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Ask Dr. SETI ®

Chapter 1: Astrophysics

Computing Doppler Shift

Dear Dr. SETI:
I was looking at the EXCEL spreadsheet for doppler corrections at:

There is mention of Doppler correction for the rotation of the Earth, but what about the rotation of the Earth around the Sun, which would be a much greater component? Is this already included in the above template or is another template/program be required for that?
Randy, Oz

The Doctor Responds:
You're right, Randy, that the absolute Doppler for the Earth's orbit around the Sun (and the Sun's around the Galactic Centre, for that matter) is large compared to Geo-rotational Doppler. And the spreadsheet doesn't address these. But we're less interested in absolute Doppler than we are in the rate of change of Doppler shift. The former, if known, would give us the actual transmit frequency (which is relatively unimportant). With the latter, we can find out very quickly whether a source is moving with sidereal time (in other words, whether it's truly extra-solar).

The contribution to total Doppler rate of our path around the sun varies with latitude and season, but for the test calculations I ran is on the order of one-fifth the Doppler rate-of-change contributed by the Earth's rotation. Over the short observing times available to us (especially in drift-scan mode), we may never see the slow rate of change in the "large" Doppler values, but we can easily determine the rapid rate of change in the "small" one. And it is rate of change of frequency, rather than the frequency change itself, which we use to separate the cosmic wheat from the terrestrial chaff.

When designing our search strategy, we also need to anticipate Doppler rate so as to determine maximum integration time and minimum bin width for our digital signal processing. In this context, all three Doppler contributions may prove siginficant, and thus we encourage our members to address the problem of analyzing the algorithms and devloping a more complete Doppler spreadsheet.

SETI League software committee chairman Dan Fox adds:

While it is true that we are more interested in the change in Doppler than the actual Doppler for SETI work, since many of us are also set up to do radio astronomy it might prove useful to have those formulas available. For instance, several people have noticed how much the hydrogen line gets shifted by the relative motion of the earth to various parts of the galaxy. If we want to search near the hydrogen band, in various frames of reference using long integration times, we should be able to figure out where the hydrogen line is Doppler shifted to.

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