# Doppler spectroscopy to verify Earth's speed around the sun

I'm looking for data points to check changes in $z$ as the Earth moves towards and away from a star. I'm finding lots of data for various objects [1] but lots of variation too (for eg, the results for M31 are quite varied from -230 to -330 though perhaps that's due to the many moving parts within M31 that could be the source in each measurement?).

I was wondering what object I should be looking at if I wanted a simple example showing how we can verify Earth's velocity around the sun using spectroscopy, as it's a value we can also calculate by other methods as around 30km/s. I'm guessing ideally this would be a star in our own galaxy that is close to lying on the plane of Earth's orbit around the sun. Measurements over time could be used to check that the only variation in $z$ correlates with Earth's orbit.

Are there tutorials or similar showing how this can be calculated? (It sounds like a good tutorial question to help people learn)

Edit: Updated to clarify question.

• Is there any reason for the -1 vote? It'd be nice to know so people know how to improve their questions. – Michael Nelson Apr 15 '14 at 13:43

If you want to do that yourself, you can look at the SDSS catalog. It provides freely available spectra over several years. The problem is, their resolution is right about the speed of the Earth, $30 km/s$ (vs $29.8 km/s$) (I wonder if they are related). There are higher resolution sources, but they are not as easy to grab (to my knowledge, but I am not a profesional astronomer).

You can probably boost your resolution a bit if you take big averages, and analyse different angles. With a good fitting model, enough data points, and a bit of boosttrapping you could get nice values.

To get the best results, I would recommend to go for bright objects (low signal to noise ratio), and simple. In a galaxy there are too many things going on, specially in the core; you are better off with single stars. Plus, in this situation, you can study them individually.

Even here there are a few caveats. You definitely don't want giant stars (too much turbulence and distortions), but luckily, most of them are in the main sequence.

Lastly, be warned, automatic processing of spectra (extracting lines and so on) is not as simple as one may wish, or think.

Edit:

If you want to avoid reducing spectra all together, you can just query for the redshifts of stars (say they are brighter than a certain magnitude). You will need accuracy of $10^{-4}$, and it seems to be provided.

Problem: you need to write a SQL query, but there are several examples that you can just copy and strip down to your need (most astronomers are not advanced programmers anyway and they mange), or just as at SO.

A very nice project idea! I wonder how far can you push it.

• Note that to get a velocity from a single measurement, you need a resolution $< 0.07 nm$ for red light. – Davidmh Apr 15 '14 at 13:57
• Thanks David. Yeah, I'd be happy for processed data that gave the unfiltered z-shift if I knew how to then apply the filters to take into account the Earth's velocity at the time of observation. It's hard to understand when and what standard filtering has already been applied. Thanks! – Michael Nelson Apr 15 '14 at 14:09
• SDSS guys provide all the details in a surprisingly nice way. You have all the documents in my first link. It is true that you can just query the data and get only the redshifts. I am editing the answser to add it. – Davidmh Apr 15 '14 at 14:13
• Very nice. Here's a first query which I'll work with... it seems pointless to filter on signal/noise there (I guess because it's also a factor in determining zErr). One thing I'm uncertain of is the SpecObject.z value, the schema comment says "Final z", so I don't know if that means after filtering for the Earth's velocity (and other factors). paste.ubuntu.com/7260907 – Michael Nelson Apr 16 '14 at 11:25

See Vogel, H.C. "On the spectrographic method of determining the velocity of stars in the line of sight" Monthly Notices of the Royal Astronomical Society, Vol. 52, pp. 87-97 (1891). http://adsabs.harvard.edu/full/1891MNRAS..52...87V
47 nearby stars were studied and the Doppler shifts of these stars were calculated on various days of the year.

• Thanks Dave. Despite the age, it looks useful (I'll just do the conversions from mph, and then check for more recent data), but I'm really looking for a tutorial or similar of the standard filters used (to take into account Earth's motion) so I can better understand. – Michael Nelson Apr 15 '14 at 14:00
• Vogel was the first to measure the seasonal variation of stars' Doppler shift due to Earth's orbit. – DavePhD Apr 15 '14 at 15:34