Model to draw an absolute straight line

[Flailan]

I am looking for information to assist me in designing a model or program to draw a straight line bisecting the universe. Ok maybe just the Milky Way galaxy. I would like to view this line from various points 1. as viewed from a point on Earth (possibly one of the poles) 2. as viewed from a point in space elsewhere in the galaxy. 3. as viewed from a point not in our galaxy. This is a project I am developing with my teenage son and would add various physical effects as it proceeds. ie: is the line a beam of light? and what are the effects on such a line. Any references to existing work or articles would be greatly appreciated.
Flailan

 

[Simon Bridge]

Welcome to PF;
I'm afraid the description is incomplete - you need to say what you mean by a straight line.

There is no such thing as an absolute straight line for example - so you do need to be clear about this. How would you now that your line is straight over galactic distances? i.e. any line you draw on the surface of the Earth would be curved - because of the curvature of the Earth.

The idea of bisecting the universe is tricky too - what does this mean? The Universe is usually understood as a 4D thingy so how could a mere 1D line be considered to "bisect" it? To just split a 3D object into two equal parts needs a plane, not a line.

Bisect the galaxy? Easier - since a galaxy is usually easier to treat as 3D.
Perhaps you mean to take the 2D projection of the Milky-Way in some orientation (through galactic north say) then find a line that passes through this projection with half the galaxy to either side?

The word "bisect" itself usually refers to angles so you see you still have some work to do properly describing the project. This seemingly simple goal turns out to be quite complicated in execution. That's pretty normal.

Even with these difficulties, some of your questions can be answered.
1. viewed from a point on the Earth - it will look like a curve across the celestial sphere. If the line passes close to a massive object, there may be a detectable kink in it due to the local curvature of space-time. You'd have to look really close though.

2. viewed from elsewhere - same thing. The details will depend on where you are. If you are at a point on the line, you won't be able to see it at all: it's a point.

3. from a point not in our galaxy - again: depends on the point and the direction you are looking.

questions 1-3 involve what is called a "projection" and it is just a matter of geometry.

is the line a beam of light?
No - it is a purely imaginary construct like the lines that join up the stars in a constellation or the lines of latitude and longitude on the globe.

and what are the effects on such a line.
Basically gravity and your point of view.

You may want to consider a less ambitious project - imagine the Earth had Saturn-like rings. What would they look like from different places on the Earth's surface, and at different times of day?

 

[Chronos]

Without a background metric, it is impossible to define a 'straight' line.

 

[Flailan]

Thanks for the reply. The idea came as a discussion of what a absolute reference line would look like from our perspective on Earth. Yes the universe idea is off the table. But a model of the galaxy with a line passing thru it's center at a right angle to it's rotation and a model of our solar system rotating within it would produce the proper output as viewed from Earth. I have not found anything helpful on the Net as of yet. The reduction of 3d to 2d would of course end up with a line that is drawn back and forth over itself which would be hard to display graphically. This may be a difficult program but I thought he (my son) had an interesting idea for a sci. fair project. It may have to wait until next year as you pointed out it is more of a geometry question. Know of anyone using "Autocad Space/Time" lol or any such program?
Flailan

 

[Flailan]

The line would reference the newly discovered gamma-ray bubbles as the north/south poles of our galaxy. Now if I could plot the orbit of our solar system using a simplified representation of the galaxy we could calculate the Earth's rotation within it. Then we could display the resulting line as it changes from our point of view.

 

[Simon Bridge]

Such lines would be "orbits" or "trajectories" rather than bisectors.
They are not normally thought of as "straight".

 

[Flailan]

now you have the correct question. the result would be a squiggly line representing a straight reference line as viewed from an orbiting planet in an orbiting solar system in an orbiting galaxy. but without the 3d this line would need to be drawn as time dependent animation showing the cursor moving back and forth as the orbits overlap. With 3D the output would rise and fall around the x-axis relative to the galaxy center line.

 

[Flailan]

Well I found a start, NASA had a vrml model of the milky way. I am in the process of importing this into Autodesk 3ds Max. I will see what "scale" they have used to produce this model. It uses a 44,000 star representation of the galaxy.

Data from NASA http://lambda.gsfc.nasa.gov/product/cobe/vrml_models.cfm

Milky Way model

The Milky Way VRML2 model is based on a statistical representation of the three-dimensional density distributions of stars of various spectral types (colors). Hot, luminous blue stars are concentrated close to the Galactic plane and in the spiral arms. Cool, red stars are distributed in a thicker layer about the plane and concentrated in the bar ("bulge") at the Galactic center. The stellar density distributions are those published by Wainscoat et al. (1992) for the main disk, and Dwek et al. (1995) for the bulge. A Monte Carlo method was used to sample the density distributions, yielding a 44,000-star representation of the Galaxy. The real Milky Way contains about 100 billion stars. Using a VRML browser, one can "fly into" the model to the location of the solar system to view the Galaxy from our unique vantage point in the disk, about 8.5 kpc from the Galactic center. Our understanding of the shape and orientation of the Galactic bulge was improved with the help of the COBE DIRBE near-infrared data. At visible wavelengths, those to which our eyes are sensitive, interstellar dust clouds block background starlight, producing an obstructed view of the center of the Galaxy, as is illustrated in the Multiwavelength Milky Way. The VRML model is similar in many respects to the Faint Source Model used by the DIRBE Team to represent the Galactic near-infrared starlight in the search for the cosmic infrared background (Arendt et al. 1998).

