About the geodesic coordinates, and their conversion into cartesian ones












0














This is more a sort of "let me know if I'm right" question, rather than a real question, but I thought that if is there a place where I can find true and solid trustful answers then it's here.



Suppose someone gives me those coordinates:



$$109^{circ} 39' N$$



$$30^{circ} 10' W$$



If I want to localize this place over the Earth surface, via cartesian coordinates (or better: if I simply want to convert them into cartesian), here is what I understood to be the process.



Please, notice that this is what I understood so if it's wrong you have to correct me because I did not find any book or notes where this has been explained clearly.



First step



Transform the coordinates I got into "true angles" that is: latitude $theta$ and longitude $phi$ according to the DMS transformation:



$$theta = 109 + frac{39}{60} = 109.65$$



$$phi = 30 + frac{10}{60} = 39.16$$



Second Step



Using the polar coordinates to find the space vector, that is:



$$x = Rsinthetacosphi$$



$$y = Rsinthetasinphi$$



$$z = Rcostheta$$



Where $R = $ Earth radius.



Finally I will obtain the space vector $mathbf{r} = (x, y, z)$ for the place in question.



Final Question



Is this all right? Are there any errors or information I shall take into account? Any remark?



Thank you all.






analytic-geometry coordinate-systems polar-coordinates spherical-coordinates geodesy







share|cite|improve this question





























    0














    This is more a sort of "let me know if I'm right" question, rather than a real question, but I thought that if is there a place where I can find true and solid trustful answers then it's here.



    Suppose someone gives me those coordinates:



    $$109^{circ} 39' N$$



    $$30^{circ} 10' W$$



    If I want to localize this place over the Earth surface, via cartesian coordinates (or better: if I simply want to convert them into cartesian), here is what I understood to be the process.



    Please, notice that this is what I understood so if it's wrong you have to correct me because I did not find any book or notes where this has been explained clearly.



    First step



    Transform the coordinates I got into "true angles" that is: latitude $theta$ and longitude $phi$ according to the DMS transformation:



    $$theta = 109 + frac{39}{60} = 109.65$$



    $$phi = 30 + frac{10}{60} = 39.16$$



    Second Step



    Using the polar coordinates to find the space vector, that is:



    $$x = Rsinthetacosphi$$



    $$y = Rsinthetasinphi$$



    $$z = Rcostheta$$



    Where $R = $ Earth radius.



    Finally I will obtain the space vector $mathbf{r} = (x, y, z)$ for the place in question.



    Final Question



    Is this all right? Are there any errors or information I shall take into account? Any remark?



    Thank you all.






    analytic-geometry coordinate-systems polar-coordinates spherical-coordinates geodesy







    share|cite|improve this question



























      0












      0








      0







      This is more a sort of "let me know if I'm right" question, rather than a real question, but I thought that if is there a place where I can find true and solid trustful answers then it's here.



      Suppose someone gives me those coordinates:



      $$109^{circ} 39' N$$



      $$30^{circ} 10' W$$



      If I want to localize this place over the Earth surface, via cartesian coordinates (or better: if I simply want to convert them into cartesian), here is what I understood to be the process.



      Please, notice that this is what I understood so if it's wrong you have to correct me because I did not find any book or notes where this has been explained clearly.



      First step



      Transform the coordinates I got into "true angles" that is: latitude $theta$ and longitude $phi$ according to the DMS transformation:



      $$theta = 109 + frac{39}{60} = 109.65$$



      $$phi = 30 + frac{10}{60} = 39.16$$



      Second Step



      Using the polar coordinates to find the space vector, that is:



      $$x = Rsinthetacosphi$$



      $$y = Rsinthetasinphi$$



      $$z = Rcostheta$$



      Where $R = $ Earth radius.



      Finally I will obtain the space vector $mathbf{r} = (x, y, z)$ for the place in question.



      Final Question



      Is this all right? Are there any errors or information I shall take into account? Any remark?



      Thank you all.






      analytic-geometry coordinate-systems polar-coordinates spherical-coordinates geodesy







      share|cite|improve this question















      This is more a sort of "let me know if I'm right" question, rather than a real question, but I thought that if is there a place where I can find true and solid trustful answers then it's here.



      Suppose someone gives me those coordinates:



      $$109^{circ} 39' N$$



      $$30^{circ} 10' W$$



      If I want to localize this place over the Earth surface, via cartesian coordinates (or better: if I simply want to convert them into cartesian), here is what I understood to be the process.



      Please, notice that this is what I understood so if it's wrong you have to correct me because I did not find any book or notes where this has been explained clearly.



      First step



      Transform the coordinates I got into "true angles" that is: latitude $theta$ and longitude $phi$ according to the DMS transformation:



      $$theta = 109 + frac{39}{60} = 109.65$$



      $$phi = 30 + frac{10}{60} = 39.16$$



      Second Step



      Using the polar coordinates to find the space vector, that is:



      $$x = Rsinthetacosphi$$



      $$y = Rsinthetasinphi$$



      $$z = Rcostheta$$



      Where $R = $ Earth radius.



      Finally I will obtain the space vector $mathbf{r} = (x, y, z)$ for the place in question.



      Final Question



      Is this all right? Are there any errors or information I shall take into account? Any remark?



