However, tetra3 can only used for large fov, build database for small fov is difficult.

That’s excellent! Thanks very much for the references.

There’s star-tracker code available on the ESA website for the Tetra tracker that also uses hash functions

https://github.com/esa/tetra3

And a simulator you can use to generate data for star-tracker evaluation

https://kelvins.esa.int/star-trackers-first-contact/scripts/

That’s amazing! Thanks

This is a common misconception. It’s the same problem either way. The gain of a directional antenna is the same, whether it’s receiving or transmitting. Concentrating your “listening power” to as restricted an area as possible is just as important as concentrating your talking power. Just as you want to avoid sending your transmitted signal in directions other than directly at the receiver, on the receiver you want to avoid receiving signals or noise from any direction than directly from the transmitter. In any case, when you’re using very high gain antennas, these are physically large, and deep space craft invariably use the same antenna for transmitting and receiving.

But you’re right about the other thing: it’s ANOTHER common misconception, it’s difficult to track the tiny Earth at great distances. The precision needed in positioning has nothing to do with distance, or the size of the target. It is determined ONLY by your antenna’s beam width. If you need to stay within the portion of your antenna pattern that is less than 0.1 dB down from its maximum, and on your antenna, this point in the pattern is 0.2 degrees wide, then you only have to be positioned within 0.2 degrees, regardless of how tiny your target looks. You don’t even need to SEE the Earth, as long as you can identify stars, and know where the Earth must be, relative to them. Which has been a solved problem for many decades.

The question wasn’t about when the chronograph was invented, it was a question about when the problem of measuring the longitude was solved, and it wasn’t really solved until the 19th century when clocks became cheap and accurate enough that other methods fell out of favor.

You’re simply arguing past the point.

You may think of the Longitude Prize as proving a concept – that you can make a clock that runs accurately enough and a procedure to use it for telling the longitude to some precision – but there’s a long way from the concept to being practical.