The Milky Way VRML model is one of six such models created for an educational project called iUniverse, which is currently under development.

 

[Flailan]

Any thoughts on using a single point instead of a line? The point representing the center of the galaxy the using the 3d model(s) to graph a 3d graph of our position relative to this point.

 

[Flailan]

I have begun the basic geometry for the formula.
1. using the center of the galaxy as the point to be graphed from our perspective.
2. our solar system's orbital period is 225M -250 Myr and it has a rotational axis is ? (read a part of a post in general astronomy but in was not much help) relative to the hypothetical galactic plane perpendicular to a assumed north/south axis.
3. the Earth's orbital period is 365.26 days and it's rotational axis is 23.5 deg. relative to the ecliptic plane.
4. the Earth rotational period is 24 hoursI will use the Earth's poles as the y-axis and the equator as x axis, the z axis will be perpendicular to the equator but set at the Earth's surface at a real location ( Ottawa, Ontario Canada). Time will be introduced in an animation to plot the points over a real period (maybe the last century)
This should produce some wonderful spirals and make the point of what a "straight line" drawn with a ruler on a piece of paper would look like to someone who was not trapped on our planet.

Now I need some physics variables to add in some more roughness to the graph.

 

[Flailan]

Just ran into the European Space Agency's Gaia telescope which launched in Dec. 2013 and it appears they are collecting just the data I/they require to produce a 3D map of the Milky Way. This should keep my son busy with real numbers for the next few years. It is most cool when science and teenager brains synchronize.

 

[bahamagreen]

Where are you going to locate the center of the galaxy? Are you going to project it where the center of the galaxy should be now, or where it appears now (where it was 26 thousand years ago)?

 

[Flailan]

I think for the for this project we should begin where we would see it now ( ? years ago ) and proceed to our relative time which would put it in the future. The difference in time of our orbit around the sun would be negligible compared to the time to the center of the galaxy, correct? Therefore the scale of one of the axis of this graph would have to be massive compared to Earth orbit. The solar systems orbit would end up somewhere relative to half the distance to the center's time.

 

[bahamagreen]

I'm not following what you mean about the axes and the Earth orbit.

The center is about 26K ly away, and the period of galactic rotation at the Sun's radius from the center is about 240M y, so in the time it takes for the light from the center to each the Sun, the rotaion has advanced about .04 degrees.

That might even be within the error of the distance to the center... a difficult measure and one of the least confident values about the galaxy.

 

[Flailan]

ok assuming sol and it's system of planets is in a circular orbit around the center of the galaxy, which is about 26k ly thus it is a constant. if we are graphing that point (the center) from Earth then the orbit of Earth around the sun is a variable and the rotation of the point on Earth we are graphing from is a variable. But they are so minute a change in comparison to the distance to the center of the galaxy I must use three different scales on a graph to display these variables. (confused yet?) so i hope the graph will show distance and direction from our point on earth. So the distance/time will be in 3 different scales. Therefore i hope to show 1 rotation of sol around the center of the galaxy and the spirals the 2 variables will produce.
I am working in autodesk 3ds to test scales so that the resulting graph is not only theoretically accurate but also easy enough for a high school level student to grasp the relationship by viewing it.

 

[Flailan]

please feel free to leave more comments while I play with the scales and I will take all information into account so that I can post a link to an example to what I am attempting to produce as soon as I have a working model. This will probably clear up what I am poorly attempting to explain as I refine the idea.
Thanks Flailan

 

[bahamagreen]

"...then the orbit of Earth around the sun is a variable and the rotation of the point on Earth we are graphing from is a variable."

True, but look at the comparative distance magnitudes...

The Earth's orbit diameter is 2 AU
One light year is 6324.1 AU
26K ly is 164426600 AU
The Earth's orbit is 1.2x10^-8 of the distance to the center.

The Earth's diameter is 8000 miles.
That is 5.2x10^-13 of the distance to the center.

Now look at the frequency magnitudes...

In the time that light arrives to Earth from the center, during which the galaxy has only rotated less than half a degree, the Earth has orbited the Sun 26,000k times, and rotated 9,490,000 times.

Wiki's latest on the galactic center is 25,000–28,000 light years. That looks like 26.5K ly +/- 1500 ly.

