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From: johnston@spp1.UUCP (Micheal L. Johnston)
Newsgroups: net.astro
Subject: Re: Re: StarDate: March 28 Goodbye Venus
Message-ID: <183@spp1.UUCP>
Date: Thu, 11-Apr-85 13:35:42 EST
Article-I.D.: spp1.183
Posted: Thu Apr 11 13:35:42 1985
Date-Received: Sun, 14-Apr-85 02:32:54 EST
References: <6@utastro.UUCP> <181@tektools.UUCP> <580@lsuc.UUCP> <7425@watrose.UUCP>
Organization: TRW, Redondo Beach  CA
Lines: 36

> > > What is the highest Venus ever gets?
> > Simplifying the
> > orbits to coplanar circles, this occurs when the Earth-Venus-Sun angle is
> > 90 degrees.  (Oddly enough, this situation was also described in net.puzzle
> > a couple of months ago -- with respect to clock hands instead of planets!)
> > Mark Brader
>  
> Before you go and brush up on your spherical geometry (I boo-booed and deleted
> his comment on that) you should brush up on your planar geometry.  Your 
> statement about highest angle above the horizon at 90 degrees is a gross
> oversimplification.  All you have to do to show this is draw the orbit of
> Venus on paper (admittedly a big sheet of paper); pick a position for the
> earth; and draw the hypotenuse of your 90 degree triangle.
> 
> You'll find that the hyp. passes inside the orbit of Venus.  Using
> circular co-planar orbits and no atmosphere, etc., the maximum angle
> above the horizon is found by drawing a line from the earth TANGENTIAL
> to the orbit of Venus (again, a very long line).
> 
> 		larry fast (Universty of Waterloo)
> 		broadcasting from exile

Maybe I missed something but I thought Mark's posting was correct. The
hypotenuse to his 90 degree triangle SHOULD pass inside the orbit of Venus
since it's going straight to the sun.
Your steps to find the maximum angle only draw a line, so I'll assume the
second line is the line tanget to the earth's surface at the observation
point to the sun at sunset time. (I think mark stated that 'how high'
meant the angle at the time the sun goes down). This second line is the
hypotenuse were talking about however, so if you're truly talking about a
different angle, I missed.
Remember, Mark's hypotenuse IS the earth's orbital radius. Venus' orbital
radius is then the closing line and the arcsin of this ratio (Venus'
figure on top) would be the angle in question.

		Mike Johnston