal drag and is in perfect resonance is very capable of never throwing a shadow, but it must be zero tidal effect, which is impossible even for locked orbits such as between Pluto and Charon.

That's a good explanation for the OP to understand how - despite stacking the deck against it with a contrived scenario - it is still a certainty that the sat will cast a shadow - given sufficient time.

 

[PeroK]

But you're betting that. It's not fait accomplii that it "must" physically happen.

If I'm being pedantic, it's fait accompli: a French phrase commonly used to describe an action which is completed before those affected by it are in a position to query or reverse it.

I guess in this case un fait certain, would be better.

 

[snorkack]

Earth has a lot of satellites that never come into Earth´ s shadow:
https://en.wikipedia.org/wiki/Sun-synchronous_orbit