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

[pishtaco]

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.

View attachment 107362

That is a great modification. I think these diagrams are great at explaining what can be very complex as all these planes are at different angles to each other and hard to present in a way that makes sense in a 3D way. Great work, I am going to share these with a budding astronomer in the family. Thank you.

 

[pliney the whiney]

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.

View attachment 107362

Wow. Great work. I was trying to do this in my head and it made my head hurt.

 

[Daystar]

Going back to fizixfan's first post and diagram, there were some comments about the solstices and equinoxes. I think that in that first diagram the solstices should be where the equinox labels are and vice versa. By the way why is fizixfan's name now struck through? Has he left the group?

 

[berkeman]

By the way why is fizixfan's name now struck through? Has he left the group?

Let's just say that he went from bad to worse in his behavior at PF over the 4 years that he was here, and by the end it was obvious that he had to leave. You won't see most of the worst of his posts, since they were obviously deleted.

 

[Kevin77]

Earth's equator from center 29°, planetary orbit 5.5° from center, 29-5.5=23.5
Planetary orbit backside of zodiac 52.5°, Earth's equator 29°, 52.5-29=23.5

 

[Humility]

Great diagram of the orientation of the celestial orbit to the galactic plane. However as a Southern Hemisphere dweller this appears to me to be a diagram that will be more correct in about 120 million years when the sun has orbited around the galactic centre so that the north pole is then facing galactic centre. Currently the south pole does hence the better view of the galactic centre from the southern hemisphere. If you move your earth orbit to the left of galactic centre then it will be correct.

 

[Bandersnatch]

so that the north pole is then facing galactic centre.

It's not immediately obvious from a 2d picture where the arrows are supposed to point in 3d space, but if you look closely at the markings on the Earth's orbit, you'll notice that it's drawn near to the winter solstice. As such, the northern hemisphere is in fact intended to be facing away from the Sun, and the galactic centre.

 

[sophiecentaur]

This is my "map" of the solar system with the orbits to scale.

10/10 for the 'enlightenment' style addition to your wall. I am all in favour for that sort of thing. I have a rather naff form of sun dial which is also a good conversation piece in the garden. There are some problems with the information that these models provide. I have vague plans to make my own orrery (you can buy kits, of course) but even the posh one (below) pays no atttention to scale. (Whipple museum, Cambridge). You would need to go outside every so often to alter the lengths of your proposed wires as the years progress. Everything is on the move constantly - even Polaris will be in the wrong place with a thousand years or so.

Kepler calculated that the planets orbit at different rates so the layout will always be on the move and your version may be nearly correct for once in a few thousand years (a stopped clock is right twice a day). Also, the actual distances (as the crow flies) do not represent how hard it would be to get from one planet to another. The energy bill for interplanetary missions varies a lot and we need to use tricks ( slingshot orbits ) to go further than Mars. You'd think that 'dropping down' to reach Venus or Mercury wouldn't be too heavy on fuel but, in fact, getting closer to the Sun involves a huge amount of 'retro' energy and that has to involve many passes close to Venus for it to kill out orbital energy.
I'd love to think of a representation of the relative efforts needed for Solar System trips between planets. It's to do with cost - benefit which is why Venus (boring and totally hostile) gets few visiting missions.

It's really good to consider the dynamic nature of ther Cosmos and to get in proportion the actual timescales involved in the fanciful ideas for manned trips out there. Colonising? They are having a laugh, IMO.

 

[DaveC426913]

I have a rather naff form of sun dial which is also a good conversation piece in the garden.

I just put a bird feeder / sundial up this week. Ripped it down off the side of the house and mounted it horizontally at the back of my yard.

I have to position it correctly and secure before I put the markings on it, but for now it's holding water.

DIL suggested it needs a little water pump and a birdcam mounted in the antenna.


Oh. Right. And I have to convince my wife it doesnt make us look like trailer trash. Which makes it technically A Conversation Piece, yes.

 

[sophiecentaur]

have been amused that the new selling point for SKY TV is that you don't need a dish. I never did get one.
Your dish won't have a water collection problem unless you are equatorial sited. But you can drill a hole at the lowest point.

As we're starting on show and tell . . . . .(It's about 18.00)

Cheers

 

[Imager]

As we're starting on show and tell . . . . .(It's about 18.00)

Wow, I never saw one vertically mounted! Verrrrry cool!!! Did you make it?

 

[sophiecentaur]

Wow, I never saw one vertically mounted! Verrrrry cool!!! Did you make it?

It's an Armillary Style. (Posh ones cost a lot!!) I started with an old bicycle wheel (a good circle) and made a semicircular band with the same radius as the bike wheel. . The long rod (the gnomon) points N-S and you get a shadow at right angles to the time scale for all seasons when it's lined up properly. (Sun high or Sun low). Apart from the hour change in spring and autumn it's easy to read throughout the year (except when the Sun dips low during the summer.

