Observational Astronomy Project Ideas to Show Special Relativity

This semester, I'm taking a class on Observational Astronomy which requires us to perform observations for a final project over the course of roughly a month (mid-March to Mid-april, although it could be a bit longer or shorter). As we get to choose the project, I'd like to take this opportunity to prove to myself on an intuitive level the occurrence of Special Relativistic effects (time dilation, length contraction, etc.). I know they do happen, but I feel that it would help me and others that may be in similar situations to do an experiment to see it in action. Preferably, the experiment would show the effect directly rather than indirectly in order to better build intuition. However, I'm not sure what a good idea for such a project would be, especially given the time frame. Some thoughts I had involved Pulsar timings and De Sitter's observation that light from both stars in a binary star system arrive at Earth at roughly the same time, despite the vastly different velocities of the light sources. However, I'm wondering if there's a better/more intuitive experiment I could do (as well as what would fit the time frame allotted). I'd love to hear some thoughts on the matter.

Measure the Doppler on a spectral line from a single star. Would that vary measurably over a month due to the orbital motion of the Earth, and would the variation be measurably different from the Newtonian prediction? (I suspect the answers are "maybe" and "no", but it shouldn't be too difficult to check.)

Sciencemaster said:

This semester, I'm taking a class on Observational Astronomy which requires us to perform observations for a final project over the course of roughly a month (mid-March to Mid-april, although it could be a bit longer or shorter).

I don't have any recommendations for SR related items, but if you aren't able to come up with something you can realistically do involving SR then I recommend exoplanet transit observations. Hot Jupiter transits often occur over a matter of days, so you should have plenty of opportunities to see them.

This website should let you see any upcoming transits in your area: http://var2.astro.cz/ETD/predictions.php

I think what you want, like on your previous thread, doesn't exist.

Think about it this way - if one could find clear and convincing evidence for SR with a telescope and a month of observing time, why wasn't relativity discovered in 1600? Why did it take another couple of centuries?

Vanadium 50 said:

I think what you want, like on your previous thread, doesn't exist.

Think about it this way - if one could find clear and convincing evidence for SR with a telescope and a month of observing time, why wasn't relativity discovered in 1600? Why did it take another couple of centuries?

I see. When you put it that way, that makes complete sense. It did take several decades even *after* SR was proposed to collect the more direct evidence. I had hoped that since we know exactly what to look for today and have better and more accessible materials available, a layman (or at least your average physics student) could perform such an experiment--it certainly would help to see it for oneself. Even if not at home, stars do move around pretty quickly (and some (like pulsars) have weird properties) and all.

Sciencemaster said:

stars do move around pretty quickly

Not so much. The sun's speed around the center of the galaxy is about 0.07% of the speed of light. And remember, relativistic effects go as the square.

You might ask how far the sun moves in a month and compare it to the size of various planetary orbits.

Vanadium 50 said:

Not so much. The sun's speed around the center of the galaxy is about 0.07% of the speed of light. And remember, relativistic effects go as the square.

You might ask how far the sun moves in a month and compare it to the size of various planetary orbits.

Oh, I had imagined there would be a bunch of stars outside our solar system moved much faster than that relative to us.
As for comparing the sun's orbit to other planets, do you mean to indirectly show relativity or just to find its velocity? I'm pretty sure it's the latter but I'm a bit unclear about what you meant.

Sciencemaster said:

Oh, I had imagined there would be a bunch of stars outside our solar system moved much faster than that relative to us.

That's not the case.

Most stars are moving along with us, more or less. Again, look at it this way: the constallations are the same as they were 2000 years ago (again, more or less). So their motion is not fast, and way too small to measure it in a month.

My other point is a homework assignment:

1. Find the orbital speed of the sun in the galaxy
2. Multiply that by 1 month to get the distance the sun has moved
3. Compare this difference to the orbit of the planets.

Vanadium 50 said:

That's not the case.

Most stars are moving along with us, more or less. Again, look at it this way: the constallations are the same as they were 2000 years ago (again, more or less). So their motion is not fast, and way too small to measure it in a month.

