I am studying celestial navigation and have come across various ways to solve the navigational triangle.
Formulas, tables etc
My knowledge is as yet too fragile to be able to evaluate different methods or formulas so here are a couple I have come across if someone else could have a look at them for me-------------------------------Damon!!
Distance and bearing between 2 points on earth.
Distance=60.ACOS(sin(latA)x sin(latB)+cos(latA)x cos(latB) x cos(longB - LongA))
Bearing=ATAN sin(longB-LongA) DIVIDED BY
sin(latA)xcos(longB-longA)-TAN(latB)xcos(latA)
Hope you can follow that.
Mike
Distance=60.ACOS(sin(latA)x sin(latB)+cos(latA)x cos(latB) x cos(longB - LongA))
Remember the trig identity
cos (x-y) = sin x sin y + cos x cos y
that means
cos (Lat A -LatB)= sin Lat A sin Lat B + cos Lat A cos Lat B)
It looks like that was used here
Do you mean
Distance=60.ACOS( {sin(latA)x sin(latB)+cos(latA)x cos(latB)} x cos(longB - LongA))
If so that is the first stab I took at the later question that I replied to before I saw this one. I believe it would only work at latitudes near the equator where the longB-LongA which is the LHA is close to the distance/60. That is the error I caught myself in.
If you mean it as posted, without the brackets, then I do not know if it is right or not. I have not figured out if that would be like my corrected formula.
Yes, it is correct without the brackets
Yes, I can follow the formula you provided for calculating the distance and bearing between two points on Earth. To explain it further:
Distance Formula:
Distance = 60 * ACOS(sin(latA) * sin(latB) + cos(latA) * cos(latB) * cos(longB - LongA))
Let's break down the formula:
1. Latitude and Longitude:
"latA" and "latB" refer to the latitudes of Point A and Point B, respectively. Similarly, "longA" and "longB" refer to the longitudes of Point A and Point B, respectively.
2. Trigonometric Functions:
The formula uses trigonometric functions like sin, cos, and ACOS (inverse cosine).
3. Spherical Law of Cosines:
The formula is based on the Spherical Law of Cosines, which relates the sides and angles of a spherical triangle.
4. Distance Conversion:
The result of the formula is multiplied by 60 to convert the distance from nautical miles to other units (e.g., statute miles, kilometers).
Bearing Formula:
Bearing = ATAN((sin(longB - LongA)) / (sin(latA) * cos(longB - LongA) - tan(latB) * cos(latA)))
Let's break down the formula:
1. Latitude and Longitude:
The formula uses the same latitude and longitude values as in the distance formula.
2. Trigonometric Functions:
The formula uses trigonometric functions like sin, cos, and tan.
3. Angular Measurements:
The result of the formula will provide the bearing as an angular measurement, such as degrees or radians.
To calculate the distance and bearing between two points on Earth using these formulas, you need to know the latitudes and longitudes of the two points. Plug in the values into the formulas, and you will get the respective distance and bearing as the outputs.
It's always a good practice to double-check the formulas and units used, as different celestial navigation texts or references may sometimes have slight variations in formulas or units.