No, I’m not talking about Gorden “Venus Flytrap” Sims from the TV show WKRP in Cincinnati… who was likely high all the time.
For the past month or so it seems to me that Venus has been astonishingly high in the sky. When I leave home for work at about 6:20 a.m. Central Time (US) it’s nearly 45 degrees up from the horizon (in the eastern sky, obviously). [angle calculated very roughly from measuring three hand-widths high at arms length]
Logic tells me that Venus would appear highest in the sky when the angle formed by the three points (Venus, Sun, and Earth when viewed from “above”) is 90 degrees. Is this assumption true? And are we at or near this maximum?
The Venus year lasts 224 days. With the Earth year of 365 days, can anyone calculate how long it is between maximums?
Oh, and to calculate the orbital configuration that will put Venus highest in the sky try this.
Note: The orbits of Earth and Venus are not completely circles, but are close enough to get the general idea. Also, the Sun and planets are not points, their width would affect things slightly as well… but not significantly.
Pick a scale for distances. 1mm per million km is pretty convenient.
Draw a point to be the Sun.
Draw another point to be the Earth. The Earth 149.6 Million km from the Sun or 149.6mm on my suggested scale.
Draw a line between the Sun and Earth.
Draw a circle with a compass around the Sun to mark the orbit of Venus. Its average distance is 108.2 Million km from the Sun, or 108.2 mm using my scale.
Draw a line from the Earth that is tangent to the orbit of Venus.
Draw a line from the where the tangent line touches the Venus orbital circle to the Sun.
Time to start measuring.
The angle formed between the the Earth/Sun line and the Earth/Venus Orbit (Earth point designates the angle) will be very close to the maximum that Venus can be above the horizon at sunrise (or at other times, sunset).
The angle formed between the Sun/Earth line and Sun/Venus Orbit line (Sun point designates the angle) will be your “90 degree” angle. You will find that it is somewhat less than 90 degrees.
While there will be years when it comes to slightly more or less than the figures you come up with here as the eliptical nature of the planet’s orbits come into play, this should give you a pretty accurate description of things.
If memory serves, Venus is never more than 48 degrees of longitude away from the Sun. scotth’s approach would help you determine how far above the horizon this would appear at various latitudes.
The declination of Venus (distance off the ecliptic) at any given time might have some affect on its apparent height in the sky as well.
scotth, this would be the perfect place to insert a hypothetical smilie indicating that “I bow down to you”.
a) You were right in your assumption. My question was how frequently is it this high in the sky and still visible.
b) I downloaded that software. It is awesome. It tells me that Venus will first again be visible this high in the morning sky in August of 2004 (viewing from Chicago), 20 months from now. At that time it will reach an altitude of 40 degrees.
c) From that software I also see that my rough calculation of altitude was off a bit. It is only 31 degrees high in the sky right now.
d) Regarding the relative positions of planets to obtain this maximum… lacking a compass and ruler, I made a rough drawing of the orbits. It appears to me that Venus reaches its maximum when the Earth/Sun and Sun/Venus angle (Sun point determining the angle) is about 40 degrees (?). Makes intuitive sense now that I see it on paper.
Thanks for the clarification Jerevan. Where’s my trigonometry when I need it. Let’s see, we have side-side-angle, right? The Venus-Sun distance. The Sun-Earth distance. And the Venus-Earth-Sun angle of 48 degrees.
So, what is the Venus-Sun-Earth angle? (where my paper drawing showed about 40-45 degrees).
I’m not sure I see how it could be less than 90 degrees. I mean, wouldn’t the maximum separation of Venus and the Sun as observed from Earth, be a 90-degree Venus-Sun-Earth angle by definition?
The biggest distance between Venus and the Sun in the sky is called maximum elongation. It occurs when the Earth-Venus-Sun angle is 90 degrees, that is, when a line drawn from Earth to Venus is tangent to Venus’ orbit. Handy Illustration.) Since Venus is .723 AU from the Sun and the Earth is 1 AU from the Sun, the Earth-Sun-Venus angle is acos(.723/1)=43.7 degrees.
Oh, I get it now. I was having trouble visualing/drawing it correctly. Thanks, Podkayne.
By this calculation, then, the maxium elongation of Venus and the Sun (Venus-Earth-Sun angle) is 46.3 degrees. But I suppose the elliptical nature of planetary orbits might mean the maximum observable elongation is somewhat larger (~48 degrees). Yes?
[self-congratulatory hijack]
Heh, heh.
My hand-drawn-with-no-tools diagram led me to estimate the angle at 40-45 degrees, and it is really 43.7 degrees.
Heh, heh.
[/self-congratulatory hijack]
