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Posting-Version: version B 2.10.2 9/18/84; site lsuc.UUCP
Path: utzoo!lsuc!msb
From: msb@lsuc.UUCP (Mark Brader)
Newsgroups: net.astro
Subject: Re: StarDate: March 28 Goodbye Venus
Message-ID: <580@lsuc.UUCP>
Date: Fri, 5-Apr-85 20:59:26 EST
Article-I.D.: lsuc.580
Posted: Fri Apr  5 20:59:26 1985
Date-Received: Fri, 5-Apr-85 21:18:02 EST
References: <6@utastro.UUCP> <181@tektools.UUCP>
Reply-To: msb@lsuc.UUCP (Mark Brader)
Organization: Law Society of Upper Canada, Toronto
Lines: 27
Summary: How high Venus gets

joels@tektools.UUCP (Joel Swank) writes:
> What is the highest Venus ever gets?

Can't resist answering this one, because it's so easy.
Venus can be seen at the zenith, meaning straight up, by daytime observers
in the tropics.  (Well, I can't say I've verified this personally, but I
have seen Venus in the daytime, and there has to be SOME place where it's
directly overhead, since the Earth is spherical.)

If you restrict the question to nighttime observation and define nighttime
as beginning when the sun would set if atmosphere effects are neglected,
you are asking what the maximum Venus-Earth-Sun angle is.  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!)

The desired angle is then the arc sine of the ratio of the orbital radii.
Taking the radii in gm, that's arcsin(108.1/149.5) = 46.3 degrees.
However, the earth's orbit is not really circular, and if the perihelion
radius is, as I think, 147.2 gm, the angle becomes 47.3.  Fortunately Venus's
orbit is very close to circular.

However, Venus can only be observed at such an angle from the tropics.
I'd have to brush up my spherical geometry before answering the question
for other latitudes.  But you didn't ask about other latitudes.

Mark Brader