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    Re: Navigation using satellite doppler shift
    From: Bill Lionheart
    Date: 2016 Jan 31, 23:12 -0800

    I asked Dominic Ford, an astrophysicist who runs the excellent web site In the Sky https://in-the-sky.org/ how accuratly we know satellite positions. Here is our conversation. If you are not interested in the (done to death here maybe) debate about GNSS vulnerability you dont need to read the second reply! The bottom line is a few hundred metres for position of typical satellites. Maybe that is good enough for a method to use on an overcast day on a long passage. One thing I didnt think of is that some scenarios that knock out GNSS might disturb the orbits of all the other Satellites.

    Dominic writes:
    The accuracy of satellite positions varies considerably. Navigation
    satellites such as GPS / GLONASS are known to metre precision (the
    military may well know them to much better precision).

    However, spacecraft tracking is an expensive business. Unless you
    actively track them, gravitational perturbations and chaos kick in and
    you lose accuracy quickly. For many satellites there's no reason to
    spend money tracking them, and their positions are probably only good
    to a few hundred metres. At low altitudes (e.g. the ISS and almost all
    CubeSATs) the situation is particularly bad, because of atmospheric
    drag. The ISS loses several hundred metres of altitude per day and
    typically thrusts up into a higher orbit every couple of weeks.
    CubeSATs, of course, don't have propulsion, so they fall to Earth
    after a few months.

    Even where spacecraft are tracked, very few have positions measured to
    better accuracy than one metre, because that's extremely hard to do.
    The Earth's surface is subject to low-frequency seismic oscillations,
    and the Earth's rotation speed fluctuates. That means you have
    systematic errors arising from not knowing where your tracking
    stations are. To add to your woes, general relativistic time dilation
    (with altitude) is easily measurable when you're tracking an object
    moving at 30 km/s to centimetre precision. Your clock on your
    satellite goes at a different speed for your clock down below....

    There's a team at BAE systems in Chelmsford who specialise in doing
    this stuff for ESA, but their services don't come cheap!

    The predictions on my website are not that accurate, I hasten to add.
    They're probably good to around the nearest kilometre, as that was all
    I needed.. I use a quick-and-dirty Javascript routine to calculate
    positions from orbital elements. There are lots of small scale
    corrections that I only did as accurately as was needed for a pretty
    diagram!

    Hope that helps!

    Bill replies:

    Thanks Dominic, that is really useful. Do you mind if I quote you on
    NavList where we were discussing this?

    I think it means we (seafarers) still have to keep up our celestial
    navigational skills in case  Kessler syndrome some other calamity
    knocks the navigation satellites out!

    That said navigation to within 1 nautical mile is as good as we can do
    with celestial so even a radius of uncertainty of a few miles is OK
    for a back up system, ie how far away you can see land visually or by
    radar.

    I am not teaching problem solving by computer this year but another
    year I might make them do orbital calculations. I am teaching Euler's
    method to Chemical Engineers and it was fun to find out he invented it
    for the Lunar distance method for Longtitude. 

    > Thanks Dominic, that is really useful. Do you mind if I quote you on
    > NavList where we were discussing this?


    No problem at all!

    > I think it means we (seafarers) still have to keep up our celestial
    > navigational skills in case  Kessler syndrome some other calamity
    > knocks the navigation satellites out!


    Yes -- our reliance on GPS is interesting and scary. Recently a
    computer failure in Moscow knocked GLONASS completely offline for a
    few hours (the satellites were sent faulty data about their
    positions). A similar error in the US could knock GPS offline, with
    global consequences. To give one trivial example, Thameslink trains
    use GPS to determine when the train is in a platform. The doors won't
    open without a GPS link.

    This dependence on an American military system (which could be turned
    off at the flick of a switch in Washington) is what's led the EU to
    feel it needs to spend billions of Euros on Galileo, even though it's
    a totally redundant copy of GPS.

    As well as Kessler, another interesting scenario is a repeat of the
    Carrington Event (1859). We'd probably get 1-3 days' notice, and then
    we'd be looking at many satellite failures all at once. We'd also
    almost certainly see serious damage to the National Grid, taking
    months to repair. Interesting to ask how the UK would cope with a
    month-long nationwide power cut. It almost happened in 2012, but the
    storm just missed us.

       
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