      Thank you all.






      analytic-geometry coordinate-systems polar-coordinates spherical-coordinates geodesy




      analytic-geometry coordinate-systems polar-coordinates spherical-coordinates geodesy






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      share|cite|improve this question













      share|cite|improve this question




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      edited Nov 26 at 0:45









      Henry

      98k475160




      98k475160










      asked Mar 8 '17 at 14:04









      Von Neumann

      16.3k72543




      16.3k72543






















          2 Answers
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          0














          if your $z-$axis travels from south to north pole, then $z = R sin(lattitude, angle)$ where North is assumed positive and south is assumed negative. (Center of earth is System of coordinates center). Consequently $x = R cos(lattitude, angle) cos(longitude, angle)$ and $y = R cos(lattitude, angle) sin(longitude, angle)$ for longitude angle : East is positive and West is negative limit is [-180,180[






          share|cite|improve this answer





























            0














            You have a BIG mistake, which is the limit of the lattitude are $90S$ which is the South Pole to $90N$ which is the North Pole. You are here mentioning a lattitude which is 109N. This is outside the range. I assume your angles should be $109W$ and $30N$ which is somewhere Texas....



            Fix your coordinates then, we can verify your transformation .






            share|cite|improve this answer























            • Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
              – Von Neumann
              Mar 8 '17 at 14:12











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            2 Answers
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            2 Answers
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            active

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            0














            if your $z-$axis travels from south to north pole, then $z = R sin(lattitude, angle)$ where North is assumed positive and south is assumed negative. (Center of earth is System of coordinates center). Consequently $x = R cos(lattitude, angle) cos(longitude, angle)$ and $y = R cos(lattitude, angle) sin(longitude, angle)$ for longitude angle : East is positive and West is negative limit is [-180,180[






            share|cite|improve this answer


























              0














              if your $z-$axis travels from south to north pole, then $z = R sin(lattitude, angle)$ where North is assumed positive and south is assumed negative. (Center of earth is System of coordinates center). Consequently $x = R cos(lattitude, angle) cos(longitude, angle)$ and $y = R cos(lattitude, angle) sin(longitude, angle)$ for longitude angle : East is positive and West is negative limit is [-180,180[






              share|cite|improve this answer
























                0












                0








                0






                if your $z-$axis travels from south to north pole, then $z = R sin(lattitude, angle)$ where North is assumed positive and south is assumed negative. (Center of earth is System of coordinates center). Consequently $x = R cos(lattitude, angle) cos(longitude, angle)$ and $y = R cos(lattitude, angle) sin(longitude, angle)$ for longitude angle : East is positive and West is negative limit is [-180,180[






                share|cite|improve this answer












                if your $z-$axis travels from south to north pole, then $z = R sin(lattitude, angle)$ where North is assumed positive and south is assumed negative. (Center of earth is System of coordinates center). Consequently $x = R cos(lattitude, angle) cos(longitude, angle)$ and $y = R cos(lattitude, angle) sin(longitude, angle)$ for longitude angle : East is positive and West is negative limit is [-180,180[







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Mar 8 '17 at 14:18









                Hmath

                1625




                1625























                    0














                    You have a BIG mistake, which is the limit of the lattitude are $90S$ which is the South Pole to $90N$ which is the North Pole. You are here mentioning a lattitude which is 109N. This is outside the range. I assume your angles should be $109W$ and $30N$ which is somewhere Texas....



                    Fix your coordinates then, we can verify your transformation .






                    share|cite|improve this answer























                    • Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
                      – Von Neumann
                      Mar 8 '17 at 14:12
















                    0














                    You have a BIG mistake, which is the limit of the lattitude are $90S$ which is the South Pole to $90N$ which is the North Pole. You are here mentioning a lattitude which is 109N. This is outside the range. I assume your angles should be $109W$ and $30N$ which is somewhere Texas....



                    Fix your coordinates then, we can verify your transformation .






                    share|cite|improve this answer























                    • Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
                      – Von Neumann
                      Mar 8 '17 at 14:12














                    0












                    0








                    0






                    You have a BIG mistake, which is the limit of the lattitude are $90S$ which is the South Pole to $90N$ which is the North Pole. You are here mentioning a lattitude which is 109N. This is outside the range. I assume your angles should be $109W$ and $30N$ which is somewhere Texas....



                    Fix your coordinates then, we can verify your transformation .






                    share|cite|improve this answer














                    You have a BIG mistake, which is the limit of the lattitude are $90S$ which is the South Pole to $90N$ which is the North Pole. You are here mentioning a lattitude which is 109N. This is outside the range. I assume your angles should be $109W$ and $30N$ which is somewhere Texas....



                    Fix your coordinates then, we can verify your transformation .







                    share|cite|improve this answer














                    share|cite|improve this answer



                    share|cite|improve this answer








                    edited Feb 6 at 8:41









                    Von Neumann

                    16.3k72543




                    16.3k72543










                    answered Mar 8 '17 at 14:11









                    Hmath

                    1625




                    1625












                    • Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
                      – Von Neumann
                      Mar 8 '17 at 14:12


















                    • Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
                      – Von Neumann
                      Mar 8 '17 at 14:12
















                    Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
                    – Von Neumann
                    Mar 8 '17 at 14:12




                    Oh, so you mean I shall have something like $109$ for $phi$ and $39$ for $theta$?
                    – Von Neumann
                    Mar 8 '17 at 14:12


















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