I'm using an API from NASA on this URL: http://api.open-notify.org/iss-now.json
It gives me the location of the ISS as a longitude and latitude. How can I find it's position in space?
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The location of the ISS, when represented as a longitude and latitude, signifies the location on the surface of the Earth directly below the ISS at a given time. The location of spacecraft orbiting the Earth are usually represented in ground-terms because they're far easier to comprehend than the actual orbital parameters.
So to visualise the ISS in space, picture the longitude and latitude. Then imagine the station about 400 kilometers above that point traveling at ~7 kilometers per second.
Edit: Here is a useful resource where you can find the location of the ISS at the current time. http://iss.astroviewer.net/