# SolvedWill the Planets Ever Align?

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#### spacelover175

##### Guest
will the planets ever align all 9

( i got in a huge argument that they would not so i was asking you part of my debate if you saw my other thread

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#### MeteorWayne

##### Guest
It depends on what you mean by "align"

Will all the planets ever be in a straight line from the sun out to space? No

Will all the planets ever be on the same side of the sun at one time? Probably.

Will all the planets ever be right next to each other in our visible sky?

No.

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#### BoJangles2

##### Guest
Hrm, I’ll take a shot at this, though I’m not sure how accurate it will be.

From a permutation perspective, you would times the orbital periods of all the planets together.

To make the maths easier let’s assume all the planets had orbital eccentricities of 0 (i.e. perfectly circular orbits) and the planets weren’t gravitationally affecting each other

Mercury * Venus * Earth * Mars * Jupiter * Saturn * Uranus * Neptune

0.24 * 0.62 * 1 * 1.88 * 11.86 * 29.46 * 84.01* 164.8 = 1,353,214

A full alignment would happen every 1,353,214 years, maybe....

Disclaimer: I'm no expert, and MW knows better

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#### spacelover175

##### Guest
the reason I don't think they will is that if they stay to there rotation plus or minus a few 1000 miles they wont ever align

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#### MeteorWayne

##### Guest
My answer is the most correct, although Bo's calculations deserve some thought.

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#### neilsox

##### Guest
As the others suggested, it depends on how you define alignment and how long is ever. I'll guess about five times per 100 trillion (million times 100 million) years if alignment is plus or minus ten million miles for 8 planets. Neil

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#### Shpaget

##### Guest
MeteorWayne":1pyh7cbn said:
My answer is the most correct, although Bo's calculations deserve some thought.
Of course it does, but he forgot to include orbital inclination of planets. So, the calculation is valid only if you consider alignment as planets aligning in the same plane, but not in the same line.
So, to see if they will ever (by ever I mean in the entire future of universe) you need to see if there is one line you can draw from sun and intersect all orbits. If you can't, there will never be alignment.

Why do you think planet will never be right next to each other in visible sky? And what do you mean by"right next to each other"? How far is acceptable?
Why wouldn't this scenario be possible? (not to scale ofc)

Of course, different inclination would make planets appear more... up or down.

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#### MeteorWayne

##### Guest
spacelover175":16arop7h said:
will the planets ever align all 9

( i got in a huge argument that they would not so i was asking you part of my debate if you saw my other thread
BTW, there are technically only 8 planets and 5 dwarf planets.

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#### crazyeddie

##### Guest
Shpaget":2c0tut9f said:
Why do you think planet will never be right next to each other in visible sky? And what do you mean by"right next to each other"? How far is acceptable?
Why wouldn't this scenario be possible? (not to scale ofc)

Of course, different inclination would make planets appear more... up or down.
Actually, it IS possible, especially if you are only talking about the planets that are visible to the naked eye. I know this, because it happened a number of years ago. They reported the rare sight in the newspapers, and I went out to look that evening, right after sunset. There was Mercury, Venus, Mars, Jupiter, and Saturn, all in a line, like beads on a string. They were not exactly close together, but all were visible at a glance.

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#### MeteorWayne

##### Guest
Which get back to my original clarification, what does the OP mean by "align"?

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#### spacelover175

##### Guest
align as in from the sun out in a straight line

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#### MeteorWayne

##### Guest
Well, yes then the answer is once every few billion years, by which time the earth will be completey toasted and all life gone from our charcoal planet. Not in any of our lifetimes for sure...there are no such events in the next few million years.

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#### eburacum45

##### Guest
At 19.20 on 22/3/04; I managed to see Jupiter, Saturn, Mars, Venus, Crescent Moon, and Mercury all in the same half of the sky. Not exactly an alignment, but very impressive.

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#### aphh

##### Guest
You can get the frequency of the alignment occurance or synodic period using harmonic sum. For outer planets you subtract the inverse of their orbital period from the inverse of earth's orbital period. You would add inverse of orbital period for inner planets.

For example, if you wanted to calculate the frequency of earth and mars and jupiter getting into alignment you would subtract (1/364) - (1/687) - (1/4332) = 1/942.

Earth and Mars and Jupiter are in alignment every 942 days. This is called the conjunction of Earth and Mars and Jupiter. If you add to the harmonic sum orbital periods of all the other planets, you will get the frequency of the conjunction of all planets.

You would not know when the alignment occurs using this calculation only, but you would get the frequency of the occurance.

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#### origin

##### Guest
aphh":2s6s81nh said:
You can get the frequency of the alignment occurance or synodic period using harmonic sum. For outer planets you subtract the inverse of their orbital period from the inverse of earth's orbital period. You would add inverse of orbital period for inner planets.

For example, if you wanted to calculate the frequency of earth and mars and jupiter getting into alignment you would subtract (1/364) - (1/687) - (1/4332) = 1/942.

