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    Re: NOW what?
    From: Frank Reed
    Date: 2015 Aug 18, 13:24 -0700

    Noell Wilson, you wrote:
    "I think the key point is that gravity, and therefore what we call level, varies with the local mass of the earth."

    Exactly. The "geoid", which is the surface that is equivalent to "sea level" worlwide, has little undulations in it.

    Many people familiar with GPS readings associate the hills and valleys of the geoid with GPS altitudes. The raw altitudes taken direct from a GPS fix are given relative to a perfectly smooth mathematical figure --an ellipsoid (specifically the WGS84 ellipsoid). But because sea level, our normal measure of altitude, undulates up and down across the Earth's surface, raw GPS altitudes have to be corrected, basically by looking up the geoid offset in a table based on latitude and longitude. It's my sense that this is now relatively normal in most GPS devices. Ten years ago it was rare. The gravity models which define the geoid have become much more accurate, thanks to various satellite missions, and the output of those gravity models is now readily available to correct the altitudes from GPS data.

    In addition to these changes in altitude on the geoid, the geoid surface is also tilted slightly relative to the perfect spheroid at any given point on the Earth. It has to be tilted to get from a high spot to a low spot, but the tilts or "deflections of the vertical" have a lot of local detail --lots of little hills and valleys that correspond rather well with a tectonic map of the Earth. For example, as we have discussed before, there is a gravity hill at Bermuda. For a navigator practicing celestial navigation approaching Bermuda, the gravitational vertical tilts away from the island by up to a minute of arc. And this means that all celestial navigation fixes and all other astronomical position fixes are skewed outward from the island. This means that astronomically determined lines of latitude and longitude will necessarily be wobbly.

    And you wrote:
    "Other traditional observing spots around the world also have varying offsets as shown in Frank's bar graph."

    Right. And the bar graph, derived from the little article by Malys, et al., also shows that the local deflection of the vertical is an excellent match for the offset in longitude at all of the sites they examined.

    "My conclusion is that a great circle determined at multiple points by a Mercury AH or a bubble level will not be a perfectly straight line around the earth and none of this detracts from practical CN."

    Right. If we could determine the location of the prime meridian by astronomical observations at various points along its length, through England, France, Spain, and Africa, as well as points at sea, we would find that it snakes back and forth by up to a mile around the "true" prime meridian. And note that the astronomically determined prime meridian would have points both west and east of the true prime meridian. Greenwich's local circumstances place it 100 meters west of the true prime meridian. If the observatory had been built somewhere else along the prime meridian, then the shift could just as easily have been to the east.

    You concluded:
    "A question: Using the best mechanical equipment available today - not GPS - would Greenwich still be at zero longitude?"

    No! And I think that's the fun part! If we map the world with theodolites and chains, conducting a nice old-fashioned trigonometric survey of the entire globe, then the same results would hold: the Airy Transit line at the Greenwich Observatory would still be about 100 meters west of the true prime meridian. There is some small dependence on the choice of a datum ellipsoid, but not much (so long as it is a globally consisent ellipsoid). And note, too, that if GPS had never been invented --in fact, if powered flight and even hot air balloons had never been invented-- all of the observations reqquired to do this, could have been carried out by old-fashioned manual surveying. Latitudes and longitudes determined by manual surveying are not quite consistent with astronomical fixes (cel nav fixes) for exactly the same reasons that GPS positions are slightly inconsistent. GPS works by methods that produce true positions in 3d space, just as if we had surveyed them on the ground.

    Finally, note that there is one more wrinkle involving consistency of directions on the celestial sphere, which can also be considered consistency of observations of UT1. Those tilts in the bar chart I posted range up to 14 seconds of arc. In terms of time, that's nearly a second, so we're talking about readily measurable differences in time. Does this mean that time was always measured "wrong" at Greenwich by a third of a second? No, because, as described in the article, the plane of the meridian at Greenwich is exactly parallel to the plane of the true meridian at the true prime meridian. To visualize the latter, imagine going to that spot in the park at Greenwich 100 meters east of the Observatory. You point a laser directly to the zenith. But here you use careful surveying observations to make sure that the nadir defined by the continuation of the laser beam in the opposite direction, underfoot, passes exactly through the Earth's axis. The tilt in the latitude direction is a little more complicated, but we can ignore that for now. This beam is vertical as defined by the perfect ellipsoid of our coordinate system. Meanwhile over at the observatory, standing right on the traditional prime meridian, you aim a laser at the zenith, but this time you make it vertical entirely using local gravity (maybe a big pan of Mercury). The two vertical laser beams will be exactly parallel, and if you extend their direction to the stars, they point to exactly the same spot on the celestial sphere. It's in that sense that the true prime meridian is as nearly consistent with the traditional prime meridian as it can be.

    Frank Reed
    Conanicut Island USA

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