03-30-2023, 08:51 PM
Carlos Pindle had mentioned he did not understand why the Astron app allows you to use a "decide for yourself" latitude and longitude for an assumed position.
I will try to shed some light on that subject if I can.
When we derive a calculated altitude (Hc) for an observed body what we are actually doing is finding a proxy value for the distance along a great circle from that assumed position (AP) to the geographic position of the body. The reason I say it is a proxy distance is because the actual distance from or AP to the GP of the body is found by
(90° - Hc) = zenith distance.
The reason for using the altitude above the horizon is simply because it would be very difficult to base our observations from a selected spot on the celestial sphere that was directly over our heads (our zenith.) But since we know that the total distance from our zenith to the true horizontal is always 90° it is easy enough to figure out the zenith distance.
We take a measurement of how high a body appears to us above the horizon, which is a little below true horizontal because the Earth is sphere and the surface falls away from us in all directions. We correct this for that dip of the horizon and for atmospheric refraction, and for some bodies parallax and semi diameter. We now have Ho. If we subtract Ho from 90° the result will be how far we are from the GP of the body expressed in degrees. Converting this to all arc-minutes converts that number into nautical miles.
Now suppose we wanted to know how far it is by great circle from New York to London? It turns out we use the same math for that calculation. We input an AP near to New York that either IS the EXACT lat and lon of New York for calculator methods, or we derive an AP nearby to New York as our starting position (usually called "the departure"
but I prefer "starting point") and we put in the location of London (usually called The Arrival, but I prefer "the end point") using its latitude in place of declination and its longitude as a Greenwich Hour Angle. Then we do a perfectly run-of-the mill sight reduction. The Zn is the initial great circle course (it changes throughout the track) and (90° - Hc) = the great circle distance. Because it is a great circle every arc minute is one nautical mile, so converting Hc into all arc-minutes gives the great circle distance in nautical miles.
Now if you are still with me consider the following:
Suppose you knew of a reef that you wanted to give plenty of berth? Or maybe a restricted zone you did not want to enter? If you can pick ANY AP you want you can pick a point on the reef's edge or on the demarcation line of the restricted zone and using that IN PLACE OF a "normal" AP you can get an HC from that spot to compare to the Ho you got of a body from your actual location-- and that result tells you how close you are to the reef.
The one thing you have to keep in mind is that the lines of position (LOP's) plot perpendicular to the azimuth so you need a body that you see in the general direction of the reef; or its reciprocal.
By extension if you want to figure out how far you progressed along your course you could pick an AP some where out on your desired track and use a body ahead or astern and by this means check your speed over the bottom.
It is perhaps for these purposes that the Astron app lets you pick your own AP. It provides increased versatility all out of the same math.
Peter
I will try to shed some light on that subject if I can.
When we derive a calculated altitude (Hc) for an observed body what we are actually doing is finding a proxy value for the distance along a great circle from that assumed position (AP) to the geographic position of the body. The reason I say it is a proxy distance is because the actual distance from or AP to the GP of the body is found by
(90° - Hc) = zenith distance.
The reason for using the altitude above the horizon is simply because it would be very difficult to base our observations from a selected spot on the celestial sphere that was directly over our heads (our zenith.) But since we know that the total distance from our zenith to the true horizontal is always 90° it is easy enough to figure out the zenith distance.
We take a measurement of how high a body appears to us above the horizon, which is a little below true horizontal because the Earth is sphere and the surface falls away from us in all directions. We correct this for that dip of the horizon and for atmospheric refraction, and for some bodies parallax and semi diameter. We now have Ho. If we subtract Ho from 90° the result will be how far we are from the GP of the body expressed in degrees. Converting this to all arc-minutes converts that number into nautical miles.
Now suppose we wanted to know how far it is by great circle from New York to London? It turns out we use the same math for that calculation. We input an AP near to New York that either IS the EXACT lat and lon of New York for calculator methods, or we derive an AP nearby to New York as our starting position (usually called "the departure"
but I prefer "starting point") and we put in the location of London (usually called The Arrival, but I prefer "the end point") using its latitude in place of declination and its longitude as a Greenwich Hour Angle. Then we do a perfectly run-of-the mill sight reduction. The Zn is the initial great circle course (it changes throughout the track) and (90° - Hc) = the great circle distance. Because it is a great circle every arc minute is one nautical mile, so converting Hc into all arc-minutes gives the great circle distance in nautical miles.
Now if you are still with me consider the following:
Suppose you knew of a reef that you wanted to give plenty of berth? Or maybe a restricted zone you did not want to enter? If you can pick ANY AP you want you can pick a point on the reef's edge or on the demarcation line of the restricted zone and using that IN PLACE OF a "normal" AP you can get an HC from that spot to compare to the Ho you got of a body from your actual location-- and that result tells you how close you are to the reef.
The one thing you have to keep in mind is that the lines of position (LOP's) plot perpendicular to the azimuth so you need a body that you see in the general direction of the reef; or its reciprocal.
By extension if you want to figure out how far you progressed along your course you could pick an AP some where out on your desired track and use a body ahead or astern and by this means check your speed over the bottom.
It is perhaps for these purposes that the Astron app lets you pick your own AP. It provides increased versatility all out of the same math.
Peter