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Re: Basic questions about Lunars
From: Geoffrey Kolbe
Date: 2013 Jan 26, 08:32 +0000
From: Geoffrey Kolbe
Date: 2013 Jan 26, 08:32 +0000
Frank, you wrote:
As I understood the primary purpose of lunars, it was to use the moon as a clock to determine time at Greenwich. From this time, and its difference to local time, (easily determined), longitude could be estimated.
In the reduction process of a lunar, you either need to measure the altitudes of the bodies or calculate them. For a single observer, there are problems in measuring the altitudes for the time of the measured lunar distance, and where one is in an urban desert like Chicago, measuring altitudes is not an option. So, there are good reasons to use some estimate of longitude so that the required altitudes of the two bodies used can be calculated instead of measured.
Using an estimated longitude (and known latitude) to calculate the altitudes could well be the biggest source of error, (indeed, one assumes that it is), which can be minimised by a recursive process, i.e. using your newly estimated longitude to go around the calculation again.
So, what angular separation of the two bodies minimises this recursive process and so is least sensitive to the observer's actual longitude? I think the answer is 90 degrees, as you have shown that the precision requirements for the altitudes are minimised at this distance, but I was just checking.
Regards
Geoffrey
Geoffrey, you wrote:
"Is there a lunar angle which is least sensitive to observer longitude and is therefore the best angle to use?"
I'm not sure I understand your question. Did you mean "MOST sensitive to observer longitude" since the goal of lunars (historically) was to determine longitude? Assuming that's the case, then no.
As I understood the primary purpose of lunars, it was to use the moon as a clock to determine time at Greenwich. From this time, and its difference to local time, (easily determined), longitude could be estimated.
In the reduction process of a lunar, you either need to measure the altitudes of the bodies or calculate them. For a single observer, there are problems in measuring the altitudes for the time of the measured lunar distance, and where one is in an urban desert like Chicago, measuring altitudes is not an option. So, there are good reasons to use some estimate of longitude so that the required altitudes of the two bodies used can be calculated instead of measured.
Using an estimated longitude (and known latitude) to calculate the altitudes could well be the biggest source of error, (indeed, one assumes that it is), which can be minimised by a recursive process, i.e. using your newly estimated longitude to go around the calculation again.
So, what angular separation of the two bodies minimises this recursive process and so is least sensitive to the observer's actual longitude? I think the answer is 90 degrees, as you have shown that the precision requirements for the altitudes are minimised at this distance, but I was just checking.
Regards
Geoffrey