My other point is a homework assignment:

1. Find the orbital speed of the sun in the galaxy
2. Multiply that by 1 month to get the distance the sun has moved
3. Compare this difference to the orbit of the planets.

Yeah, you're right. I just looked it up and the fastest star ever seen moves at roughly 8% of c, and even those moving at ~600 km/s are considered hypervelocity stars (and this is MUCH larger than other objects like comets and stuff). My initial thought was that some would just happen to be moving quickly since there's nothing special about our frame (aside from how similar it is to the Milky Way's center, which I suppose matters a lot) or at least that binary stars might move at relativistic speeds relative to one another (it seems they don't). It seems pretty much the only space stuff (for lack of a better term off the top of my head) we can observe moving at relativistic speeds are cosmic rays and the like.
I suppose astrological observations aren't really going to work (which makes sense given your earlier point). As for my original question, it does seem pretty infeasible to do such an experiment DIY. Unfortunately, it turns out my university only has one scintillator so I suppose the only thing left to do for me (or someone else in my position) is continue along and hope that someday I have access to a lab with the proper equipment (and be proactive about performing such an experiment). That is, Unless there's some other experiment to be done with basic undergraduate lab equipment--the professors were very helpful, we just didn't have the equipment).
As for your excercise, that makes sense, I was just a little confused by the wording.

Sciencemaster said:

I suppose astrological observations aren't really going to work

Astronomical! Astronomical!

Drakkith said:

Astronomical! Astronomical!

Oops! My bad, good catch. Too late to edit it, though... :(

Would it be possible using the orbit of Mercury? I don't think a very long observational campaign would be needed to show deviations from the predictions using just Newtonian physics. It was puzzling astronomers decades before Einstein.

You could also use the upcoming eclipse in April the way Eddington did in 1919 and show measurements of the positions of stars near the Sun deviate from where they should be without relativistic effects. That is about General Relativity though, not Special Relativity.

Mendrys said:

Would it be possible using the orbit of Mercury? I don't think a very long observational campaign would be needed to show deviations from the predictions using just Newtonian physics.

The error in position of the perihelion (not even the position of Mercury, but the location of its perihelion) is 43 seconds of arc per century. And it's swamped by the perihelion shift caused by the effects of other planets. This is a really hard observation with some heavy data analysis.

Mendrys said:

You could also use the upcoming eclipse in April the way Eddington did in 1919 and show measurements of the positions of stars near the Sun deviate from where they should be without relativistic effects.

That's more plausible, but it's a gamble on good weather, even assuming the eclipse is visible in the observation window.

Some questions for @Mendrys

(1) What is Mercury's orbital period?
(B) How many perihelia will you observe in 30 days?

(III) Is the school's observatory in the path of totality?
(Δ) If it is, what are the chances it will be unused and available during the few minutes of totality?

(questions re-labeled to appease @berkeman )

Vanadium 50 said:

(III) Is the school's observatory in the path of totality?
(Δ) If it is, what are the chances it will be unused and available during the few minutes of totality?

I know these questions were rhetorical/not meant for me, but I figured I'd give a bit of background anyway. In my specific instance (although it may not be true if someone else is in my position), the school is *close*, but not quite in the path of totality (maybe a couple of counties away...fine for observing it on your own but not great for a stationary observatory).

As for the second part, I'm not quite sure. Maybe if planned well in advance and luck is on my side? I can't think of any ongoing projects that would explicitly require it...but then again, I'm just a student taking a class, so any actual research would obviously take precedence. I'm going to go out on a limb and say it's definitely unlikely, but not impossible.

To repeat the Eddington observation, "close" won't cut it, You need totality.

You also need two observations, more than a month apart. (Can you explain why?)

Sciencemaster said:

I know these questions were rhetorical/not meant for me, but I figured I'd give a bit of background anyway. In my specific instance (although it may not be true if someone else is in my position), the school is *close*, but not quite in the path of totality (maybe a couple of counties away...fine for observing it on your own but not great for a stationary observatory).