Your variables for the orbit and rotation compared to the center location error:
Center location error is 4,743,075 times Earth orbit diameter.
Center location error is 7X10^18 times Earth diameter.

Don't these variables of orbit and rotation seem too insignificant with respect to the distance to the center and too frequent for the time scales at this distance to justify accounting for them and simply doing it all based on the Sun's position?

 

[Chronos]

There is no way to construct a 'straight' line bisecting the universe. It begs the question by insisting on some sort of absolute coordinate system.

 

[Simon Bridge]

When plotting the trajectory of the Earth wrt the center of the galaxy(!), for the wiggle caused by the orbit of the Earth to be about the width of a the pencil line used to draw it (0.5mm) the diagram would have to be more than 84km across. Space is big - real big!

There is still the issue Chronos and I keep trying to draw your attention to - you still have to define what you mean by the "straight line". So far you look like you are taking a fairly simplistic approach to the coordinate system you want to use but there is still the actual reference line to describe so it is not actually clear what you hope to achieve.

I think to get decent help with your project you need to nail down those issues.

 

[Flailan]

Thanks all for the data. So here is the project for this year ( child is in grade 9 but has been into astrophysics and relativity for years now). We will draw a line apprearing straight to the artist on various planets in our solar system. The imaginary viewer (our output) will be just outside pluto somewhere traveling in sync with the sun. So our alien observer will see the line as a product of the planets rotation and orbit around the sun. This should limit out data to some spirals and wiggles and make a good example of each planets actual movement in space relative to the sun (or a point in sync with it). Next year we will tackle the BIG picture and use a similar model to display various sun's movements around the galaxy. Keeping the scales similar and hope fully displaying some similar results. In year 3 (grade 11-12) we can bring massive distances and the effects of gravity into the picture and using the previous groundwork and some real data being collected now hopefully demonstrate the real effects of time and space in our tiny nieghbour hood of the universe.

 

[Chronos]

Everything in the universe is in motion, so the points plotting any line you attempt to define have no 'absolute' coordinate references - even in a purely Newtonian universe.

 

[Simon Bridge]

I think the project has been refined to the point where an absolute reference frame is no longer part of the description. The observer is now described as stationary wrt the Sun center of mass, for instance.

We also have a context:
The project is to be suitable for an advanced 9th grader (i.e. 13-14yo).
It is reasonable, at this level, to have an investigation that cannot succeed provided, in the process, learning happens.

Instead of a line on the planets of interest, I'd suggest picking a spot on the planet instead - then you can trace the trajectory of the spot wrt some observer. You'd expect a weaving trajectory ... say if you looked "down" on the ecliptic. (your choice of observation point will likely have a very oblique view of the orbits - you won't get much detail that way - but the details will get boring anyway, see below.)

You still don't seem to appreciate the relative scales - on a scale where the Sun is 1m across, drawing all the planets (That is, out to Uranus) in would need a bit of paper 6km on each side. On that scale, the Earth is about 10cm across so the wobble you get tracing a spot on it's surface would be sort-of visible. It will have an amplitude of 5mm (0.2") and repeats every 1.7m (about 60").

The smallest you can get the picture and still have the wiggles bigger than the pencil line would be about 600m on a side.

The investigation is still worthwhile - it will show you how much those wall posters of the solar system are misleading you to begin with. To avoid too much frustration, take it slow: start by working out what it would take to build a scale model of the solar system. Putting the Sun scaled to 1m diameter - beach-ball, or some common round object - is handy because the other planets come out to easy to handle sizes ... then represent the distances to the planets in terms of common spaces - like if you put the Sun at one end of a football field, where would the orbit of the Earth go? Get your son to do it.

 

[Chronos]

It might be more practical to model distance on a log scale.

 

[Flailan]

that's what I was thinking log or exponential growth along the axis using a non-linear graph. I have found some interesting sites that use this approach to demonstrate relativity. As you have mentioned everything is in motion so the graph will end up being a dynamic animation. I also am very interested in developing a chaos theory type graph that use the "center" of the galaxy as a strange attractor this would eliminate the problem of not knowing the exact location of said center. As it has been pointed out repeatedly that there is no such thing as a straight line ( which was a given at the beginning of this thread) it was my son's idea was to demonstrate that point. My background is in math and computer science so I end up out of my comfort zone when astrophysics questions from a 14y old go beyond my comprehension. He did a model of the solar system (to scale) when he was 8. So his understanding of the distances are clear. He even has a pretty good grasp of relativity (beyond mine). I have relayed the information from this site and as it has been pointed out the scale is the issue we are developing a graph not based in the linear scales that most of the replies seem to be stuck in. Personally I am hoping to discover a equation that works independent to scale (wishful thinking). I can see that a simplified "wall poster" approach will be required for most kids to grasp the distances and curvatures involved.