Orientation of the Earth, Sun and Solar System in the Milky Way

[fizixfan]

I've been tinkering with a few diagrams in an attempt to illustrate the motion of the solar system in its journey around the Milky Way. I also wanted portray how the celestial, ecliptic and galactic coordinate systems are related to each other in a single picture. Note: in the Celestial, or Equatorial system, the Celestial North Pole (an extension of the Earth's axis of rotation), uses the default setting of North as "up." The Ecliptic and Galactic also use North as "up" with reference to the Celestial North Pole. Some people say that in space there is no such thing as "up" or "down," but in determining the position of a celestial object (e.g., declination and right ascension of a star or deep-sky object) is DOES matter.

Please have a look at these diagrams and feel free to comment on any errors, or make suggestions as to how I could make them better. I drew these images, but anyone is free to re-use them without restriction.

Figure 1 shows the motion of the Earth and Sun around the Milky Way. The solar system is actually well within the galactic disk, which is about 1,000 light years thick. The sun and the planets that circle it is roughly 50 light years above the galactic plane, and passed northward through it about 3 million years ago in its undulating path around the galactic center. Note: this diagram is not to scale. The northernmost excursion of the solar system takes it about 250 light years above the galactic plane. This means it would only subtend an angle of about 0.55° relative to the galactic center.

Figure 1. Motion of Earth and Sun around the Milky Way

Figures 2. and 3. show the orientation of the Earth, Sun & Solar System in the Milky Way - similar diagrams, just presented in different ways.

Figure 2. Orientation of Celestial, Ecliptic and Galactic Poles and Planes

Figure 3. Orientation of astronomical coordinates projected on the Celestial Sphere.

The angle between Celestial Equator (an imaginary plane passing through the Earth's equator) and the Ecliptic Plane (an imaginary plane extended through the Sun's equator) is 23.4°. The angle between the North Celestial Pole (an imaginary line extending through Earth's axis of rotation) and the North Ecliptic Pole (an imaginary line extending through the Sun's axis of rotation) is the same - 23.4°. This is the familiar value for the "tilt" of the Earth in its path around the Sun.

The angle between the Ecliptic Plane and the Galactic Equator (an imaginary plane passing through, and parallel to, the disk of the Milky Way) is 60.2°. The angle between the North Ecliptic Pole and the North Galactic Pole (an imaginary line extending through the Milky Way's axis of rotation) is also 60.2°.

The angle between the Celestial Equator and the Galactic Equator is 62.9°, as is the angle between the North Celestial Pole and the North Galactic Pole.

These three angles = 23.4°, 60.2° and 62.9° cannot be shown or calculated in two dimensions, because they represent separate planes which do not intersect at a common point. If you look at Figure 3, you can see that this is so.

References:
https://en.wikipedia.org/wiki/Celestial_coordinate_system#Galactic_system
https://www.eso.org/public/news/eso0932/
http://www.engineeringanddesign.com/1/054.htm

 

[phyzguy]

Nice! I didn't check the accuracy, but they look reasonable. My only comment is that in the first diagram, I would change "Celestial Plane" to "Celestial Equator" as you have done in the other two diagrams.

 

[Janus]

I'd just make one small point. In your first diagram, it appears as if you are showing the Moon's orbit as being on the same plane as the Celestial plane/equator, where, in reality, it is inclined by ~5 degrees to the ecliptic (~18 degrees to the Celestial equator).

 

[fizixfan]

Nice! I didn't check the accuracy, but they look reasonable. My only comment is that in the first diagram, I would change "Celestial Plane" to "Celestial Equator" as you have done in the other two diagrams.

Thanks phyzguy, and appreciated. I called it Celestial Plane to be consistent with the terms Galactic Plane and Ecliptic Plane I used in this diagram. But you're right - it should be referred to as the Celestial Equator - I will adjust accordingly. See image attached to my following reply to Janus.

Cheers.

 

[fizixfan]

I'd just make one small point. In your first diagram, it appears as if you are showing the Moon's orbit as being on the same plane as the Celestial plane/equator, where, in reality, it is inclined by ~5 degrees to the ecliptic (~18 degrees to the Celestial equator).

Thanks Janus - I knew the moon's orbit was inclined relative to Earth's equator, but I didn't know it was inclined TOWARD the ecliptic. Interesting! I've included your suggestion in my diagram, which also includes phyzguy's suggestion. Really appreciate the input, hope this diagram isn't getting too busy.

