Planets are a dynamic group. From the perspective of the earth, these celestial bodies not only move in the sky, but also glow and fade in turn.
The distance between the planet and the Earth may be the most important factor in determining its apparent brightness. For example, in October last year, Mars was brighter than Jupiter, thanks in large part to this red planet being so close to Earth before 2035. In contrast, Mars is now sinking into the western night sky, further deepening. Afterglow, because the earth and Mars are actually on either side of the sun.
But the overall brightness of a planet is also affected by its distance from the sun, which determines the intensity of sunlight illuminating its surface. When the two brightest planets, Venus and Jupiter, are close to each other in our sky (as they will be on April 30, 2022), look at them through a telescope and you will find that the disk of Venus looks better than that. Jupiter is more dazzling, partly because it is closer to us, but mainly because it is also more than seven times from the sun.
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Another factor is the size of the planet in question. For example, Mars is only about twice the size of our moon, so as it gets farther and farther away, its brightness tends to decrease faster than a significantly larger planet like Venus.
A less obvious factor is the appearance of the planet, its sunlit part of the hemisphere rotating towards the earth. Mercury and Venus, the two planets closest to the sun than Earth, the so-called “lower” planets, show a complete phase cycle like our moon. At the same time, Mars is obviously convex near orthogonal time, that is, 90 degrees west or east of the sun. In contrast, Jupiter and Saturn only show a slight bulging effect, mainly because they are much further away from the earth and the sun.
Another factor to consider is the reflectivity or albedo of the planet. This factor depends on the surface of the planet, including the light and dark areas that can rotate in and out of the field of view. Compared to other planets, the albedo of Venus is very high, around 70%, thanks to its highly reflective clouds. On the contrary, our moon (you will be surprised) is a rather poor reflector: in the visible spectrum, it reflects only 12% of the light and absorbs the rest.
An “illumination” formula
When calculating the brightness of a planet, we have noticed that the first thing to consider is its distance from the sun. To do this, we must use the inverse square law, which states that the specified physical quantity is inversely proportional to the square of the distance to the light source. Therefore, from a distance of 2 feet, the candle appears to be only 1/4 of the brightness at a distance of 1 foot. Its brightness is 1/9 from 3 feet, 1/16 from 4 feet, and so on. This is a law that affects nature, not only light and other forms of radiation, but also gravity.
The next factor, how far the planet is from us, is also derived from the inverse square law. The closer the planet is to us, the greater its apparent size. And its apparent surface area increases correspondingly with the square of its diameter. By mid-September, Mars will be 395 million kilometers from Earth and will orbit a small 3.5 arcsecond disk. In contrast, on August 27, 2003, Mars was close to a record 34.6 million miles (55.7 million kilometers) away, with a diameter of 25.1 arc seconds.
The gibbous moon as seen from the International Space Station in May 2021.
The gibbous moon as seen from the International Space Station in May 2021. (Image source: NASA)
goes through a stage
The impact of the stage effect is more difficult to calculate. For the moon, anyone can see it, the closer it is to full phase, the brighter it appears.
But consider Venus, its clouds are nearly uniform and orbit the Sun in a nearly circular orbit. Therefore, its brightness depends almost entirely on its distance from the ground and its phase. Therefore, when Venus is very close to the lower conjunction (the planet passes the point between the earth and the sun), it will rapidly approach our planet, and as the phase becomes thinner, its disk appears to grow substantially. .
This planet reaches its maximum brightness (approximately 4.9 etc.) when it appears in the shape of a crescent, with a brightness of approximately 25%, and appears approximately 36 days before and after the CC. We call it the “maximum illumination range” of Venus, a compromise between the number of illuminated discs and their apparent size. Although it’s just a long, thin crescent moon, we see more Venus than ever in the total area illuminated per square arc second.
Venus will reach this point when it appears on the night of December 3, when its brightness will be almost three times brighter than it is now, and its disk will look almost 3.5 times larger!
However, this is a different story for Mercury, which is a planet similar to the Moon. In fact, its albedo is actually 11% lower than that of the moon. Although this fast planet oscillates close to us during the lower conjunction, we see less sunlight reflected off it because it looks like a new moon. Therefore, like the moon, Mercury is brightest during the “full moon” when it is on the other side of the sun and the earth.
In his book “The Solar System and the Return” (Doubleday, 1970), the late great science fiction writer

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