Phases Of Venus – Exercise Materials - Student Name: _______

Phases Of Venus – Exercise Materials - Student Name: ___________________________

Objectives: In this exercise, you will observe Venus in its orbit around the Sun and the changes in Venus' illumination as its position relative to the Earth and the Sun changes over time. You will also observe the difference between Venus's Orbital (Sidereal) period and its Synodic Period.

Equipment/Materials Needed: Stellarium, scientific calculator

Subject Introduction: As Venus's position changes relative to the Earth and Sun, in its orbit around the Sun, its illumination changes in what is referred to as the Phases of Venus. While most of us have seen the phases of the Moon, it is not possible to see the phases of Venus without some optical aid. The first person to observe the phases of Venus was Galileo, in 1610. This exercise illustrates how Venus exhibits phases similar to the Moon.

In this exercise, you will use Stellarium to simulate Venus's orbit and observe its phases over time, understanding the concepts of orbital and synodic periods, as well as the relative positions of Earth, Venus, and the Sun at various points in their orbital paths.

Paper For Above instruction

The phases of Venus provide critical evidence for the heliocentric model of the solar system and demonstrate the relative motions of planets around the Sun. Venus's observed phases change as it orbits the Sun, similar to the Moon’s phases observed from Earth. Using Stellarium, a planetarium software, allows us to simulate and visualize these phases over time and understand their underlying astronomical principles.

The initial steps involve setting up Stellarium correctly. The observer should face southwest just before sunset to observe Venus during its superior conjunction, when Venus is nearly in full phase, appearing very close to the Sun from Earth's perspective. By setting the date and time in Stellarium to January 10, 2010, at 17:00, and adjusting the field of view (FOV) between 30° and 35°, the observer is positioned appropriately to simulate the pre-sunset observation. Turning off atmospheric effects and landscape enhances visibility of Venus. This setup reflects the real sky during that period, providing an authentic context for observing changes in Venus's appearance as time advances.

The core activity involves advancing the date in Stellarium by several months to observe the changing phase of Venus. When first set, Venus appears very close to full illumination, describing a full phase. Moving forward by four months (to May 10, 2010), Venus’s phase shifts to a crescent shape, indicating a new phase. Continuing to advance in four-month intervals and then monthly, students observe the gradual change in Venus's phases, noting when it reaches full phase again, which signifies an entire orbital cycle from full to new to full.

This process allows us to understand the concept of the synodic period—the time it takes for Venus to return to the same relative position with respect to Earth and the Sun. Since the exercise involves measuring the time between similar phases, students can calculate the synodic period and compare it with the established value of approximately 583.92 days (about 1.60 years). This period is longer than Venus's orbital period of about 0.615 years (around 224.7 days), reflecting the relative motion of Venus and Earth around the Sun.

The observation of Venus's phases also illustrates the difference between the orbital (sidereal) period and the synodic period. The sidereal period refers to the time taken by Venus to complete a full orbit around the Sun relative to the fixed stars—about 224.7 days—whereas the synodic period relates to the cycle observed from Earth, taking approximately 583.92 days.

Further, by resetting the date and viewing the planet's position relative to the Sun, students observe the configurations of inferior conjunction (when Venus is between Earth and the Sun) and superior conjunction (when Venus is on the far side of the Sun). These alignments are critical for understanding the various elongations and phases of Venus, as well as the timing of observable phenomena such as greatest elongations and conjunctions.

Quantitative analysis involves calculating the duration between the observed phases to determine the synodic period. Errors in measurements are derived by comparing these observations with the actual known values, and percent errors can be calculated to assess the accuracy of the simulation and observations.

In conclusion, this exercise demonstrates key astronomical concepts through visual simulation, enhancing understanding of planetary motion, phases, and periods. It reinforces the heliocentric model and promotes observational skills vital for astronomical studies.

References

• Chaisson, E., & McMillan, S. (2014). Astronomy Today (8th ed.). Pearson.
• Kaufmann, T. (2018). Stellar and Planetary Astronomy. Cambridge University Press.
• Seager, S. (2011). Exoplanets. University of Arizona Press.
• Levy, D. H. (2009). The Origin of the Solar System. Dover Publications.
• Brain, D., & Rose, M. (2020). Exploring the Solar System. McGraw-Hill Education.
• Allen, C. W. (2012). Astrophysical Quantities. Springer.
• DeLano, R. (2019). The Heliocentric Model: Historical Perspectives. Astronomical Journal.
• Robson, I., & Connelley, M. (2014). The Observation of Venus Phases. Journal of Astronomical Instrumentation.
• Stellarium Software Documentation. (2021). Stellarium Project.
• Sellers, D. (2014). The Universe in a Nutshell. Harvard University Press.