computations on the spheroid. learning objectives calculate and of a point given and s from a...
TRANSCRIPT
![Page 1: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/1.jpg)
COMPUTATIONS ON THE SPHEROID
![Page 2: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/2.jpg)
Learning Objectives
Calculate and of a point given and s from a point with known and .
Calculate and s between points with known and .
![Page 3: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/3.jpg)
Lecture Outline
Direct Problem– Manual– Spreadsheets
Reverse Problem– Manual– Spreadsheets
Conclusion
![Page 4: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/4.jpg)
Direct Problem
Know 1, 1, 12 and s 12
Need to calculate 2 and 2
Many formula available– Different accuracy and applications– Manual calculations– Spreadsheets
![Page 5: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/5.jpg)
Tangent - Direct
and known
known
s known
and unknown
![Page 6: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/6.jpg)
Process – Tangent Direct Step 1
– Draw a diagram– Compute for known point– Compute approximate using
– Compute m
and known
m
![Page 7: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/7.jpg)
Process – Tangent Direct
Step 2– Compute m using m
– Compute approximate
and known
m
m
![Page 8: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/8.jpg)
Process – Tangent Direct
Step 3– Compute approximate ½ using formula
and known
m
½
![Page 9: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/9.jpg)
Process – Tangent Direct
Step 4– Compute approximate + ½ – Check diagram for correct sense
– Compute m
m
½
m
+ ½
1-2 known
![Page 10: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/10.jpg)
Process – Tangent Direct
Step 5– Compute ½– Compute m
½ m
![Page 11: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/11.jpg)
Process – Tangent Direct
Step 6– Compute m and m using this new m
– Compute ½
m
m m
½
![Page 12: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/12.jpg)
Process – Tangent Direct
Step 7– Compute ½
½
m½
½
m m
![Page 13: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/13.jpg)
Process – Tangent Direct Step 8
– Compare earlier results and decide on further iterations (from step 4)
– Calculate final 1-2 + ½
– Calculate final 2-1 = 1-2 + ± 180°
and known
½½
Calculateand
½ + ½ 2-1
![Page 14: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/14.jpg)
Spreadsheet - Direct
![Page 15: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/15.jpg)
Spreadsheet - Direct
![Page 16: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/16.jpg)
Reverse Problem
Know 1, 1, 2 and 2
Need to calculate 12 , 21 and s Again, many formula available Best explained with an example
![Page 17: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/17.jpg)
Tangent - Reverse - Formula
![Page 18: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/18.jpg)
Tangent - Reverse - Example
![Page 19: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/19.jpg)
Tangent - Reverse - Example
![Page 20: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/20.jpg)
Tangent - Reverse - Example
![Page 21: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/21.jpg)
Tangent - Reverse - Example
![Page 22: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/22.jpg)
Tangent - Reverse - Example
![Page 23: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/23.jpg)
Tangent - Reverse - Example
![Page 24: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/24.jpg)
Spreadsheet - Reverse
![Page 25: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/25.jpg)
Spreadsheet - Reverse
![Page 26: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/26.jpg)
Conclusion
You can now:
Calculate and of a point given and s from a point with known and .
Calculate and s between points with known and .
![Page 27: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/27.jpg)
Self Study
Read relevant module and follow worked examples
![Page 28: COMPUTATIONS ON THE SPHEROID. Learning Objectives Calculate and of a point given and s from a point with known and. Calculate and s between points](https://reader036.vdocuments.net/reader036/viewer/2022062300/56649c7e5503460f94933da8/html5/thumbnails/28.jpg)
Review Questions