I need to convert geographical coordinates( Latitude and longitude) to cartesian

Question

I need to convert geographical coordinates( Latitude and longitude) to cartesian coordiantes in the x and y plane, using a function in Matlab, I been trying using a Mercator proyection and these function( Covert lat, lon, alt to ECEF Cartesian ) but I couldn' t convert them.

if you can explain me step by step it woul be great, here is the Latitude and longitude that I copy from an Excel sheet

Here is the Latitude

-77,4773629999999
-77,4000000000000
-77,3954009999999
-77,3901979999999
-77,3833010000000
-77,3705970000000
-77,3613960000000
-77,3492969999999
-77,3412010000000
-77,3284990000000
-77,3251040000000
-77,3175959999999
-77,3124020000000
-77,3113009999999
-77,3113009999999
-77,3095010000000
-77,2985989999999
-77,2946019999999
-77,2910990000000
-77,2893989999999
-77,2846989999999
-77,2795030000000
-77,2742990000000
-77,2639999999999
-77,2386010000000
-77,2316979999999
-77,2230010000000
-77,2149960000000
-77,2016969999999
-77,1884989999999
-77,1745989999999
-77,1561970000000
-77,1481009999999
-77,1325009999999
-77,1249999999999
-77,1100010000000
-77,1001959999999
-77,0829019999999
-77,0697009999999
-77,0518029999999
-77,0408019999999
-77,0252989999999
-77,0085979999999
-76,9838030000000
-76,9567039999999
-76,9462969999999
-76,9329989999999
-76,9100050000000
-76,8961020000000
-76,8695979999999
-76,8684009999999
-76,8545990000000
-76,8395999999999
-76,8285979999999
-76,8234019999999
-76,8084029999999
-76,7893969999999
-76,7633969999999
-76,7130959999999
-76,7133039999999
-76,7241979999999
-76,7305979999999
-76,7362980000000
-76,7478029999999
-76,7536009999999
-76,7628019999999
-76,7679979999999
-76,7761010000000
-76,7766040000000
-76,7754969999999
-76,7736960000000
-76,7720029999999
-76,7690969999999
-76,7679979999999
-76,7685019999999
-76,7714010000000
-76,7759999999999
-76,7863999999999
-76,7921979999999
-76,7973009999999
-76,8053969999999
-76,8105999999999
-76,8198010000000
-76,8233039999999
-76,8354040000000
-76,8423009999999
-76,8509000000000
-76,8590019999999
-76,8647999999999
-76,8704979999999
-76,8808979999999
-76,8854969999999
-76,8825980000000
-76,8682029999999
-76,8543999999999
-76,8394010000000
-76,8202980000000
-76,8058999999999
-76,7955009999999
-76,7846000000000
-76,7817009999999
-76,7696010000000
-76,7602999999999
-76,7580019999999
-76,7563019999999
-76,7556999999999
-76,7556999999999
-76,7534029999999
-76,7492979999999
-76,7435000000000
-76,7349009999999
-76,7298269999999
-76,7274019999999
-76,7353979999999
-76,7412030000000
-76,7441019999999
-76,7520989999999
-76,7648009999999
-76,7866959999999
-76,7969979999999
-76,8143009999999
-76,8235020000000
-76,8303989999999
-76,8394540000000
-76,8424990000000
-76,8695979999999
-76,8816979999999
-76,8990029999999
-76,9094009999999
-76,9300999999999
-76,9462969999999
-76,9520039999999
-76,9607019999999

And longitude

4,20459200000005
4,19120000000009
4,19350200000014
4,19690000000008
4,19860000000006
4,19860000000006
4,19390000000004
4,18580000000003
4,17880100000002
4,18160000000000
4,18860100000001
4,20010000000002
4,20640099999997
4,21450100000015
4,22489899999999
4,23120100000011
4,24039900000014
4,23979999999995
4,23290100000008
4,22370000000012
4,20860100000010
4,19530000000003
4,17970100000008
4,16580099999999
4,16279900000012
4,16909900000002
4,17370000000005
4,17940100000015
4,18399999999997
4,18050099999999
4,17060100000015
4,16190100000006
4,15490000000011
4,14040000000011
4,12710100000004
4,11839899999995
4,11429900000002
4,11070100000001
4,10840099999996
4,10709900000006
4,10709900000006
4,10990100000009
4,11209999999994
4,11550000000011
4,10440099999994
4,09340000000009
4,08300000000008
4,07530100000008
4,06659900000000
4,01570200000015
3,99780100000015
3,96879899999999
3,94450100000006
3,92710000000005
3,90810100000016
3,88080000000008
3,86630000000008
3,86390000000011
3,86357600000008
3,86140000000000
3,85800099999994
3,85390100000001
3,84880000000004
3,83670100000012
3,83040099999999
3,82060100000007
3,81369999999998
3,79810100000003
3,78480000000013
3,76919900000001
3,76230000000010
3,75360100000012
3,74840000000000
3,73920100000004
3,73450000000014
3,72989999999999
3,72879900000004
3,72309900000005
3,72080000000005
3,71670000000012
3,70870000000008
3,69490000000008
3,68389999999999
3,67579999999998
3,67299900000006
3,67190100000016
3,67020100000002
3,66849999999994
3,66849999999994
3,66800100000006
3,66400100000004
3,65940000000001
3,64259999999996
3,62920100000014
3,62110100000001
3,59040100000004
3,59030100000012
3,57759900000002
3,56829999999997
3,54920100000015
3,53879900000015
3,52019899999999
3,49590100000006
3,48150000000010
3,46590100000014
3,45140100000015
3,43350100000004
3,41390000000007
3,39370000000008
3,36760000000010
3,35720000000003
3,34739300000007
3,34270000000009
3,32539899999995
3,30810100000014
3,28970100000004
3,27180100000010
3,25160100000011
3,21469900000005
3,19050000000010
3,14550000000003
3,12710100000004
3,10860100000002
3,08250000000010
3,08270100000004
3,08110099999999
3,07879899999995
3,07830000000007
3,07780099999997
3,07090000000011
3,06930000000006
3,06410100000011
3,07220100000006

Explanation / Answer

According to the Cartesian coordinate system, the x-axis goes through long,lat (0,0) so longitude 0 meets the equator and the y-axis goes through (0,90).

The conversions are x = R * cos(lat) * cos(lon) and y = R * cos(lat) * sin(lon),Where R is the approximate radius of earth.If the functions sine and cos need in radians have to convert longitude and latitude to radians first. The formula for back conversion is lat = asin(z / R) and lon = atan2(y, x).

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