It hasn't needed winding once!!

 

[WHT]

I have a related question about the lunar declination with respect to celestial latitude, i.e. tracking the moon instead of a satellite. The declination goes from +/- excursions with a period of 27.2122 days and then slowly evolves between maximum excursions (max lunar standstill) at a period of 18.6 years (the precessional cycle of the lunar nodes). This becomes a trig sinusoidal expansion of the main period of 27.2122 days (aka the draconic period) with two sidebands. One is 27.3216 days (aka the tropical period) and the other is 27.1036 days. What is that latter period called? I can't find reference to it anywhere.

Interesting too is the etymology, as the sidebands are often referred to as satellite sidebands, which is not literal but more figurative in the sense that they are in proximal orbit to the main frequency. So that 27.3216 day would be the - sideband (slower frequency) while the 27.1036 day is the + sideband (faster).

 

[Ibix]

Apart from the hour change in spring and autumn it's easy to read throughout the year

Can you rotate the scale to deal with that, or do you just have to remember to correct for BST?

It hasn't needed winding once!!

The dung beetle gets pretty tired though.

 

[sophiecentaur]

Interesting too is the etymology, as the sidebands are often referred to as satellite sidebands,

This is normal terminology for a spectrum with one major component and identifiable groups of low level spectral components above and below the main component. The spectrum of narrow band phase modulation (in RF signalling etc.) has readily identifiable side bands. When the phase of a carrier wave varies by only a few tens of degrees (+/-) the sidebands look symmetrical. If a satellite is in orbit and is regularly disturbed by the presence of a nearby satellite you have the right sort of conditions to be described as phase modulation.

 

[sophiecentaur]

Can you rotate the scale to deal with that,

The scale can be rotated around the gnomon by releasing a clamp. Also, because of the oddities of the Earth's spin and solar orbit, the actual angle varies over the year. I sort of planned to adjust the scale on a weekly basis, to take care of that but, I actually don't bother to compensate for 'The Equation of Time' (Law of diminishing returns). Google "Analemma" for some nice images.

 

[Imager]

Google "Analemma" for some nice images.

I haven't thought it through, but I was surprised it flips in the southern hemisphere.

 

[sophiecentaur]

I haven't thought it through, but I was surprised it flips in the southern hemisphere.

It's not a 'positional' thing; it's a timing thing. You are so luck that there's such a lot of graphical help with these problems compared with the 60s.
1. The Earth's orbit is an ellipse (as with all orbiting bodies in practice)) and that means its angular speed varies. So the Sun is not overhead in exactly 24 hour steps; observed time is gained and lost on the way round.
2. The tilt of the Earth's axis distorts has another effect on observed noon time. The two variations are not in phase so the crossover of the figure 8 on the analemma is not half way up. The crossover depends on relative phases and not where you're looking from (North or South) a few thousand km compared with 150 million km distance to the Sun.

The graph of equation of time shows those two distinct components of the overall variation with time.

Nothing up there has fixed periods and one variation will drift in phase. There is a clear four year cycle in the equation of time but other perturbations mean no four year groups are the same.

 

[WHT]

Thanks for the clarification as to the origin of satellite subbands, as they do seem to associate with a cyclic "orbit" perturbing a primary cycle.

Still don't have an origin story for the unnamed +subband I was asking about. One place it may come up is in long-period tidal excursions. In the Bay of Fundy, where the most extreme tides occur, there's a maximum excursion that is large enough to fill up surrounding marshes every 4.53 years¹. I can calculate this number directly from the interference of the perigee/anomalistic cycle of 27.5545 days with the unnamed 27.1036 day cycle. 1/(1/27.5545-1/27.1036) = 1656 days = 4.53 years

What this implies is that the fast +sideband of the moon's declination cycle is amplified by the stronger lunar force as the moon nears the Earth during its perigee/apogee cycle. The slower -sideband amplification results in the 8.85 year cycle, which is called the apsidal precession cycle. So again this -sideband cycle has a name but the 4.53 year cycle doesn't. Both of these (27.1036 day and 4.53 year) probably should have a name, as there are names for many of the eclipse cycles.

¹ Desplanque, Con, and David J. Mossman. "Tides and their seminal impact on the geology, geography, history, and socio-economics of the Bay of Fundy, eastern Canada." Atlantic Geology 40.1 (2004): 1-130.

 

[sophiecentaur]

I never made the connection to the fact that the spiral arms spin out clockwise

The arms are 'just' density waves, in which some stars are closer together and others are further apart. All (most) stars at a given radius have similar speeds in the same sense. The arms are 'virtual' objects (not sure if that's the right term) but they move through the positions of the stars (and will contain a different set of stars over time). This is the same as with sound waves, in which the air molecules themselves do not travel far during a second but the sound travels 330m.
The stars' orbits perturb each other in a form of resonance - as do satellites round the Earth - although their mean speeds are all much the same.

