Usefulness of Stellar Parallax?

[NatFex]

This isn't a very technical series of questions, just some passing thoughts I had whilst looking over some notes I had on stellar parallax distancing.

Stellar parallax is always described as a means of "measuring the distance to stars." But from where?

What I mean is, the distance, or the side of the right-angled triangle that's calculated is not a line joining the Earth and said star. It goes down from the star to some arbitrary point between the two positions of the Earth seen over a 6-month interval. If that wasn't clear I've made a drawing and stuck it in the spoiler below (see red 'x'):

Spoiler

Is this distance value typically adjusted later on in any way to make it more meaningful? If it is, what becomes the new reference point, since the Earth is constantly in motion? Is it the Sun?

Thanks

 

[phyzguy]

The stars are so far away that it really doesn't make much difference whether you are talking about the distance from the Earth at one side of the orbit, the distance from the Earth at the other side of the orbit, or the distance from the Sun. It's like asking whether the distance from where you are to Moscow is the distance from your left eye or your right eye. But, to answer your question, I think astronomers generally use the distance to the sun as the reference point.

 

[JCMacaw]

Stellar parallax is always described as a means of "measuring the distance to stars." But from where?

What I mean is, the distance, or the side of the right-angled triangle that's calculated is not a line joining the Earth and said star. It goes down from the star to some arbitrary point between the two positions of the Earth seen over a 6-month interval. If that wasn't clear I've made a drawing and stuck it in the spoiler below (see red 'x'):


Is this distance value typically adjusted later on in any way to make it more meaningful? If it is, what becomes the new reference point, since the Earth is constantly in motion? Is it the Sun?

Thanks

Your picture should look like this: The Sun, Earth and star make a 90 degree triangle

 

[NatFex]

The stars are so far away that it really doesn't make much difference whether you are talking about the distance from the Earth at one side of the orbit, the distance from the Earth at the other side of the orbit, or the distance from the Sun. It's like asking whether the distance from where you are to Moscow is the distance from your left eye or your right eye. But, to answer your question, I think astronomers generally use the distance to the sun as the reference point.

Yeah that's what I was thinking, the difference is probably tiny (relatively) Thanks

Your picture should look like this: The Sun, Earth and star make a 90 degree triangle View attachment 98337

Yeah that was actually my next question, does it matter? I was wondering if it would be right to say that if the two angles from the star were added up and divided by 2 that would be equivalent to if the star were equidistant from both positions of Earth. So that's not the case, can I know why my assumption was wrong? Cheers

 

[phyzguy]

I was wondering if it would be right to say that if the two angles from the star were added up and divided by 2 that would be equivalent to if the star were equidistant from both positions of Earth. So that's not the case, can I know why my assumption was wrong? Cheers

What's wrong with your drawing is that we choose the times during the year that maximize the parallax, which is when the line between the two Earths is perpendicular to the line from the sun to the star. So the point halfway between the two Earths is at the position of the sun.

 

[newjerseyrunner]

It's not very useful, it's useful for only a handful of the nearest stars. It may not be useful because it doesn't work at great distances, but works very accurately for close stars, and considering we have no other way to determine distances accurately except for extreme distances like to cephiad variables and type iib supernovas, I'd say it's usefulness is pretty high.

 

[phyzguy]

It's not very useful, it's useful for only a handful of the nearest stars.

This was true in the past, but no longer. The Hipparcos satellite measured accurate parallaxes to over 100,000 stars, and the Gaia satellite is currently in the process of measuring parallaxes to over 1 billion stars. The accuracy goal for Gaia is 20 microacrseconds, so it will be able to measure the parallax of an object up to 10's of thousands of parsecs away, which is most of the galaxy.

 

[NatFex]

What's wrong with your drawing is that we choose the times during the year that maximize the parallax, which is when the line between the two Earths is perpendicular to the line from the sun to the star. So the point halfway between the two Earths is at the position of the sun.

Pardon my asking but I have a few more questions

If we choose specific times of the year to maximise parallax, how is that done if we don't know how far away the star is?

Also if that's the case then the two angles measured at the opposite ends of Earth's orbit are going to be the same. Why measure both angles when you could just measure one, if you know that the angle is going to be the same on the other end? Is it to average them and reduce error?

 

[phyzguy]

Maybe it helps to look at the actual data taken by the Hipparcos satellite. Does this answer your questions? The reason the curves look different depends on where the star is in the sky. If the star is in a location perpendicular to the Earth's orbit, then the path will be a circle (superimposed on the proper motion). If the star is in the plane of the Earth's orbit, then it will be a highly flattened ellipse, basically a straight line(superimposed on the proper motion).

