Is constant planetary alignment (syzygy) possible ?

In summary, a solar system with two planets orbiting a sun with different distances and eccentricities can have the same orbital period if their semi-major axes are equal. This also applies to a situation where one planet is a captured rogue. However, this type of constant planetary alignment (syzygy) is only possible for two point masses, and any deviation from this ideal scenario will result in the orbits decaying and eventually leading to perturbations and potentially collisions.
  • #1
B0b-A
155
32
Is a solar system possible where there was constant planetary alignment (syzygy)

Let's make it the simplest scenario : just two planets orbiting a sun [the planets are different ]
 
Astronomy news on Phys.org
  • #2
Try applying Kepler's third law and see what happens.
 
  • #3
Bandersnatch said:
Try applying Kepler's third law and see what happens.

So no two (native) planets can have the same orbital period ? (unless they have the same orbit).

How about if one of the planets was a captured rogue ?, (i.e. not a native of that solar system) , would Kepler's third law still apply ?
 
Last edited:
  • #4
Indeed.

For two planets to orbit the star with the same periods, their distances from it have to be equal. There's no way around it.

Two bodies can share the same orbit, though. Look up "three-body problem", and in particular the solutions to it called Lagragian points.

Of the Lagrangian points, only L3 allows for all three bodies to be aligned in syzygy, with the two planets offset by 180°, and the star in the middle.

Of course, you could not see one planet from the other, as it'd be obscured by the star.
Additionally, L3 is unstable. Any, even a slightest, deviation from it will change the orbits in analytically unpredictable fashion.[edit]:
I should probably clarify that the lagrangian points are solutions to the three body problem where one of the bodies is much less massive than the other two, so in general they do not apply to the situation with two planets and a star where masses are comparable. But if the two planets are of equal masses, they can still share the orbit in each other's L3 points(with the unstability caveat still applying). This, however, doesn't work for other Lagrangian points that otherwise allow a test particle(m<<M1,M2) to orbit in constant syzygy like L1 and L2.

Also, it's worth noting that the concept of Lagrangian points as actual points applies to idealised scenario where orbits are circular. For elliptical orbits, the points are more like centres of areas around which the bodies librate.
 
Last edited:
  • Like
Likes 1 person
  • #5
B0b-A said:
So no two (native) planets can have the same orbital period ? (unless they have the same orbit).

How about if one of the planets was a captured rogue ?, (i.e. not a native of that solar system) , would Kepler's third law still apply ?

Two planets can have the same orbital period without having the same orbit.
As you know, the orbit of a planet traces an ellipse, of which the circle is a special case.

What is necessary for two planets to have the same orbital period is that the semi-major axis of the ellipse for both has to be the same, and this will hold true regardless of the eccentricity of the orbit.

For the earth, having an orbit which is nearly a circle, the distance of the Earth to the sun can be considered to be the semi-major axis, and that the sun is at one focus ( or both foci ) of the Earth orbit.

The other planet would need an orbit of higher eccentricity, with the sun being again one focus of the orbit, but not the midpoint of the major axis. At times during the orbit the planet would be closer to the sun than the Earth and at other times farther away.
 
  • #6
"Constant" is a relative term. For celestial mechanics, where time is reckoned in billions or years, a constant syzygy for a three-body problem (any of the 5 Lagrange solutions to the gravity potential well problem) can only exist if 2 of the bodies are point masses. Otherwise tidal forces (gravity gradients) will deform the rotating bodies and dissipate kinetic energy into heat. The orbits will gradually decay as energy is reduced and angular momentum is conserved. That's is probably how Theia met Proto-earth and gave birth to the Earth - Moon system, which continues to change - slowly - 4 billion years later.
 
  • #7
256bits said:
Two planets can have the same orbital period without having the same orbit.
As you know, the orbit of a planet traces an ellipse, of which the circle is a special case.

What is necessary for two planets to have the same orbital period is that the semi-major axis of the ellipse for both has to be the same, and this will hold true regardless of the eccentricity of the orbit.

For the earth, having an orbit which is nearly a circle, the distance of the Earth to the sun can be considered to be the semi-major axis, and that the sun is at one focus ( or both foci ) of the Earth orbit.

The other planet would need an orbit of higher eccentricity, with the sun being again one focus of the orbit, but not the midpoint of the major axis. At times during the orbit the planet would be closer to the sun than the Earth and at other times farther away.

I guess that that would lead to collision if you take the mutual attraction into account.
 
  • #8
my2cts said:
I guess that that would lead to collision if you take the mutual attraction into account.

A collision could be possible, but not necessarily the final outcome.

Perturbation of the orbits would occur and could be calculated in the same manner as that which what is done for the solar system planets.
The planet with the more elliptical orbit would also suffer a perihelion advance due to relativistic effects than that of planet of the more circular orbit, but it could takes millions of year for a complete turn of the orbit, depending upon the eccentricity.
 

1. Is constant planetary alignment (syzygy) possible?

Yes, constant planetary alignment, also known as syzygy, is possible. However, it is a rare occurrence and requires specific conditions to be met.

2. What is syzygy and how does it occur?

Syzygy is the alignment of three or more celestial bodies in a straight line. This can occur when the planets, moons, and sun align in a specific position and their gravitational pull causes them to line up.

3. How often does constant planetary alignment happen?

The frequency of constant planetary alignment depends on the specific planetary positions and their orbits. Some alignments, like the Great Conjunction of Jupiter and Saturn, occur every 20 years, while others may happen even less frequently.

4. Can constant planetary alignment have any effects on Earth?

While constant planetary alignment itself does not have any direct effects on Earth, it can contribute to the gravitational pull and tides of our planet. It can also affect the orbits and movements of other celestial bodies in our solar system.

5. Is there any significance or meaning behind constant planetary alignment?

Many cultures and belief systems attribute spiritual or astrological significance to constant planetary alignment. However, from a scientific standpoint, it is simply a natural occurrence in our solar system and does not hold any specific meaning or influence on human life.

Similar threads

  • Astronomy and Astrophysics
Replies
11
Views
2K
  • Astronomy and Astrophysics
Replies
1
Views
927
Replies
12
Views
2K
  • Astronomy and Astrophysics
Replies
5
Views
1K
  • Astronomy and Astrophysics
2
Replies
52
Views
3K
  • Astronomy and Astrophysics
2
Replies
45
Views
4K
  • Astronomy and Astrophysics
3
Replies
98
Views
8K
  • Astronomy and Astrophysics
Replies
1
Views
1K
  • Astronomy and Astrophysics
Replies
5
Views
1K
Back
Top