As for the second part, I'm not quite sure. Maybe if planned well in advance and luck is on my side? I can't think of any ongoing projects that would explicitly require it...but then again, I'm just a student taking a class, so any actual research would obviously take precedence. I'm going to go out on a limb and say it's definitely unlikely, but not impossible.

If you get to an observatory that is on the path of total eclipse, you can bet that any telescope will have a LONG waiting list of people wanting to use it. Many will be professionals who have traveled from the other side of the world.

Vanadium 50 said:

To repeat the Eddington observation, "close" won't cut it, You need totality.

You also need two observations, more than a month apart. (Can you explain why?)

That makes sense. I figured it'd help to provide context to my current situation.

As for why, I imagine it's because after a month, the Earth will be at a different position/rotation relative to the sun, so the amount of lensing will change (i.e. classically, we'd only see the star move across the sky because of the Earth's/solar system's motion, but relativistically, the star will also appear to be at a different position relative to the star). For example, at one position, we might see a star, but after rotating around the sun, we could measure its position and see that it should have been blocked by the sun (or just at a different point in the sky) at the previous angle.

I suppose that was pretty wordy. TL;DR: in addition to the 'main' observation, we need to compare it to a 'control' image to show where the star would be without lensing.

Sciencemaster said:

TL;DR: in addition to the 'main' observation, we need to compare it to a 'control' image to show where the star would be without lensing.

Yes. But where will the stars be in the sky one month after they were just next to the Sun?

Ibix said:

Yes. But where will the stars be in the sky one month after they were just next to the Sun?

Ah. They'd be near the sun and the eclipse would be over. So we couldn't see it because it would be in the sky during the day. So we'd need to wait roughly 4-6 months until we were on the other side of the sun so Raleigh scattering wouldn't block it out.

Also, a thought--earlier in the thread, it was discussed that stars we observe are moving pretty slow compared to the speed of light. What about galaxies? I imagine it's possible to see some of those with a university observatory, and given Hubble's law and the fact that they aren't part of (gravitationally tethered to) the same galaxy, I'd imagine there's a higher chance that there's at least one visible moving at relativistic speeds as there's nothing special about our frame of reference.
My guess is that we can't see any moving that quickly with a university observatory as there just aren't any with such large velocity nearby, and we can't see far enough to observe fast galaxies. However, I wanted to make sure I covered all bases here.

Sciencemaster said:

My guess is that we can't see any moving that quickly with a university observatory as there just aren't any with such large velocity nearby, and we can't see far enough to observe fast galaxies. However, I wanted to make sure I covered all bases here.

You could look up the kit that Slipher and Hubble used for the earliest work - how does it compare to your university setup?

But note that you really need to do enough of a survey to verify Hubble's Law. Just spotting a couple of fast moving galaxies doesn't really prove much unless you can show that they fit reasonably well to a straight line on a redshift/distance graph. Redshift is obviously fairly straightforward to measure if you have enough light for your spectrometer to work with (do you, with the integration time available?), but what is the appropriate distance measure for the galaxies you can see and can you measure that in the observation time you have?

Suppose you could see NGC 999999 (I made that up) and it is receding at 0.9c.

Now what?

Vanadium 50 said:

Suppose you could see NGC 999999 (I made that up) and it is receding at 0.9c.

Now what?

Maybe you could compare the redshift to a classical analogue--although the survey might only be able to show Hubble's law at best rather than comparing relativistic redshift to its Newtonian counterpart.... My point was more that there might be objects moving at relativistic velocities that *can* be observed using a telescope (as opposed to stars).

Sciencemaster said:

Maybe

Sciencemaster said:

might

Sciencemaster said:

might be

I think you will need to do better. What exactly are you planning on measuring and what are predicted values?

Sciencemaster said:

comparing

How do you compare one thing? And if you need multiple measurements of multiple objects, how many of each? (You seem to be arguing Hubble is simpler than what you want to do. How many measurements did he make?)