When Will the Planets Align Again with Varying Year Lengths?

[caters]

okay so here are the lengths of years and days on the planets:

Mercury:
Day: 176 Earth days
Year: 88
1 year on mercury is daytime and the other is nightime

Venus:
Day: 243 Earth days
Year: 224.7 Earth days

Earth:
day: 1 Earth day
Year: 365 Earth days

Mars:
Day: 1.03 Earth days
Year: 687 Earth days

Jupiter:
Day: 9.8 Earth Hours
Year: 11.86 Earth years

Saturn:
Day: 10.2 Earth hours
Year: 29.46 Earth years

Uranus:
Day: 17.9 Earth hours
Year: 84.07 Earth years

Neptune:
Day: 19.1 Earth hours
Year: 164.8 Earth years

Pluto:
Day: 6.39 Earth days
Year: 247.7 Earth years

Now here is a good question:
If we start at Earth year 1 and all the planets are in the same place before they start rotating when are they all going to intersect again(in other words form a straight line) with the data I gave you. now I know that if you multiply all the year data together you will get a point of alignment but will all the planets be aligned again before then?

In other words what years would all the planets be aligned besides Earth year 1?

 

[phyzguy]

Three comments:

(1) You have Mercury's day wrong. Mercury's day is 58 Earth days. It is in a 3:2 resonance so that 3 Mercury days equals 2 Mercury years.

(2) Do you just mean aligned in longitude? The planets' orbits are in different planes, so even if the longitudes are exactly aligned, they won't be truly in a line.

(3) You have to specify a tolerance of alignment. If you start with the longitude of the planets exactly aligned, they will never again be exactly aligned. How close do you want to come?

 

[caters]

(1)no if you go to enchantedlearning.com or any other website talking about mercury they will say that 1 mercury year is daytime and the other is nightime and thus 1 mercury day is 2 mercury years. They will also say that a mercury day is 88 Earth days.

(2) I mean in a straight line(just like it started out in a straight line)

(3) Yes they will be exactly aligned at the year which is all the planets years multiplied together.

 

[tfr000]

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

Mercury:
rotation period:1407.6 hours = 58.7 days
length of day: 4222.6 hours = 175.9 days

exercise for the student: why are these different?

 

[phyzguy]

(1)no if you go to enchantedlearning.com or any other website talking about mercury they will say that 1 mercury year is daytime and the other is nightime and thus 1 mercury day is 2 mercury years. They will also say that a mercury day is 88 Earth days.

I don't know what enchantedlearning.com is, but what you are saying is wrong. Try going to http://solarsystem.nasa.gov/planets/profile.cfm?Object=Mercury&Display=Facts&System=Metric, or Wikipedia, or any reputable source. Mercury's day is 58 Earth days.

(2) I mean in a straight line(just like it started out in a straight line)

Like I said, the planets orbit in different planes, so they are never in a straight line.

(3) Yes they will be exactly aligned at the year which is all the planets years multiplied together.

No, this is wrong. This is only true if the periods are integers or some integer multiple. If the numbers are non-commensurate real numbers (which they are), they will never align again.

 

[caters]

Mercury is the smallest and closest to the Sun of the eight planets in the Solar System, with an orbital period of about 88 Earth days.

Sidereal rotation period
58.646 d

the 58 days you are referring to is the sidereal rotation period.

 

[caters]

http://nssdc.gsfc.nasa.gov/planetary/factsheet/

Mercury:
rotation period:1407.6 hours = 58.7 days
length of day: 4222.6 hours = 175.9 days

exercise for the student: why are these different?

The 175.9 is the sum of the year in daytime and the year in nightime.

The 58.7 days is how long the siderial rotation is.

The length of the orbit(which is not the same as the sidereal rotation) is 88 days and they always refer to this when they translate a year on a certain planet to Earth time.

 

[Drakkith]

Not sure. Perhaps find the least common multiple of each planet's year?

 

[tfr000]

Because of perturbations, it's unlikely that the planets would ever "line up" again. Some perturbations accumulate in a way that is non-periodic... in other words, they are chaotic.
Besides all that, it is unlikely that our current state of knowledge of the system is adequate to predict that far ahead. Because of data we don't yet have, we can only go a few thousand years with any accuracy. So even if multiplying all of the orbital periods would work, other things would throw it off.

 

[phyzguy]

Mercury is the smallest and closest to the Sun of the eight planets in the Solar System, with an orbital period of about 88 Earth days.

Sidereal rotation period
58.646 d

the 58 days you are referring to is the sidereal rotation period.

You're right here, I apologize. The 58 days is the sidereal day. The solar day (noon-noon) is indeed 176 days, or two years, as you said.

I think the other things I said about planetary alignment are correct.