 

[picnics]

quote: I drew these images, but anyone is free to re-use them without restriction.

Thanks for sharing this great diagram!

quote: feel free to comment on any errors, or make suggestions as to how I could make them better

The definition of an ellipse is that it has 2 focus points,
therefore the the Sun is not at the center of the Earth's elliptical orbit.
The direction of the "Super Galactic Center"
would be a perpendicular line to the Earth's orbit, at about October 11.

 

[fizixfan]

The definition of an ellipse is that it has 2 focus points,
therefore the the Sun is not at the center of the Earth's elliptical orbit.

Thanks for your input. Yes, the Earth's orbit around the Sun is elliptical, but it's very nearly (97%) circular. Earth's apogee distance from the Sun is 152.1 million km, and its perigee distance is 147.1 million km. The orbit is shown to scale in the diagram below. Looks much like a circle, doesn't it?

The Earth-Sun system orbits a common center of mass called the barycenter. But because the Sun is so much more massive (99.9% of the mass of the entire solar system), the Earth-Sun barycenter is only about 449 km from the center of the Sun.

The direction of the "Super Galactic Center"
would be a perpendicular line to the Earth's orbit, at about October 11.

"Super Galactic Center" is not an astronomical term, as far as I know. If you mean the Galactic Center, I still have trouble visualizing what you mean by "a perpendicular line to Earth's orbit." A diagram might help.

 

[Dr Wu]

Looking at the Sun's direction of travel arrow on fizixfan's 'Motion of Earth & Sun around the Milky Way' diagram, does this mean then that the solar system is orbiting the Galaxy in a clockwise direction? Also, which hemisphere of Earth's is (mostly?) facing the direction the solar system is taking during its orbit round the galactic disc? North or South? Or do they each take turns during the course of a terrestrial year? I can't quite put it all together it somehow.

 

[fizixfan]

Looking at the Sun's direction of travel arrow on fizixfan's 'Motion of Earth & Sun around the Milky Way' diagram, does this mean then that the solar system is orbiting the Galaxy in a clockwise direction?

The short answer is yes, it is. In astronomy, there are conventional means for defining the positions and locations of celestial objects. The three most commonly used are the Celestial Coordinate System (with Earth as the primary point of reference), the Ecliptic Coordinate System (with the Sun as the primary point of reference) and the Galactic Coordinate System (Sun at center, with the primary direction aligned with the approximate center of the Milky Way galaxy).

In all three of this systems, Earth's North Pole is pointing "up" (you have to start somewhere). So in this frame of reference the Earth spins counterclockwise (CCW) on its axis, and orbits around the Sun in a CCW motion. The Sun also spins CCW on its axis. But the Solar System is moving clockwise in its orbit around the Milky Way. A lot of illustrations you'll find on the internet get this last part wrong, and if it's pointed out to them, many of them will say, "It doesn't matter, there is no up or down in space." That's true, but if does matter if you're using any kind of astronomical coordinate system.

Also, which hemisphere of Earth's is (mostly?) facing the direction the solar system is taking during its orbit round the galactic disc? North or South? Or do they each take turns during the course of a terrestrial year?

That's an interesting question. If you look at my diagram below, and observe the yellow arrow pointing toward the North Celestial Pole - that is aligned with the Earth's axis of rotation. You'll see that the Earth's northern hemisphere is inclined toward (facing, or "leaning into") its direction of motion around the galactic disk.

 

[Dr Wu]

Thanks, fizixfan. Speaking as an amateur stargazer, the Earth's orientation with respect to the Milky Way has always been something of a puzzle to me. But no longer!

 

[rbelli1]

The definition of an ellipse is that it has 2 focus points,

These two points can be the same and we usually call that a circle. Just like a rectangle with length and width equal is often called a square. The more specific figure still satisfies the definition of the more general figure. This does not apply here but may in other examples of orbits.

BoB

 

[rootone]

Looking at the Sun's direction of travel arrow on fizixfan's 'Motion of Earth & Sun around the Milky Way' diagram, ... does this mean then that the solar system is orbiting the Galaxy in a clockwise direction?

Yes if you are looking at the Milky Way from a point of view above it's North pole.
If you are viewing from below the South pole, the orbit of the solar system appears to be the opposite direction.