 

[DaveC426913]

Yeah. Density waves. Where they bunch up together, like sound waves.

 

[WHT]

What this implies is that the fast +sideband of the moon's declination cycle is amplified by the stronger lunar force as the moon nears the Earth during its perigee/apogee cycle. The slower -sideband amplification results in the 8.85 year cycle, which is called the apsidal precession cycle. So again this -sideband cycle has a name but the 4.53 year cycle doesn't.

What is intriguing about this 4.53 year cycle is in how it gets conflated with the half-8.85 year cycle, which being 4.4 years is close to 4.53. There are many references to extreme tidal cycles being dominated either by (1) the 18.6 year nodal declination cycle or (2) the 4.4 year half-perigean cycle. So one is a moon declination effect and the other is a moon distance effect. But that specific 4.4 number never made intuitive sense, in that how can extreme tides occur due to both an apogee and a perigee? I think it gets explained as a precession of the apsides, in that an additional apogee occurs when the moon is on the opposite side of the planet from where the strongest direct apogee is. So the moon "sees" through the earth, or if tidal forces are partially tangential and thus tractive to the surface, an apogee would alternate on each horizon. This also means that the 27.5545 day anomalistic period has a virtual harmonic at 1/2 that cycle. One such recent reference is an article on nuisance flooding (NF) ¹

The role of long-period tides in modulating NF frequency​

In addition to secular changes in NF frequencies due to tidal changes, we also detect a ~4.5-year cycle in the time series of additional/reduced NF days (fig. S3), which is close to the half perigee cycle that modulates tides at a period of 4.4 years. The perigean (4.4 years) and nodal (18.6 years) modulations of tides affect high water levels (10). We quantify the impacts of these cycles on NF events by removing them from the tidal prediction and recalculating the number of NF days (assuming that these cycles would not exist); this is only done for the dataset with the observed tides, not the one with historic tides, as we assume that changes in the amplitudes of the 4.4- and 18.6-year cycles were negligible. The oscillations in NF days due to the low-frequency tidal modulations are evident, and their influence increases over time (Fig. 4D). The 4.4-year cycle adds up to 20 NF days across all locations (Fig. 4D) when it peaks under present-day sea level, whereas the 18.6-year cycle causes an additional 30 NF days during its peak compared to average conditions (Fig. 4D)

Like the Bay of Fundy example I referenced above, the consensus theory says 4.4 years, but the measurements are closer to 4.5 years. The behavioral difference between the two is that 4.5 years includes both declination and perigee wheres 4.4 years is just perigee.

I guess what I find odd about this is the disparity in precision and detail for this attribution in contrast to the incredible detail needed for total solar eclipse calculations. Consider the grade school science teacher that promised his class in 1978 that they would meet up again in 2024 to watch the eclipse near their school location in upstate New York -- and they did just that. Incredible precision needed for that.

Another piece of evidence is the plotting of data from the JPL Horizons on-Line Ephemeris System. I didn't create this plot (courtesy of Ian Wilson) but I don't doubt that it is correct, since the JPL tool is used for satellite orbit modeling.

¹ Sida Li et al.,Evolving tides aggravate nuisance flooding along the U.S. coastline.Sci. Adv.7,eabe2412(2021).DOI:10.1126/sciadv.abe2412

 

[WHT]

I tried recreating this chart I posted using the online NASA JPL Horizons ephemeris program, but couldn't duplicate the 4.53 year modulation cycle that Ian Wilson had managed to find.

What I always find is the 4.42 year modulation by multiplying the absolute value of the lunar declination cycle by the R lunar distance. This develops the beat 2/27.3216 - 2/27.5545 = 1/(365.242*4.425)

Declination of the moon with respect to the equator is different than with respect to the obliquity of the earth's rotational axis to the earth's orbit around the sun. IOW that's with respect to the ecliptic plane -- and when the moon crosses that leads to total solar eclipse cycles like we had in the USA the other week

The beat frequency when interacting with the perigee/apogee month would be 1/27.3216+2/(365.242*18.6) - 1/27.5545 = 1/(365.242*4.534)

So that the moon's declination wrt to the equator goes in and out of perfect alignment with the ecliptic plane at cycles related to the 18.6 year lunar nodal precession, which is related to the other extreme flooding cycle of 4.53 years (as mentioned upthread, occurring in Bay of Fundy as well as elsewhere). I have to conclude that the extremes at 18.6 and 4.534 years are more likely lunar ecliptic alignments than wrt declination?

I assume some sort of coordinate transformation is needed to get the NASA JPL Horizons output to align with an ecliptic orientation rather than the geocentric equatorial orientation it does now. I think it requires applying a rotation matrix using the obliquity ϵ such as:

x′=x
y′=y⋅cos(ϵ)−z⋅sin(ϵ)
z′=y⋅sin(ϵ)+z⋅cos(ϵ)