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The distance l from a point at a height h above the Earth's surface to the horizon can be approximated using Pythagoras theorem by the expression:
l = h * SQRT(1 + (2*re/h)) , where re is the radius of the Earth.
(a) Sketch the dependence of l versus h on Cartesian axes.
(b) Thus determine approximations for l by taking limits associated with the view expected by:
(i) an astronaut in space;
(ii) a person on a beach.
Please help me understand how do I sketch the dependence of l vs h on Cartesian axes and how can I approach part b?
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Solution gives steps for part a, following which you should have enough information to give a general description of the graph.
I am going to refer to the function as f(h)=l for simplicity.
You do not need an exact value for the earth's radius, just use a rounded value (you are just looking for shape).
For part a) you have to find:
- h and l ...