 

[Chronos]

Yes, the Hipparcus project accurately measure the parallax of over 7000 stars out to a distance of about 500 light years. Prior to this mission astronomers had only rough measurements on about 100 stars - a significant improvement. You can read about it here http://wwwhip.obspm.fr/heritage/hipparcos/SandT/hip-SandT.html,
From Hipparchus to Hipparcos by Catherine Turon.

 

[jtbell]

If we choose specific times of the year to maximise parallax, how is that done if we don't know how far away the star is?

For that, we don't need to know how far away the star is, do we? Only its direction.

 

[|Glitch|]

It should also be noted that of all the various methods for determining the distance of celestial objects, parallax is by far the most accurate. That makes it very useful indeed, despite its limited range.

 

[newjerseyrunner]

I didn't know we had anywhere near the sensitivity we had for that. I wonder how far out in the solar system we'd have to send a telescope to detect parallax of distant galaxies.

 

[Janus]

I didn't know we had anywhere near the sensitivity we had for that. I wonder how far out in the solar system we'd have to send a telescope to detect parallax of distant galaxies.

With the accuracy of the Gaia satellite, to measure a parallax out as far as the Andromeda galaxy( ~2.5 million ly), you would need need to orbit some 15.5 times further from the Sun than the Earth. (somewhere between Saturn's and Uranus' orbits.)

 

[NatFex]

Many thanks @phyzguy and others on this thread who've helped, this has really cleared up all the misconceptions I've had

 

[newjerseyrunner]

With the accuracy of the Gaia satellite, to measure a parallax out as far as the Andromeda galaxy( ~2.5 million ly), you would need need to orbit some 15.5 times further from the Sun than the Earth. (somewhere between Saturn's and Uranus' orbits.)

Interesting... doable, but not practical right now.

 

[Janus]

Interesting... doable, but not practical right now.

And Andromeda is the closest of the major galaxies. To measure the parallax for Sextans B, which is just on the edge of our own local group, you would have to have a base nearly equal to the diameter of Neptune's orbit, and you still haven't gone further than the local group of galaxies.
For Centaurus A, some 13 mly distant, you'd have to move out to twice the distance of Pluto and where the orbital period would be ~701 years. Not only would this make for a long wait between measurements, but is also likely that during that time more sensitive equipment will be developed that could do the same measurement with a much smaller base.

 

[newjerseyrunner]

And Andromeda is the closest of the major galaxies. To measure the parallax for Sextans B, which is just on the edge of our own local group, you would have to have a base nearly equal to the diameter of Neptune's orbit, and you still haven't gone further than the local group of galaxies.
For Centaurus A, some 13 mly distant, you'd have to move out to twice the distance of Pluto and where the orbital period would be ~701 years. Not only would this make for a long wait between measurements, but is also likely that during that time more sensitive equipment will be developed that could do the same measurement with a much smaller base.

Uh, you seem to have forgotten something major: you don't need to wait for it to do an orbit, you just need two readings. There is no reason that they have to come from the same telescope. It's still wildly impractical, but not for the reasons stated here.

 

[Janus]

Uh, you seem to have forgotten something major: you don't need to wait for it to do an orbit, you just need two readings. There is no reason that they have to come from the same telescope. It's still wildly impractical, but not for the reasons stated here.

Sure, if the object you are measuring the parallax for is properly aligned with the two telescopes at the moment of the measurement. But what about other objects? Remember, to maximize the parallax measurement, the direction of the object needs to be at a right angle to the line joining the telescopes. This limits the maximum parallax measurement to four directions for any particular alignment of the telescopes. To measure objects in other directions you need to wait for the whole system to rotate. And with a period of 701 years, even a ten degree shift would take almost 20 years. A full sky survey of all objects in range would take 175+ yrs.

 

[snorkack]

Hipparcos measured parallaxes with errors of 2000 μas.
Gaia is supposed to measure parallaxes with errors of 7 μas.
300 times more exact.
How?
By having a bigger mirror and less diffraction from aperture?
Hipparcos has a 29 cm telescope. Gaia should then have a 80 m aperture.
Does not look like this. Actually, the aperture of Gaia is quoted as just 145 cm. Mere 5 times the size of Hipparcos.
How does Gaia achieve that precision?
Could you have a telescope which is many times more precise than Gaia again, without being many times bigger?

 

[phyzguy]

This site has a fairly detailed description of the optical system. It is not a simple telescope, it has a complex optical system with two optical paths pointing in two different directions and it somehow uses this to measure small changes in direction. I don't understand it in detail, but if you want to know more, you could dig into this.

 

[AgentCachat]

Pardon my asking but I have a few more questions

If we choose specific times of the year to maximise parallax, how is that done if we don't know how far away the star is?