 

[Dr Wu]

Thanks for the info. Just one other question, though: I've since learned that the solar system is moving towards a point in the Milky Way presently marked by the 4th magnitude star, Lambda Hercules.* This being so, and to give a better idea about the trajectory of the solar system, at which point in the heavens does the solar system appear to originate from? I assume this point probably lies somewhere in the Southern Hemisphere - if only because the constellation of Hercules is in the Northern Hemisphere, but I have no proof of this. PS. I've tried to find out via Google, but despite my best efforts all I get are responses that have little or no bearing on this question.

*There are several variations concerning this location, but Lambda Hercules still appears to be leading the pack.

Note: I've since found out from Wikipedia that the 'solar antapex' is near the star, Zeta Canis Minoris! I could delete this query of mine, but I'll include it on this thread just in case others may wish to know the answer to this admittedly obscure question. Many thanks!

 

[chasrob]

Excellent renderings. Figure 3 reminds me of the illustrated The Astronomical Companion by Guy Ottewell.

 

[Dr Wu]

Just another last thought: does the Sun have anything corresponding to a 'pole star' - north or south? I mention this because if the Sun (and the solar system) is truly heading towards Lambda Hercules, that appears to conflict with the orientation of Earth's own axis (there being a whopping 65 degree difference in declination between Polaris and Lambda Hercules, one which Earth's 23.5 degree axial tilt doesn't appear to address). Or is the plane of the solar system moving at an oblique angle with respect to the centre of the Milky Way? If so, I'm still curious to know where the solar 'north pole' is orientated. My apologies for refusing to let this issue die of natural causes.

 

[Janus]

Just another last thought: does the Sun have anything corresponding to a 'pole star' - north or south? I mention this because if the Sun (and the solar system) is truly heading towards Lambda Hercules, that appears to conflict with the orientation of Earth's own axis (there being a whopping 65 degree difference in declination between Polaris and Lambda Hercules, one which Earth's 23.5 degree axial tilt doesn't appear to address). Or is the plane of the solar system moving at an oblique angle with respect to the centre of the Milky Way? If so, I'm still curious to know where the solar 'north pole' is orientated. My apologies for refusing to let this issue die of natural causes.

It points to the middle of Draco. The closest object I could find to that point is NGC 6543, which is the Cat's Eye nebula.

 

[Bandersnatch]

I mention this because if the Sun (and the solar system) is truly heading towards Lambda Hercules, that appears to conflict with the orientation of Earth's own axis (there being a whopping 65 degree difference in declination between Polaris and Lambda Hercules, one which Earth's 23.5 degree axial tilt doesn't appear to address).

What's this angle?

 

[Imager]

I’m not following the curved (yellow) path of Sun around the Galactic Plane (blue). I would have thought the sun’s path though the galaxy would be on the same plane or tilted. What would cause the sun to “rise and fall” relative to the galactic plane?

 

[Bandersnatch]

I’m not following the curved (yellow) path of Sun around the Galactic Plane (blue). I would have thought the sun’s path though the galaxy would be on the same plane or tilted. What would cause the sun to “rise and fall” relative to the galactic plane?

Since Milky Way isn't a 0-thickness disc, any given new star will be born either above or below the plane bisecting the galaxy. This results in a component of gravitational attraction pointing normal to the galactic plane due to all the matter in the disc pulling the star in.
If the star was born above, it'll be pulled down, pass the middle point (where gravitational forces will be purely radial), and overshoot on the other side, where opposite direction of gravity will again pull it into the disc, which it again overshoots. And so on.
As such, it's not much different than a pendulum.

 

[Imager]

Since Milky Way isn't a 0-thickness disc, any given new star will be born either above or below the plane bisecting the galaxy. This results in a component of gravitational attraction pointing normal to the galactic plane due to all the matter in the disc pulling the star in.
If the star was born above, it'll be pulled down, pass the middle point (where gravitational forces will be purely radial), and overshoot on the other side, where opposite direction of gravity will again pull it into the disc, which it again overshoots. And so on.
As such, it's not much different than a pendulum.

Got it, thank you! Would this "pendulum" motion be common for most stars in a spiral galaxy like the Milky Way?

 

[Imager]

@https://www.physicsforums.com/members/fizixfan.506800/ Great Diagram!

 

[Bandersnatch]

Got it, thank you! Would this "pendulum" motion be common for most stars in a spiral galaxy like the Milky Way?

All stars, more like. Just to a varying degree.

 

[rbelli1]

All stars, more like. Just to a varying degree.

And even if a star is born perfectly on center it will be perturbed out of true in very short order by other masses it interacts with.

BoB

 

[Uterr]

What is the angle between axis of the ecliptic and radius of the Galaxy? Exact 90 degrees?

