Threaded Mode | Linear Mode

ijabbott · (This post was last modified: 03-31-2019 05:14 PM by ijabbott.)

Code:

VIS%=HEIGHT*50/(HEIGHT+RADIUS)

For example:

Radius of Earth = 6378 km
Distance of Apollo 17 from Earth's surface at 1972-12-07T10:39Z = 29000 km
Visible percentage of Earth's surface in 1972 "Blue Marble" photograph = 40.99% (41%)

StephenG1CMZ · (This post was last modified: 04-02-2019 07:44 AM by StephenG1CMZ.)

I was just wondering whether this formula holds up if the height were negative (for example, if the GPS shows you in a valley).

I'm thinking in such a case the physics would suggest 100% visible (for a hollow sphere or Earth), or 0% (for an opaque sphere or Earth), rather than a negative value. Geometrically, I think I'd choose 100% - except its the interior of the surface you can see, not the outside. Perhaps - 100%? With the negative flagging an interior view? I'm not sure what result would be preferred.

ijabbott · (This post was last modified: 04-02-2019 07:46 AM by ijabbott.)

For a negative height, the simple formula will give a negative percentage visibility, but I have no idea how that should be interpreted geometrically!

I only posted the formula because it turned out to be so simple and elegant compared to how I was expecting it to turn out.

SlideRule · (This post was last modified: 04-02-2019 03:19 PM by SlideRule.)

An interesting formulation from 1913
[attachment=7091]

as well as an un-referenced web source …
[attachment=7092]

BEST!
SlideRule