The Brightness of Venus

Anyone, even the most casual observer,  looking at  the evening sky in the last month will have noticed the brilliant white planet Venus shining in the west. Often known as the Evening Star, Venus is the third brightest natural object in the sky after the Sun and the Moon. In this post I’ll talk about why Venus is so bright.

Because Venus is a planet it doesn’t emit any visible light of its own like a star does. All planets shine by reflecting starlight from the star they orbit, which in the case of Venus is the Sun. The brightness of a planet is determined by a combination of three different factors.

Factor one is the planet’s distance from the Sun. This is because the intensity of sunlight falling on a planet diminishes as the square of its distance from the Sun. This is the well-known ‘inverse square law’, which many of you will have studied in high school science lessons.

 

 

The Intensity, which is the amount of radiated power falling on a unit area, falls as the square of the distance

 

Clearly the more radiation falling on a planet the brighter it is, all other factors being equal. If we compare Venus to Mars, then Venus is on average 2.1 times closer to the Sun than Mars. So, it receives 4.4 (which is 2.1 squared) times as much sunlight per unit area.

 

Factor two is the proportion of sunlight hitting the planet which is reflected back into space.  This is known as the albedo (strictly speaking the Bond albedo) and has a value between zero and one. An albedo of zero means that the planet reflects no sunlight back. Such a planet would be totally black and thus invisible. Clearly no such bodies exist, but a hypothetical planet covered in soot would have an albedo of only 0.04, meaning that only 4% of the sunlight hitting it would be reflected back. At the other end of the scale an albedo of one means that all the sunlight hitting it is reflected back. Although no bodies exist with an albedo of one. A planet completely covered in fresh snow would have an albedo of 0.9. The albedo of Venus at 0.77 is higher than any other planet in the Solar System. For comparison, Mars has an albedo of only 0.25.

 

Factor three is how large the illuminated part of the planet appears in the sky. This depends on:

  • the diameter of the planet – factor 3A,
  • its distance from Earth – factor 3B and
  • its phase i.e. the percentage of its sunlit face which is visible from Earth – factor 3C.

Both the distance from Earth and the phase are continually changing as the planet and the Earth move around the Sun in their respective orbits.

Examples of phase for the Moon

The way that these three factors interplay to make Venus the brightest object in the sky is best illustrated if we take the examples of the three brightest planets Venus, Mars and Jupiter.

Data from Williams (2018 a, b, c)

*An astronomical unit (AU) is the average distance between the Earth and the Sun and is equal to 149 597 871 km.

** Because the planets travel in elliptical, rather than circular orbits, their distance of closest approach to Earth and thus their maximum brightness achieved varies from orbit to orbit. The ranges of the distances from the Earth for Venus, Mars and Jupiter are given below.

In the main table the areas are given in arc seconds squared (arcsec sq.). When viewed from Earth, planets are very small and appear to the naked eye as points of light because they are too small for the human eye to resolve them into discs. Astronomers measure the apparent size of small objects in the sky in arcseconds. An arc second is 1/3600 of a degree (or roughly 1/1800 of the diameter of the Moon). It is the size that an object 2 cm in diameter, such as a US 1 cent or British 1 pence coin, would appear from a distance of 4 km.

The relative sizes and phases of Venus, Mars and Jupiter when they are at their brightest. Venus is shown in the crescent phase, because that is its phase at it brightest

 

Planets which are outside the Earth’s orbit, such as Mars and Jupiter,  are always at their brightest when they are at their full phase (i.e. 100% illuminated) and are at their closest to Earth. This is known as the opposition and is discussed in detail in a previous post  Venus orbits inside the Earth’s orbit and when Venus is closest to Earth its sunlit side faces away from the Earth and the planet is at its lowest brightness. Venus is at its maximum brightness when its phase is around 26%, shown as the two points labelled A in the diagram below.

And finally…

 

I hope you have enjoyed reading this post and have plenty of clear skies to observe Venus in these difficult times, when many of my readers are having to remain at home due to corona virus. If you want to read any of my previous posts on Venus, please click on explainingscience.org/tag/venus.

 

 

Notes on Magnitude

When discussing the brightness of objects in the sky, astronomers use a scale called magnitude, where the lower the magnitude the brighter the object.  The scale was originally invented by the ancient Greek astronomers who classified all the stars visible to the naked eye into six magnitudes. The brightest stars were given a magnitude of 1, and the faintest a magnitude of 6.

Values in the magnitude scale were standardised by nineteenth century astronomers to make each decrease in magnitude value by 1 an increase in brightness of 2.512. The range of values was also extended as well, to cater for the brightest stars and most planets which are brighter than magnitude 1 and stars fainter than magnitude six.

