What is the Earth's path in relation to the sun and the expanding universe?

[simon willetts]

This maybe a basic question to the educated. I wondered if anyone can describe or show the path the Earth takes not only in relation to orbiting the moving sun but taking into consideration the movement of the milkyway as in rotation and expansion of the universe. Hmm thinking of it as i write maybe that's not so basic a question. Just a random interest of mine with not relevant education to work it out. Thanks in advance if anyone can explain in laymans terms. I can at present see the helical path (all be it bent) around the moving sun.

 

[rootone]

The Earth is of course in orbit around the Sun, and the solar system as a whole is orbiting the Milky way center, along with other solar systems.
Expansion of space is not an issue, locally gravitationaly bound systems do not expand, gravity keeping them together is stronger

 

[simon willetts]

Thanks . i was trying to visualize the shape of the path the Earth takes in its whole existence if that makes sense. I am not a university educated chap but have a working life in engineering and a general interest and pretty basic understanding of the subject. I just sometimes get questions come to mind that are a bit complex for me to work out

 

[rootone]

You'll get to hear the term 'frame of reference' quite a lot.
The path taken is relative to that.
Using the Sun as a frame of reference, the Earth is in a nearly circular orbit around it.
If you use the Earth as your reference frame it isn't moving at all, everything else is.
Galileo and others got into a lot of trouble by suggesting that the Earth might not be a very sensible reference frame when studying the movements of other bodies.

 

[simon willetts]

Looks like I've opened up something that will be huge learning curve to me [emoji4]

 

[Drakkith]

Seems to me like it would just be a helical path that slowly bends as the solar system orbits the milky way. So it might look a bit like a piece of string with a very fine helical weave that loops back on itself.

 

[russ_watters]

Somewhere there is a reasonably good youtube animation showing Earth's corkscrew trajectory around the galaxy...

 

[simon willetts]

I will be looking out for that. The joys of random questions that come to us early in the a.m. [emoji6]

 

[Bandersnatch]

Somewhere there is a reasonably good youtube animation showing Earth corkscrew ingredients around the galaxy...

Actually, I'd advise against looking for that, without first steeling oneself against crackpottery. The most popular one I know of is 1. somewhat inaccurate, 2. loaded with nonsense annotations (paraphrasing: see Earth does not circle around the sun, but rather it's a 'vortex'! therefore scientific cabal; ivory tower; we're being lied to; etc.).

As for the question, it's all a matter of choosing a reference frame (i.e. with respect to what you want to describe the motion) and adding all component motions together.
For the reference frame, on the largest scale, since cosmic expansion was mentioned, I'd choose the CMBR-rest frame. It's a family of frames in which the radiation coming at us from the earliest universe looks roughly the same in every direction. It's not a bad way to think of it as 'how is the Earth moving w/r to the average distribution of matter in the universe'.

1. So you start with Earth going around the Sun in somewhat wobbly, nearly circular ellipses. It does so at 30km/s.

2. Add to that the motion around the galactic centre. Here, we need a few steps:
- include the roughly circular orbit due to the bulk rotation of the galaxy. This changes the circular path into a helical one, where the distance between the 'bends' in the helix are approx. 40 times the its radius (so it's a pretty elongated one). But the helix is angled backwards - like a slinky toy leaning to one side. This is due to the plane of the solar system being angled at approx 60° w/r to the direction of its motion.
Kinda like this:

For added complexity, this alignment does not change as the Sun orbits the galaxy - the helix gets slowly squashed sideways, then relaxed, then squashed again.
- if we looked at this elongated, bent helix from afar, it'd be just a line. This line has to bend around the galactic centre to form a circle. The radius of curvature is so large, however, that it would not be noticeable at the scale where you can resolve the helix.
- additionally, it needs to follow a sinusoidal path perpendicular to the plane of rotation (plane of the galaxy). This is due to peculiar motion in the plane-normal direction taking it slightly above the disc, where mass in the disc pulls it back, and the Sun overshoots in the opposite direction, moving below the disc. And so on. I don't remember the estimated frequency of those oscillations, but it's probably on the order of a dozen per orbit. Again, only really noticeable when you zoom out from the helix.
The two above look like this:

(the picture has the +z axis pointing towards the galactic south)
- finally, the remaining motion due to interactions with local stellar neighbourhood should be added (i.e., the remaining 'peculiar motion'). This further changes the circular base orbit into a somewhat elliptical one.
The peculiar motions are subject to local interactions, and are likely to chaotically change over time.

3. Adding to that motion of the Milky Way w/r to the Local Group of galaxies - this means mostly just the hurtling towards the Andromeda galaxy.
This changes the wobbly, elliptical orbit around the galactic centre into another leaning, helical one. This one looks very squashed, since MW moves towards Andromeda almost edge-on, with inclination of only 20°

The distance between bends of this helix is approx 3 times its radius. It's much more tightly wound than the previous one.

4. Finally, add the motion of the Local Group w/r to the CMBR-rest frame. This is pretty much a straight line in the direction of the Pump (Antlia) constellation.
This changes direction of the last helix like so (rather crudely eyeballed and drawn, I know, but mostly preserves proportions):

You need to imagine the already twisted helix from 3 as going towards Andromeda changing direction towards the 'net motion' one. Think of it, again, as a slinky toy with one end at the origin, and the other being dragged from the one arrow to the other. The trick is to preserve the angle of the bends as you do so.
So this step makes the helix from 3 more elongated and twisted in yet another way.

