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Venus

Summary: In this lab you will observe the planet Venus trough the telescope, note and draw its phase, and use your sketch along with your observation of the position of Venus in the sky to determine its distance from Earth.

Background: Venus is the third brightest object in the sky, after the Sun and the Moon. As a matter of fact, it is so bright that it can been seen during full daylight if you know where to look and search patiently! This unusual brightness takes many people by surprise and is responsible for countless reports of UFO sightings (I am not making this up!). For a long time, Venus was thought to be Earth's "sister planet". It is nearly of the same size as of the Earth and has a substantial atmosphere.  Since it orbits the Sun at 0.77 AU, it has always been thought to be warmer than the Earth. Venus is entirely covered with clouds, however, which explains why it is so bright (clouds being far more reflective than soil). These thick clouds hide the surface of the planet at all times and have prevented astronomers from learning much about this planet for a long time. Speculation abounded and only a century ago, Venus was thought likely to be inhabited and to have hot, humid climate with abundant vegetation. Many saw the planet as a vast swamp. It is only in the early 1960's that new tools allowed astronomers to probe the atmosphere and assess the conditions at the surface of the planet. They are close to what most people would call "hell". The atmosphere is mostly composed of carbon dioxide (CO₂), there is no water at all, and the surface temperature is about 500^oC. The atmospheric pressure is 90 times that of the Earth. That's the equivalent of 2700' under the surface of the ocean, roughly the highest pressures that submarines can withstand!. To top the list, the bright clouds are made of droplets of sulfuric acid. Several Russian and American probes have landed on the surface and taken measurements and a few pictures before being destroyed by the forbidding conditions. The entire planet was mapped in the early 1990's by the Magellan spacecraft using a radar to "see" through the opaque clouds. Venus has mountains, a few craters, and much evidence for intense volcanic activity in the past. Look at several pictures reconstructed from the radar data.

Note: The Venus observations should be done always at the beginning of the lab period because the planet always stays fairly low in the south-western sky and sets early during its evening periods of visibility. Clear skies are relatively rare in Nashville, so you should make the very best of your time at the telescope and use it to OBSERVE. Use it to make sketches, make notes and write down measurements and discuss the questions asked in the lab. Leave out all calculations, writing down your answers to the questions, etc., for later, and complete the lab in the comfort of a heated, well-lit room.

Procedure

1. Getting Started: As always, note the date and time. Make notes describing the atmospheric conditions tonight. Is the sky clear, partly cloudy, high cirrus clouds? Is the air humid? Is it windy? How does this night compare with other nights on which you have observed (better? worse? in which way?). Think about how the weather may affect your view of Venus.

2. Sketch Venus: Acquire Venus with the 25mm eyepiece and then switch to the 10 mm eyepiece. You will notice that Venus is not round but shows a phase, like the Moon. It is unlikely that you will see any feature on the planet as it is completely covered with rather uniform clouds. Nevertheless, look for shadings in the clouds. Draw the disk of Venus using the planet template provided. Have a look at the examples kept in the storage shed. You will have to be patient and wait for steady and clear views of Venus through brief patches of still air. Take your time! Draw the phase as accurately as you can. This is important for the calculation in #3 below. Indicate on your sketch the directions of North and East. Remember, the sky rotates from East to West, so when you turn off the motor drive of the telescope, objects drift westward in the eyepiece. If you move the telescope in declination toward the South (lower declinations), objects will drift North in the field of view.

3. How far away is Venus? The phase of Venus as seen through a telescope depends on the relative positions of the Sun, the Earth, and Venus. We can use this phenomenon to determine the distance between Venus and the Sun and between the Earth and Venus. Once you have sketched Venus (with a precise rendering of the phase) and plotted its position on the 200% blow-up of the SC001 sky chart (Venus' orbital motion lab), you have all the observations in hand to do the calculation. The following figures show the geometry of the problem. A modest amount of high school trigonometry is required to understand the method. There is a very slight variation on the calculation of the distance, depending on whether Venus shows a gibbous phase (Figure 1) or a crescent phase (Figure 2). Use the one that is appropriate for your observation.

   
   

   Figure 1

   
   

   Figure 2

   
   

   Figure 3

   Our goal is to determine the size of the orbit of Venus (D) and the distance between the Earth and Venus (L). This can be done by using a little bit of trigonometry and algebra. In Figure 1, the Sun-Earth distance is 1 Astronomical Unit (this defines this unite of distance: 1 A.U. = 1.496×10⁸ km, or about 93 million miles). If we apply the Law of Sines to the traingle in Figure 1, we have:

   

   The angle a is ismply the Sun-Earth-Venus angle and can be measured by plotting the position of Venus on the star chart (SC001 or the 200% blow-up) and reading off the difference of ecliptic longitude between the Sun and Venus (note that the position of the Sun along the ecliptic on a given day of the year is shown on the star chart). The angle b is what determines the phase of Venus, as can be seen in Figure 2. To apply the above formulae, we need to determine the angle b We first consider the case where Venus shows a gibbous phase. In this case, we have:

   

   Applying the Pythagorean themrem, we find (see Figure 3):

   

   where W is the width of the dark, or missing part of the disk (Figure 3). Measure W and R (in mm) on your sketch of Venus, and compute Y, sin(b), and finally the angle b.

   If Venus shows a crescent phase, the procedure is slightly different. Now W becomes the width of the crescent (bright) part of the disk. Comptue Y wth the above formula and the angle d from:

   

   Now the angle b is simply b=180^o-d. In both the gibbous and crescent cases, the angle c is simply given by c=180^o-a-b. We now know all three angles of the triangle in Figure 1 (or Figure 2), and the length of one side. You can compute the other two sides, D and L, using the formulae above. Give your results in A.U. and km. It is quite remarkable that we can determine such vast distances with such simple measurements and calcuations!

   Question: Does your value for the distances make sense? Explain.