Earth and Mars and Jupiter are in alignment every 942 days. This is called the conjunction of Earth and Mars and Jupiter. If you add to the harmonic sum orbital periods of all the other planets, you will get the frequency of the conjunction of all planets.

You would not know when the alignment occurs using this calculation only, but you would get the frequency of the occurance.
I don't think so.

Are you saying the frequency of alignment is every 942 days? But if you start out with and alignment and then look at the planets 942 days later (using your numbers) you find that the earth has had 2.59 orbits and mars has had 1.38 orbits and jupiter has had 0.22 orbits they are clearly not aligned. Did I miss something?

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#### aphh

##### Guest
origin":2wrddit6 said:
Are you saying the frequency of alignment is every 942 days? But if you start out with and alignment and then look at the planets 942 days later (using your numbers) you find that the earth has had 2.59 orbits and mars has had 1.38 orbits and jupiter has had 0.22 orbits they are clearly not aligned. Did I miss something?
You're right. It appears that the harmonic sum only works for 2 planets at a time. I have to think it over, but in the mean time the formulas are here (S for Synodic Period): http://en.wikipedia.org/wiki/Orbital_period

Clearly Earth and Mars first need to be in alignment, which occurs every 1/364 - 1/687 = 1/774 days, then you add Jupiter in the equation, but I need to look up for the correct formula.

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#### R1

##### Guest
...And where does the asteroid belt come from ? Could there have been another planetoid or two
in the neighborhood that collided and formed the belt ?

...Or could it be that in the belt's specific orbit a planet could never easily form?

...If you only considered 8 or fewer planets, how often would they align?
...Would it be known when the 8 were last aligned, if they were ?

(I don't think I could spend too much effort calculating this, though. The alignment of the big 8 balls
probably doesn't matter much that I know of. For example, a video program recently described
how Venus' sky path thousands of years ago intersected Orion, then made a loop around
him, then went about its original path. This is due to occur once again, oddly or not, in the year 2,012.)

(edit-add: Strange things can happen when they're out of line. )

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#### MeteorWayne

##### Guest
the asteroid belt is stuff that might have been able to form a planet if Jupiter didn't exist. Jupiter's gravitational effects on material in that region removed over 90% of the material there within a few thousand years after Jove formed.

What is left in the belt is a mere shadow of what was there before. Most was ejected from the solar system, became part of the Oort ccloud, or was sent into the sun.

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#### R1

##### Guest
Interesting. I suspect asteroid belts could be quite common.

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#### MeteorWayne

##### Guest
Yes they are. However, around other stars they are at different distances from the star. Our solar system was shaped more than anything else by Jupiter's existance. It has more mass than everything else other than the sun in our system combined. It has shaped how our system evolved. In stars that don't have a Jupiter in a 12 year nearly circular orbit, things evolved very differently.

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#### aphh

##### Guest
Earth and Mars are in alignment for app. every 774 degrees. So if Jupiter was aligned with the two, it would now have to move 774 degrees aswell before having a chance of being aligned with the two.

In 774 days Jupiter has moved 64 degrees. Another 774 days later Jupiter has moved total of 128 degrees. When about ten more 774 day periods have passed, the three planets would meet again, which means the alignment of the three planets would occur in roughly 9288 days.

Is this correct thinking?

Edit: I think it is, because in 9288 days the Earth - Mars alignment would have occurred 12 times (9288 / 774) and the Earth - Mars alignment would have shifted roughly 9288 degrees (12 * 774), so the three meet again and have a conjunction.

Edit 2: Now you can add Saturn to the equation, knowing that the alignment of the three planets occurs every 9288 degrees. When four planets are aligned, Saturn would need to travel 9288 degrees before having a chance of being aligned with the three again. Saturn travels 360 degrees in 10 579 days, so the alignment frequency would be 9288 degrees / 360 degrees * 10 579 days = 272 938 days ~ 750 years.

Pretty rare occurance to have four planets aligned, huh?

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#### origin

##### Guest
Earth and Mars are in alignment for app. every 774 degrees. So if Jupiter was aligned with the two, it would now have to move 774 degrees aswell before having a chance of being aligned with the two.

In 774 days Jupiter has moved 64 degrees. Another 774 days later Jupiter has moved total of 128 degrees. When about ten more 774 day periods have passed, the three planets would meet again, which means the alignment of the three planets would occur in roughly 9288 days.

Is this correct thinking?
No, that does not result in an alignment. Mars and Earth are lined up pretty good but Jupiter is not. It is easy to determine if they alignment has occured, by plugging in the orbital period into the time you give, but frankly I do not know how to calcuate the frequency of alignment for 3 or more planets off the top of my head, probably some sort of series calculation, er something...

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#### aphh

##### Guest
You're right, it's not yet correct.

One Earth - Mars alignment occurs every ~2.1 Earth orbits (774 / 364), so the Earth - Mars alignment shifts 0.1 earth orbits from the original conjunction base point every 774 days. That would be 36 degrees. Hence 12 Earth - Mars alignments in 9288 days would shift the base point 12 * 36 = 432 degrees from the original conjunction base point of the three planets. 432 - 360 = 72 degrees past the base point of original conjunction of three planets.