It is worth keeping in mind that these are the motions that can be thought of as representing reality only in this particular moment in time or in rough terms. As millions of years go by, and the stars and galaxies dance around each other in their gravitational ballet, there will come deviations and largely unpredictable changes.Now, can you imagine all these component motions happening at the same time? If so, good for you. :)
Personally, I tend to stick to the geocentric frame most of the time, else I get dizzy every time the Sun rises over the horizon.

 

[simon willetts]

Thank you for such a comprehensive answer . I am sure steam will come out of my ears as i digest all that information hehe. That was just what i was looking for. Pictures really help

 

[Farshaad Khorram]

Actually, I'd advise against looking for that, without first steeling oneself against crackpottery. The most popular one I know of is 1. somewhat inaccurate, 2. loaded with nonsense annotations (paraphrasing: see Earth does not circle around the sun, but rather it's a 'vortex'! therefore scientific cabal; ivory tower; we're being lied to; etc.).

As for the question, it's all a matter of choosing a reference frame (i.e. with respect to what you want to describe the motion) and adding all component motions together.
For the reference frame, on the largest scale, since cosmic expansion was mentioned, I'd choose the CMBR-rest frame. It's a family of frames in which the radiation coming at us from the earliest universe looks roughly the same in every direction. It's not a bad way to think of it as 'how is the Earth moving w/r to the average distribution of matter in the universe'.

1. So you start with Earth going around the Sun in somewhat wobbly, nearly circular ellipses. It does so at 30km/s.

2. Add to that the motion around the galactic centre. Here, we need a few steps:
- include the roughly circular orbit due to the bulk rotation of the galaxy. This changes the circular path into a helical one, where the distance between the 'bends' in the helix are approx. 40 times the its radius (so it's a pretty elongated one). But the helix is angled backwards - like a slinky toy leaning to one side. This is due to the plane of the solar system being angled at approx 60° w/r to the direction of its motion.
Kinda like this:
View attachment 193714
For added complexity, this alignment does not change as the Sun orbits the galaxy - the helix gets slowly squashed sideways, then relaxed, then squashed again.
- if we looked at this elongated, bent helix from afar, it'd be just a line. This line has to bend around the galactic centre to form a circle. The radius of curvature is so large, however, that it would not be noticeable at the scale where you can resolve the helix.
- additionally, it needs to follow a sinusoidal path perpendicular to the plane of rotation (plane of the galaxy). This is due to peculiar motion in the plane-normal direction taking it slightly above the disc, where mass in the disc pulls it back, and the Sun overshoots in the opposite direction, moving below the disc. And so on. I don't remember the estimated frequency of those oscillations, but it's probably on the order of a dozen per orbit. Again, only really noticeable when you zoom out from the helix.
The two above look like this:
View attachment 193715
(the picture has the +z axis pointing towards the galactic south)
- finally, the remaining motion due to interactions with local stellar neighbourhood should be added (i.e., the remaining 'peculiar motion'). This further changes the circular base orbit into a somewhat elliptical one.
The peculiar motions are subject to local interactions, and are likely to chaotically change over time.

3. Adding to that motion of the Milky Way w/r to the Local Group of galaxies - this means mostly just the hurtling towards the Andromeda galaxy.
This changes the wobbly, elliptical orbit around the galactic centre into another leaning, helical one. This one looks very squashed, since MW moves towards Andromeda almost edge-on, with inclination of only 20°
View attachment 113456
The distance between bends of this helix is approx 3 times its radius. It's much more tightly wound than the previous one.

4. Finally, add the motion of the Local Group w/r to the CMBR-rest frame. This is pretty much a straight line in the direction of the Pump (Antlia) constellation.
This changes direction of the last helix like so (rather crudely eyeballed and drawn, I know, but mostly preserves proportions): View attachment 113465
You need to imagine the already twisted helix from 3 as going towards Andromeda changing direction towards the 'net motion' one. Think of it, again, as a slinky toy with one end at the origin, and the other being dragged from the one arrow to the other. The trick is to preserve the angle of the bends as you do so.
So this step makes the helix from 3 more elongated and twisted in yet another way.

It is worth keeping in mind that these are the motions that can be thought of as representing reality only in this particular moment in time or in rough terms. As millions of years go by, and the stars and galaxies dance around each other in their gravitational ballet, there will come deviations and largely unpredictable changes.Now, can you imagine all these component motions happening at the same time? If so, good for you. :)
Personally, I tend to stick to the geocentric frame most of the time, else I get dizzy every time the Sun rises over the horizon.

hi. I am new here. I have a little science back ground. I am wondering if there is an explanation and mathematical definition for elliptic path of a mass rotating a center of mass?

 

[russ_watters]

hi. I am new here. I have a little science back ground. I am wondering if there is an explanation and mathematical definition for elliptic path of a mass rotating a center of mass?

A mathematical explanation for an orbit? Of course! This is why you know who Isaac Newton is!

http://faculty.washington.edu/storm/121C/lecture_notes/ellipse1.pdf
https://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica

 

[JMz]

And so on. I don't remember the estimated frequency of those oscillations, but it's probably on the order of a dozen per orbit.

25-30 MY as I recall, ~8 per orbit (which is indeed on the order of a dozen).