Quote:
Originally Posted by Rockin Robbins
Now, is Greenwich Hour Angle the same as the Right Ascension of an astronomical object? I'm inclined to say close but no cigar, because astronomers use the Right Ascension to find an object. You use it for navigation.
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Right ascension is not used in navigation, but a related concept is: "SHA" or Sidereal Hour Angle. To understand both, you need to understand the "first point of Aries", usually referred to as just "Aries"
*. This is the point at which the ecliptic (the path that the Sun seems to follow in its apparent course through the stars throughout the year) crosses the celestial equator (the projection of the Earth's equator onto the "celestial sphere") when the Sun is ascending in declination. Ultimately, it's just a completely arbitrary point from which everyone agrees to measure positions.
Right ascension is the apparent arc distance of a body from Aries, measured from west to east. It is usually measured in hours, minutes and seconds. It's most handy for astronomers, because of something called "sidereal time". When Aries is on the observer's meridian, local sidereal time equals 00:00. About 6 hours later
*, Aries will be on the observer's western horizon (setting) and sidereal time will be 06:00. Now, if a body has an RA of 6h0m0s
* it will be on the observer's meridian - the best time to view it through a telescope. So, if we want to view a body with an RA of say...15h27m43s, we simply watch our local sidereal clock until that time, point our telescope at our meridian at the proper elevation, et voilą! There it is.
Now, SHA is also measured from Aries. But, unlike RA, it is measured from east to west in degrees, arc minutes and arc seconds. In celestial, it is usually only used for stars. The reason for this is to keep the almanac at a reasonable size. You see, there are 57 stars traditionally used in navigation (plus Polaris). They were selected based on their magnitude and distribution in the sky, such that, for an observer anywhere on Earth, the probability would be high that the positions of enough stars visible at twilight would be available for a "fix".
You are correct that GHA (Greenwich Hour Angle) is tabulated for each hour on the daily pages of the almanac, but even that is not enough precision for navigation. The rate of change in GHA varies between stars, planets and the Sun and Moon, but in every case it's fast enough to matter. Therefore, tables are included towards the back of the book which allow for interpolation down to each second of each minute of each hour of every day in a year. However, listing the GHA for all 57 stars, even hourly, would result in a massive tome...much too bulky to be practically usable...let alone even carried on a small vessel, where space and weight are at a premium. So instead, the GHA of Aries is listed, along with the SHAs of the 57 stars. (
See here for a sample "opening" of an almanac, courtesy of
Navsoft.) To obtain the GHA of a star, one needs to add the SHA of the star to the GHA of Aries (subtracting 360° when exceeding that value), and then interpolate for minutes and seconds. Longitude is then added (for east longitudes) or subtracted (for west longitudes) to obtain LHA, or Local Hour Angle. (Again, subtracting 360° when necessary.)
LHA along with declination (also listed on the daily pages of the almanac) are the two variables needed to calculate the position a body occupies at a given location. In practice, the position is calculated for an "assumed position" (AP) which is then compared to an actual observation (corrected for various factors) and an "azimuth" (direction) and "intercept" (distance) are obtained, allowing the navigator to draw a "line of position" (LOP) relative to the AP. The result is the intersection (if you're lucky) of the lines at the fix. As you mentioned earlier, the more likely scenario due to errors is a series of lines describing an area (a triangle for three observations) which contains the "most probable position" (MPP).
Since RA and SHA are both measured from Aries, just in different directions, SHA can be obtained from RA by converting RA to degrees (by multiplying by 15) and then subtracting it from 360. And RA can be obtained from SHA by subtracting SHA from 360. (Dividing the resultant degrees by 15 to obtain h:m:s, of course.) It should be noted that this is rarely necessary, due to the aforementioned fact that these two values are seldom used in the same pursuit. The main exception being when a navigator is plotting the positions of the Sun, Moon and planets on a "star finder" for planning purposes.
You may be wondering why the SHAs and declinations are listed on each three-day page of the almanac. It's because they are changing more rapidly than every 25 to 50 years due to "proper motion". Some more than others, but enough that it makes a difference for navigational purposes. However, there are a few pages in the almanac which list the SHAs and declinations for many additional stars for six month periods in case those stars need to be used in an emergency where the traditional stars are not visible due to cloud cover or some other reason.
Finally,
see here for an animation I made which attempts to explain how SHA and declination are measured. As I said, I sympathize with visual learners, being one myself.
...And that is probably way more than you ever wanted to know about that.
*Not to be confused with the Zodiac sign or constellation. Although, Aries gets its name from the constellation, because when it was first described, that's where it resided. Now, due to precession, its apparent position has moved.
*A "sidereal day" is about 4 minutes shorter than a solar day. Therefore, if you look at a particular star each day at the same time, it will appear to have shifted position to the east by about four minutes of time, or about one degree. This is due to the motion of Earth revolving around the Sun.
*Note that when referring to minutes and seconds of
time, we use "m" and "s". When referring to arc minutes and seconds, we use ' and ". That's how we avoid confusion.