Is Jupiter 72 degrees past the original conjunction base point after it's travelled 9288 days? Not exactly, Jupiter would have travelled only ~2.1 orbits (9288 / 4332), which means it's only app. 36 degrees past the original conjunction base point.

If somebody has a clue, now is the time to shine and lend a hand here.

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#### aphh

##### Guest
It requires calculus and integrals. It's not simple calculation.

Tycho (Brahe) and Johannes (Kepler) in their time tried to solve this exact same equation, but couldn't. They lacked the mathematical tool, calculus. Integrals had not yet been invented when Tycho and Johannes empirically derived Kepler's laws. Only after Newton and Leibnitz came up with calculus and integrals, an equation like this could be mathematically solved.

This is a suitable problem for a real "wanna-be" astronomer who can do calculus and integrals. I'll try to look it up as soon as I have the time.

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#### InnyBinny

##### Guest
I wouldn't know how to mathematically solve it formally, but I think you can kind of do a little educated guess work.

Let's say planet x has an orbital period of 1 year, planet y of 3 years and planet z of 5 years.

The synodic period of planet x and y is 1.5 years, according to the wikipedia link aphh gave:

T(syn) = 1/|1/1 - 1/3| = 1.5

Now, every 1.5 years when the planets line up, they displace an angle of 0.5 orbits (planet x moves a distance of 1.5 orbits, planet y a distance of 0.5 orbits, common decimal so -> displacement of 0.5 orbits).

Every 1.5 years, planet z displaces 0.3 orbits.

Now, when all three planets are aligned, they must have moved some distance each, where each distance is separated by an integer number of orbits:

0.5n - 0.3n = p

where n,p are part of I

(n is amount of 1.5 year iterations, p is the integer difference in orbits)

And so we can informally solve for when n is the lowest it can be:

0.2n = p -> n=5

When n is 5, that means 5 1.5 year iterations have passed or 7.5 years, and so every 7.5 years, planet x, y and z (with periods 1, 3 and 5 years respectively) align, given they were aligned in the past (I'm not sure if it is a certainty they must be aligned given all possible starting points).

This can be verified by checking the angle each has gone through in 7.5 years - planet x at 7.5 orbits, planet y at 2.5 orbits and planet z at 1.5 orbits. All have displaced 0.5 orbits, and so are aligned.

Using Earth, Mars and Jupiter, relative to Earth period:

Earth: 1.0000 years
Mars: 1.8808 years
Jupiter: 11.8590 years

Earth and Mars (E/M) have a synodic period:

T(syn[E/M]) = 1/|1/1 - 1/1.8808| = 2.1353 years

Every one of these periods, the E/M alignment goes through a displacement:

distance = 2.1353 / T(earth) = 2.1353 -> displacement of 0.1353 orbits

Every 2.1353 years, Jupiter goes through a displacement:

distance = 2.1353 / T(Jupiter) = 0.1801 orbits

So 0.1353 orbtis and 0.1801 orbits must align at some point:

0.1801n - 0.1353n = x; n,x part of I
0.04473n = x
n = 313

You'll notice that 0.04473*313 doesn't exactly yield an integer, but it does come very close - and as in physics we deal with approximate measurements, any number that is very close can essentially be called an alignment. How did I figure this was the smallest number that would give an integer to 2 decimal places? Just iterated through on my calculator. :lol: I really have no idea how to formally solve the problem.

313 sets of 2.1353 year orbits yields an alignment period of 668.36 years.

We can verify this by testing how many orbits each would have gone through after 668.36 years:

Earth: 668.36
Mars: 355.36
Jupiter: 56.36

Therefore alignment after every 668.36 years.

This of course assumes that they were aligned in the past...I have no idea if it is a requirement that planets go through all possible spatial arrangements in that time. It also obviously assumes circular orbits...no idea how ellipses change things.

I guess you could repeat this same thing for all planets.

Venus: 0.61519 years

displacement made by Earth/Mars/Jupiter alignment (EMJ) every 668.3588 years = 0.3588 orbits
distance made by Venus every 668.3588 years = 1086.4266 orbits -> displacement = 0.4266 orbits

0.4266n - 0.3588n = x; n,x part of I
0.06781n = x
n = 59

With n = 59, amount of years per alignment = n*668.3588 = 39433.167

Check:

Earth: 39433.17 orbits
Mars: 20966.17 orbits
Jupiter: 3325.17 orbits
Venus: 64099.17 orbits

Therefore there is alignment of Venus, Earth, Mars and Jupiter every 39433.167 years, where alignment is considered alignment when planets are within an angle of 1/100 of an orbit (3.6 degrees).

I'll stop there for now. I hope that's actually right, if anyone finds errors then please specifiy so I can know exactly what made this an unfortunate waste of time. :lol:

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