Angular Sizes and Venus’ Brightness

Angular size of Venus

Starting this January, the planet Venus will begin to appear gradually brighter in the western sky, right after sunset. Venus’ phase is changing from a roundish gibbous shape, into a half-moon shape, and then into a crescent shape, as seen in Figure 1.

Figure 1: Venus changing phases as the weeks go by

At first glance, this seems rather counter-intuitive—why would it get brighter, when the fact is, the area of Venus filled with the reflected light from the sun is getting smaller and smaller as it changes shape into a crescent? This is because not only is Venus changing shape, it is also getting closer and closer to the planet Earth. Let’s examine Figure 2.

Figure 2: Initial position of Venus with respect to Earth, in the solar system.

Being closer to the sun than our planet, Venus is orbiting the sun in a much smaller, tighter path, compared to the earth. If we apply Kepler’s Laws, this means that Venus is also orbiting the sun much faster than the Earth is. So even if Venus was seemingly lagging behind this January, there will come a point along their orbits wherein Venus will overtake the Earth.

Thus, viewed through a telescope, the angular size of Venus actually increases dramatically as the weeks and months go by, as it steadily gets closer to the Earth. Using an eyepiece of the same magnification as you keep observing it regularly, you will notice that the overall appearance of Venus is noticeably larger every week or month. Refer to Figure 3.

Figure 3: Venus Changing Phase and Increasing in Size

 It will appear like a half-moon by mid-March, and it will start to appear like a crescent soon after that. By May 4, it will be at its brightest.

But again, why? The answer is revealed when we superimpose the appearance of Venus in January 15, 2020 with the appearance and apparent size of Venus on May 4, 2020. See Figure 4. Notice that while the crescent shape means that less light is being reflected by Venus’ surface, the fact that it’s much larger in angular size compared to the January Venus, means that more light is actually being reflected by the crescent Venus. Calculating the area of the crescent-shaped Venus (this by the way, is an interesting field of Geometry called Lune Geometry), and calculating the area of the gibbous Venus will yield a larger value for the Crescent Venus.

Figure 4

However, this will not last very long, and just after a week or two, as Venus is about to overtake the earth, this crescent Venus will quickly dim and not be visible anymore. It will then shift from being an “Evening Venus” into a “Morning Venus” (or the more common term is “Morning Star” as it was mistakenly called in the olden times).

Finally, another factor to Venus’ brilliant shine when May 2020 arrives has something to do with the Inverse-Square Law, which states that brightness intensity is inversely proportional to the square of the distance from the source. By May, the crescent Venus is almost at right angles between the Sun and the Earth, so not only the crescent has a bigger angular diameter, the light coming from that crescent shape is closer to the earth as well, compared to the reflected sunlight back in January.

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