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I am looking to find the distance from a point on the earth's surface to a fixed point within the earth, not at its center. This fixed point would not be on either of the earth's axis. It would be 10 km away. I want to code this into some software so it can update the distance as the earth rotates. I want to see how latitude affects the variation in distance. I have drawn a crude picture of what I am trying to achieve. I have done some searching on the internet to try and find something that works but I haven't really hit on anything yet.

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  • Assuming that $\vec{a}$ and $\vec{b}$ are the two points from which you would like to know the distance, you just have to calc $|\vec{b} - \vec{a}|$. So I don't get your problem. – Semoi Dec 26 '19 at 20:05
  • The fixed point is not on the same plane as the moving point on the surface of the earth. It makes a cone with a moving focus point in relation to the surface –  Dec 26 '19 at 21:18
  • That doesn't matter. If you like to go fancy, you use so called homogeneous coordinates. That's how robots are programmed. However, in the end it all comes down to the norm of the difference vector. – Semoi Dec 26 '19 at 21:55
  • Set up an earth-centered earth-fixed coordinate system. Find the position of the point in that system (it'll be a 3-vector). Find the position on the surface of the earth in that system. Subtract, find the norm. Done. – TimWescott Dec 26 '19 at 22:42
  • Uh, $(\hat i \cos \theta + \hat j \sin \theta)\sin \phi + \hat k \cos \phi$, where $\phi$ is the latitude and $\theta$ is the longitude + rotation of the earth. That was hard? – TimWescott Dec 27 '19 at 01:54
  • Thanks for the responses –  Dec 27 '19 at 22:37
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    I think this is a mathematics (or programming) problem rather than a physics problem. I don't see how it might be a mechanics problem. – sammy gerbil Dec 29 '19 at 22:59

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