 

[phyzguy]

What is the angle between axis of the ecliptic and radius of the Galaxy? Exact 90 degrees?

No, why should it be? They are just random orientations. Look at Figure 2 in Post #1 from this thread. It looks like the angle you are asking about is 60.2 degrees.

 

[Uterr]

60.2 is the angle between ecliptic and plane of the Galaxy. I am asking about the angle between radius of the Galaxy and axis of the ecliptic. The radius which connect center of the Galaxy and Sun. From many pictures this is 90 degrees but there is no information about that.

To be more precise - what is the angle between axis of the Galaxy projected on the plane of the Galaxy and the radius of the Galaxy that connects center of the Galaxy and Sun.

 

[Bandersnatch]

What is the angle between axis of the ecliptic and radius of the Galaxy? Exact 90 degrees?

96 degrees.

 

[Uterr]

Astonishing! Thank you. What is the source of this information?

Is it true that axis of the ecliptic stays still like a gyroscope and therefore this angle will change over the movement around the Galaxy?

I see that this angle is now in increasing mode. Am I correct?

 

[Bandersnatch]

What is the source of this information?

The celestial coordinates to the X-ray source Sgr A identified as the supermassive black hole at the centre of our Galaxy are known (~18h RA, ~-29 dec). The axis of Earth's rotation happens to be angled in such a way w/r to the ecliptic, that it's just a matter of adding its inclination (~23 degrees) to get the 6 degrees between the ecliptic plane and the galactocentric radial direction (or 90+6 if you want an angle with the normal to the ecliptic).
Best seen if you launch some planetarium software (I recommend Celestia) and turn on galactic, ecliptic, and celestial coordinate grids.

Is it true that axis of the ecliptic stays still like a gyroscope and therefore this angle will change over the movement around the Galaxy?

I see that this angle is now in increasing mode. Am I correct?

That's also my understanding.

 

[Janus]

Astonishing! Thank you. What is the source of this information?

To add to Bandersnatch's reply, here's a screen shot taken from the Worldwide Telescope software. The blue grid are the galactic coordinates, where (0,0) marks the center of the galaxy. The white grid are the ecliptic coordinates, with the ecliptic marked out 260, 270, 280, etc. Note that the ecliptic crosses the plane of the galaxy ~6 degrees from the galaxy center coordinates.

 

[Uterr]

I made a mistake in my 'precision':

To be more precise - what is the angle between axis of the Galaxy projected on the plane of the Galaxy and the radius of the Galaxy that connects center of the Galaxy and Sun.

Should be:
To be more precise - what is the angle between axis of the ecliptic projected on the plane of the Galaxy and the radius of the Galaxy that connects center of the Galaxy and Sun.
(can't edit post now)

Anyway thank you for understanding and answers!

 

[Uterr]

I made a sketch about this angle (lets hope it's correct;)

 

[Dr Wu]

All this would be wonderfully easy to visualise in 3D, of course

 

[Delphinus]

Hello there! Thanks for the interesting conversation, I have another question:

The solar apex has in consideration the movement of the surrounding context (respect to the so called local standard of rest). Because of that, it does no say what direction the sun is really going in respect to the milky way center.

So what is the direction of the solar system irrespective of the local standard of rest? I'd say it should be near 90º from the center of the Galaxy (because the solar system should be moving over the tangent), so somewhere near Deneb.

Thanks

 

[fizixfan]

Excellent renderings. Figure 3 reminds me of the illustrated The Astronomical Companion by Guy Ottewell.

I redrew this (Figure 3 from my OP) from an illustration I found in the Wikimedia Commons https://commons.wikimedia.org/wiki/File:Ecliptic_equator_galactic_anim.gif
It was one of the best visualizations of the relative orientations of the Celestial Equator, Ecliptic Plane, and Galactic Plane that I could find anywhere. Figure 2 was an attempt to show the angles between the Celestial, Ecliptic and Galactic North Poles and their respective planes. This is something that can't be done by simply adding or subtracting say, the angle of the Celestial Equator relative to the Ecliptic Plane (23.44°) and the angle of the Ecliptic Plane relative to the Galactic Plane (60.19°), to get the angle of the Celestial Equator relative to the Galactic Plane (which is 62.87°). You need spherical trigonometry for that, because the three planes don't intersect at a single point .

Oddly enough, what started me off on this whole quest many years ago was that I wanted to know the angle between the Earth's axis of rotation (Celestial North Pole) and the Galactic Plane. Turns out it is 27.13°.