(Printer-Friendly Version)

Venus

Goals of the Lab

• To observe phases of Venus and to calculate its distance from Earth based on observations.

Required Equipment: Observation Template, SC001 Map, Calculator

Background: Venus is the second planet from the sun. Named after the Roman goddess of love and beauty, it rightly deserves its name when seen from Earth. Shining at an maximum apparent magnitude close to -5, it is only outshone by the Moon and Sun. Glittering in the morning or evening sky (you may have heard it termed the "morning star" or "evening star"), Venus's brightness is due to its proximity to Earth and it being completely enshrouded in clouds that give it a high albedo – the fraction of sunlight it reflects.

Venus is often termed "Earth's sister" because its diameter is only 650 km smaller than Earth's. The similarities end there. Due to a runaway greenhouse effect, the average temperature at the surface is around 850 °F (460 °C or 730 K), hot enough to melt lead. The thick clouds and atmosphere are made of toxic chemicals such as carbon dioxide and sulfuric acid, a primary constituent of batteries. Pressures at the surface are equivalent to being under a kilometer of ocean on Earth.

Venus is also unique in that it exhibits retrograde rotation - it spins backward on its axis, resulting in the sun rising in the west and setting in the east (don't get retrograde rotation confused with retrograde motion). Its day (243 Earth days) is longer than its year (225 Earth days). Since Venus' orbit is inside of Earth's (an average orbital radius of 107 million kilometers compared to Earth's 149 million), we should see it go through phases just like the moon, a hypothesis Galileo came up with to test the heliocentric model of the solar system. When he looked through his telescope and watched Venus over the course of its orbit, he indeed saw that the planet exhibited phases.

There have been quite a few attempts to land probes on the Venusian surface to do scientific analysis. Most were to no avail due to malfunctions or to the heat and pressure of the atmosphere essentially crumpling and melting the probes. Magellan was the first planetary orbiter to map the entire surface with cloud-penetrating radar. Results showed the surface to be very young since very few craters were found.

Part I: Plotting Venus's Position on the Sky

1. In order to ultimately determine the distance to the planet, you will need to know some of the angles in the triangle formed by Venus, the Earth, and the Sun. You will be provided with the right ascension and declination of the Sun on the day of the lab. Find the coordinates of the Sun and plot its position on the provided blank SC-001 star map.

2. Using your crossbow or other measurement technique, measure the position of Venus among three close-by (preferably bright) stars, and plot its position on your blank SC-001 map using the same method you have been using in the other lab to plot Venus' movement among the stars.

Part II: Observing Venus and its Phase

Note: All observations need to include directions N/S and E/W, the time, the date, and the weather conditions.

1. Using the 25mm eyepiece, locate and center Venus in the field of view. Sketch the field of view, including any stars in the field of view. Indicate the scale of your drawing, based on your measurement of the field of view you made earlier.

2. Switch to the 10mm eyepiece. Sketch Venus making sure to try and make a very accurate sketch of the phase, i.e. try to get the crescent shape as realistic as possible since you will be using this sketch to determine the "phase angle" and, from the phase angle, the distance to the planet. It is recommended that you sit and study the image in the eyepiece for several minutes to get a really good feel for the size of the crescent/gibbous because the accuracy of your other results is going to depend solely on how well you draw the sketch. Also, it may be possible to note some very slight cloud features if the seeing is pretty steady and you have a well-focused image. If you cannot see any cloud features, don't worry about it.

Part III: Estimating the Distance to Venus

1. When Venus is not on the other side of the sun or almost directly between us and the sun (superior and inferior conjunction, respectively) it is relatively easy to observe a phase. When Venus is approaching inferior conjunction, it is getting closer and closer to Earth as it nears the point where it will almost be directly between the Sun and the Earth. Therefore, its proximity makes it appear much larger than when it is near superior conjunction. If you watch Venus over its full cycle of phases, you will notice that the crescent phases appear larger while the gibbous phases appear smaller. From the sketch of your observation, determine the how much of the disk of Venus is visible to Earth.




Figure 1




Figure 2

From Figure 1, if W is the percentage of Venus' diameter that is visible to us from Earth (in the figure, W is about .66 or 2/3 of the diameter) and R is the radius of the planet, then




2. To ultimately solve for the distance (using the law of sines), we have to solve for theta

   
   

3. Next, we need to know the angle V. This is just the apparent angle between Venus and the Sun. You have already plotted the position of these two objects on your star map. Determine the angle between the two objects by using the declination scale on your star map.

4. Finally, we can determine the angle d through the formula

   

   We already know that the value for E, the Sun-Earth distance, is 1 A.U. (A.U. = astronomical unit). Since we have all of the angles, we can find all of the other distances in Figure 2 by using the law of sines:

   

   Determine the distance to Venus from Earth (D) and Venus' average orbital radius (V).

   Question: Do your values for the distances make sense? Explain.