In the standardised scale for example

  • a bright star having magnitude 1 is 9 times brighter than a star of magnitude 4. This is because 2.512 x 2.512 x 2.512 = 15.9.
  • a star having magnitude 1 is 100 times brighter than a star of magnitude 6. This is because 2.512 x 2.512 x 2.512 x 2.512 x 2.512 = 100

 

The brightest natural objects in the sky are (obviously) the Sun, which has a magnitude of -26.7, followed by the Moon, which has a magnitude of -12.7 at a typical full Moon.  Third comes Venus, with a magnitude of around -4.5 at the two points in its orbit when it is brightest.  The magnitude of the faintest star that can be seen by someone with good eyesight in a rural location, once their eyes have fully adapted to the dark, is normally taken to be around 6.5 to 7.0.

Update 22 November 2020

There is now a video on the Explaining Science YouTube Channel which describes Venus’s orbit and phases. To view it, please click on the link below

References

 

Williams, D (2018) Venus Fact Sheet.  Available at: http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html (Accessed: 25 March 2020)

Williams, D (2018) Mars Fact Sheet.  Available at: http://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html (Accessed: 25 March 2020)

Williams, D (2018) Jupiter Fact Sheet.  Available at: http://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html (Accessed: 25 March 2020)

 

 

 

 

 

 

 

 

23 thoughts on “The Brightness of Venus”

  1. A very nice article, I read it with much pleasure.

    Seeing Jupiter and Saturn so nice together in the southern sky, inspired me to think about the brightness of planets. Especially the maximum brightness for inner planets. After some work on this, I posted a problem on the subject, see https://brilliant.org/problems/brightest-elongation-of-a-planet/. Looking for other sources to back my theory up, I found your nice post!
    I calculated the elongation of Venus where it is brightest to be 26.7° (based on circular orbits of Venus and Earth at 0.72 and 1 AU).

    Lokking forward to following posts!

    Liked by 1 person

      1. Thank you and glad my post was useful 🙂

        Though of course because the Earth and ( to a much lesser degree Venus ) move in elliptical orbits, things are a little more complex and the elongation will vary a little from orbit to orbit

        Steve

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  2. When Mars is at its best opposition and brightest,not an average opposition but the best possible,does it get brighter than Jupiter ever gets at its oppositions? Also with the closest Mars opposition does it occupy a larger apparent image size than does Venus when Venus is at its brightest (Venus of course then being a crescent rather than a round image like Mars at opposition

    Liked by 1 person

    1. Some Interesting questions.

      As you know Mars moves in a much more elliptical orbit than Jupiter which means of course that its maximum brightness at opposition will vary more than Jupiter. The average magnitude of Mars at opposition is -2. However, the maximum brightness of Mars at its closest opposition is magnitude -2.94. (of course at other oppositions Mars won’t even get as bright as magnitude -2 )

      The average magnitude of Jupiter at opposition is -2.7 and its maximum brightness at its closest opposition is magnitude 2.94. So yes, although Jupiter is on average brighter than Mars at opposition, sometimes Mars will be brighter.

      The answer to your second question is yes. At its closest opposition Mars occupies a larger apparent image size (measured as the illuminated part of the planet ) than Venus when Venus is at its brightest

      BTW if you want to find out more details on properties of the planets The NASA factsheets are a good reference, I have attached a link to the Mars and Jupiter factsheets below
      https://nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html
      https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html

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      1. When Mars has a good opposition it appears extra impressive to me because of the reddish color vs. Jupiter’s near white. I believe different peoples’ vision varies slightly as to relative color sensitivity so it could be that I am more sensitive to red than someone else. (At their brightest these planets trigger cone/color vision while dim stars probably don’t.)
        Does the appearance of Mars very slightly due to variability of the Mars atmosphere/dust/weather? If so that might affect the appearance of Mars at opposition
        (Mars) Opposition coming up in a couple more months or so,Mars is now in the morning sky and appears to me brighter than Saturn (which seems to be hanging out near Jupiter,both I think near opposition.

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        1. Yes,

          the weather conditions on Mars, can affect its albedo. The value quoted in this post is its average value[ 0.25] and weather conditions could make affect this value a little. either raising it – making Mars brighter or lowering it – making Mars fainter.

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  3. Interesting equation of brightness of Venus. Every I learn something new. It’s like a candy inside a treasure hunt. Can’t get enough.

    Thank you for taking time to share such insightful information.

    Cheers.

    Like

  4. Clear and interesting as always! I find the idea of a planet covered in soot strangely unappealing, but you reminded me of Hawking’s pronouncement that ‘Black Holes ain’t so black.’
    I hope you are staying safe!

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  5. Thanks Steve for this clear, concise explanation. So above 26% illumination, greater distance from Venus reduces its brightness more than enlargement of the illuminated portion increases its brightness. But below 26% illumination, enlargement of the illuminated portion increases brightness more than greater distance reduces it? Perhaps this is because above 26% illumination distance increases more for every unit enlargement of illuminated area, owing to shape of Venus’ orbit?

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  6. Wow. Great explanation. The best part is all Mars and Jupiter plus Saturn are visible right now in morning with Venus taking stage in the evening.

    Like

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