How often are all the planets in align?

Hi Jason!

Wow! you have some very long, complicated answers to a rather simple question.

The visible planets line up in our skies every few years. It's not a case of the planets literally "lining up" in the sky, with a military-like precision formation. Rather, all the planets come out at the same time in the evening sky, or perhaps the morning sky.

Sometimes a planet can be seen in the morning sky, that is, before the sun comes up, and sometimes in the evening sky after the sun sets. Last year, in August 2008, by coincidence all five of the naked-eye planets lined up in the evening sky.

There's nothing especially remarkable about such a coincidence, and it certainly does not foreshadow anything significant (except perhaps in the minds of astrologers, and they make up their horoscopes as they go along anyway). If you calculate the probability, the chances come out at one in 16 that all five planets will be on the same side of the sun, unusual, but not any more than that.

I saw all five together in the sky at one time in May 2002, and again in August 2008,

When astrologers speak of the planets being aligned (something which doesn't really concern astronomers) they don't mean that the planets will actually all lie on a straight line at some instant of time. One calculation of alignments within around thirty degrees (about as close as they can get) shows that the last such alignment was in 561 BC, and the next will be in 2854. All eight planets are somewhat aligned every 500 years, and are grouped within 30 degrees every 1 to 3 alignments.

Source(s):

curious.astro.cornell.edu/question.php...

There has to be one point in time where they all align as they all have to pass eachother at some point (take a clock for example it has 3 hands at some stage during 24hrs they ALL align).

For planets though, it would take a lot of calculations... speeds each planet is travelling at, the time of earth years to each planet so as to get the correct day and time blah blah to complicated lol but have to agree probably wont happen for a gazillion years.

Let us say that you are willing to accept a 2-dimensional alignment (meaning, we don't care about the different orbital planes).

We look at the Solar system from above and we draw the orbits on a sheet of paper.

Let's also say that we would be happy if planets fall within a 1 degree sector, traced out from the Sun.

To make matters easier (for calculations), let's keep this sector centred on Earth (this is how the ancient astronomers would have done the calculations -- they spent centuries on this problem, so we might as well profit from their work).

The time it takes for another planet to return to this sector is called a "synodic period".

For Mercury, it is 115.88 days. Every 115.88 days (on average), Mercury passes within this sector of interest. Since the sector is 1 degree wide (1/360 of an orbit), then Mercury is inside the 1 degree sector for almost 8 hours.

In reality, things are a bit more complicated. Because orbits are not perfect circles, the 115.88 days is only an average. The real period is sometimes longer, sometimes shorter.

But, let's keep it easy and stick with averages.

The synodic period of Venus is 583.90 days (I'm using Earth-days of 86,400 seconds for the calculations). If we begin with all planets in line, when Venus comes back to the sector (583.90 days later), Mercury will have done 5 synodic orbits. It will be just passed the sector, by 14 degrees. After two Venus passages, Mercury will be ahead by 28 degrees, ans so on.

We have to find how many synodic periods of Venus are needed, before Mercury once again falls within the one degree sector.

After 103 Venus periods (= 60,141.7 days = 164 years 8 months), we will have returned to having Mercury, Venus and Earth lined up within a one degree sector.

60,141.7 / 115.88 = 519 Mercury synodic periods (minus 0.06 degrees)

60,141.7 / 583.90 = 103 Venus synodic periods (exactly)

60,141.7 / 365.2425 = 164.6624 average Gregorian years (Earth-years).

An alignment of three (or more) objects is called a Syzygy. We will call the period of this syzygy the "inferior syzygy period" because it involves the simultaneous inferior conjunctions of Mercury and Venus.

ISP = 60,141.7 days.

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The synodic period of Mars is 780 days (almost exactly). However, the ISP is not exactly divisible by 780.

During one ISP, there will have been 77 Mars synodic periods, plus 37.7 degrees.

We are looking for a number of ISP (it has to be an integer) such that the total number of days (# of ISP * 60,141.7) is almost exactly divisible by 780 (it has to be within 1/360).

This problem is difficult enough with calculator. You can imagine what it was like in the old days, when decimals were not even invented yet (the had to use actual fractions).

Using a few tricks from the ancients, I find the first candidate at 105 ISP (6,314,878.5 days = 17,289.55 years)

This puts Mars within 0.7 degrees of the line up. Venus should still be OK, however we have to check Mercury (since it was not exact)

Mercury:

6,314,878.5 / 115.88 = 54,495 periods, less 6.5 degrees (Mercury has drifted out of syzygy)

The next candidate is 401 ISP (not a multiple of 105)

24,116,821.7 days = Mercury is 25 degrees out.

... and so on ...

By this time, I am beyond 24 million days (66,000 years) and I still can't line up the first four planets to within one degree.

One degree is still a relatively large angle: it is twice the apparent diameter of the Sun's disk, as seen from Earth.

Define "in Align"

A. All in a straight line on one side of the Sun?

B: All in a straight line on both sides of the Sun?

C. 4 in a straight line on one side of the Sun, and 4 on the other side, 180 degrees apart.

D. 2 each in-line at 90 degree angles apart from the Sun, but in a straight line

Answer:

Never to all of them, the plane of the elliptic is not exact, so they are never in perfect alignment.

Never. Even negating their inclinations to the ecliptic.

Well, let me rephrase that. The time scales for that to happen are so great, that if they all started out "aligned," when the Solar System formed, even the age of the universe is less than 1% of the length of time for it to happen again.

In a "straight" line all one side of the Sun? About once every 47 bazillion years. And not in 2012.