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106 views

two points on a unit sphere

Consider the two vectors to the points on the unit sphere, $${\bf v}_i=(\sin\theta_i\cos\varphi_i,\sin\theta_i\sin\varphi_i,\cos\theta_i)$$ with $i=1,2$. Use the dot product to get the angle $\psi$ ...
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1answer
501 views

Coordinates of interception point Y with XY being the shortest distance of X to AB on sphere

How would one calculate the interception point $Y$ with $\overleftrightarrow{XY}$ being the shortest distance of $X$ to $\overleftrightarrow{AB}$? This answer to the question How to find the ...
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1answer
142 views

Find third point in mapping system

I have two points defined: $A$ and $B$ For both I know $x,y$, longitude, and latitude (gps coordinates). How do I calculate $x,y$ of a third point $C$ when I know its longitude and latitude? I know ...
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4answers
1k views

How to find the distance between a point and line joining two points on a sphere?

How do I calculate the distance between the line joining the two points on a spherical surface and another point on same surface? I have illustrated my problem in the image below. In the above ...