Also if that's the case then the two angles measured at the opposite ends of Earth's orbit are going to be the same. Why measure both angles when you could just measure one, if you know that the angle is going to be the same on the other end? Is it to average them and reduce error?

You need the maximum separation between your observation points. Its like having a wider distance between your eyes(our eyes have evolved for an optimum distance for our environment.) Then you can use the "skinny triangle" approximation for most cases. Wikipedia has an article on skinny triangles. ALL observations of stars involve skinny triangles. I know, I know, for optimum results don't approximate. The you might get the distance as 10.01 pc as opposed to 10 pc.

 

[Chronos]

The accuracy of GAIA vs HIPPSRCOS is not just a matter of instrumentation. As noted in this paper; http://arxiv.org/abs/1202.2064, From Hipparcos to Gaia: "Compared to Hipparcos, it [GAIA] will bring a gain of a factor 50 to 100 in position accuracy... During its 5-year flight, Gaia will measure objects repeatedly, up to a few hundred times. ...The length of the [HIPPARCOS] mission was 3.3 years, during which a mean of 110 measurements per object were collected". The number of measurements per object plays a big role in limiting positional uncertainty.

 

[mfb]

With the accuracy of the Gaia satellite, to measure a parallax out as far as the Andromeda galaxy( ~2.5 million ly), you would need need to orbit some 15.5 times further from the Sun than the Earth. (somewhere between Saturn's and Uranus' orbits.)

The parallax would be 20 microseconds, but 20+-20 is hardly a useful result. Also, Gaia needs ~70 observations of stars of magnitude ~15 or brighter to achieve this resolution, and no star in the Andromeda galaxy is that bright sufficiently long.

@snorkack: To measure parallax, you only need the central position of the diffraction pattern, you are not limited by diffraction. Gaia's optics is a bit "misaligned" on purpose to smear the starlight out a bit - this spreads it more evenly over the sensors, and helps fitting the central position with higher accurary. Gaia has no way to (optically) separate a binary star at 20 µas, that would indeed need a much larger telescope.

@phyzguy: the second observation window is necessary to get the absolute positions right. Parallax relative to nearby background sources wouldn't need it. But with that second point of view, you can measure things that are 60 degrees apart. Do this in multiple different directions and you can produce an all-sky map (which is a complicated problem mathematically, but it is solvable).Gaia is the first telescope where the variable distance between Earth and stars becomes relevant for parallax measurements. It is not sensitive enough to see parallax changing over time, but to improve the measurement stellar radial motion over the observation perid and radial motion of Earth should be taken into account as a small correction.

 

[snorkack]

@snorkack: To measure parallax, you only need the central position of the diffraction pattern, you are not limited by diffraction. Gaia's optics is a bit "misaligned" on purpose to smear the starlight out a bit - this spreads it more evenly over the sensors, and helps fitting the central position with higher accurary. Gaia has no way to (optically) separate a binary star at 20 µas, that would indeed need a much larger telescope.

The point spread function of a telescope, for continuous wave/infinite number of photons, is known exactly. It follows that even if you have a big Airy disc, you can analyze the precise distribution of light in the Airy disc, and detect small deviations from the point spread function, caused by other light sources well inside the Airy disc.

 

[mfb]

I said "separate" for a good reason.
Anyway, we do not have an infinite number of photons, and we also do not have a 100% accurate model of Gaia's optics at every time.
20 µas is about the diameter of an atom within the size of Gaia.

 

[Fervent Freyja]

Pardon my asking but I have a few more questions

If we choose specific times of the year to maximise parallax, how is that done if we don't know how far away the star is?

Because, the distance can be derived alone by another method measuring spectroscopic parallax, which should not be mistaken for stellar (geometric) parallax or grouped in together as it often is...

One can only hope that Gaia has an entire committee devoted to establishing and maintaining good terminology. Hope that helps!

 

[mfb]

Spectroscopic parallax needs a calibration, which is based on geometric parallax (and our sun, but that is just a single data point).

 

[phyzguy]

Because, the distance can be derived alone by another method measuring spectroscopic parallax, which should not be mistaken for stellar (geometric) parallax or grouped in together as it often is...

One can only hope that Gaia has an entire committee devoted to establishing and maintaining good terminology. Hope that helps!

I would submit that the term "spectroscopic parallax" is a misnomer, since it does not involve parallax at all. A better name would be "spectroscopic distance determination".

 

[Fervent Freyja]

Spectroscopic parallax needs a calibration, which is based on geometric parallax (and our sun, but that is just a single data point).

Oh.

I would submit that the term "spectroscopic parallax" is a misnomer, since it does not involve parallax at all. A better name would be "spectroscopic distance determination".

Oh.

Next time, water it down a little more for me will you all? It is an excellent motivator- I truly appreciate it!