Probably most people know that stars and planets are very different. Very different. A star is a massive collection of plasma sustaining nuclear reactions, so far away (apart from our own Sun) that its light takes many years to get to us. A planet is much smaller and is a rocky/gaseous ball that orbits our Sun (planets do orbit other stars too, but we can’t see any of those with the naked eye, so in this article when we say planet, we are restricting ourselves to our own solar system). A planet doesn’t shine by itself and is only visible by borrowing light from the Sun to reflect. So far, so familiar.
However, my experience tells me that fewer people can distinguish a star from a planet when they see one in the night sky. Many people look at Mars or Jupiter, for example, and think they are looking at a star. Some are surprised that they can see a planet at all.
Given that we can see a planet, then, surely it must look different from a star. After all, we have just said planets and stars are so different! For a start, planets are all different colours – we get taught that Mars is red, for example. That may be true, but there are at least two reasons why it doesn’t help!
- Stars have colour too: there are quite a few bright, distinctly reddish stars, such as Betelgeuse and Antares, that can easily be mistaken by the uninitiated for Mars
- At the light levels involved (i.e. not much light, because it’s night time…), the human eye is pretty bad at seeing in colour. So yes, Mars is ‘the red planet’, but it’s not that red. Beginners often have to be shown that you can see colour in the night sky
Maybe the relative sizes and distances of planets and stars will help us? Stars are so far away they always look like point sources of light, whereas planets can look like a ‘disc’ to the naked eye – a circle in the sky. However, a planet makes a very small circle in the sky, so that people who don’t realise it’s true don’t always notice the effect.
Stars and planets really can look similar. Below is an image borrowed from nakedeyeplanets.com that shows Saturn (a planet) in the constellation (of stars) of Leo. There’s a planet there…
(reproduced with permission © Martin J Powell, nakedeyeplanets.com)
Which one is Saturn? It’s the brightest one, half way up on the right-hand side. Would you be able to tell? It’s not easy, is it?
Perhaps we should concentrate on what stars and planets do, rather than what they look like, in order to distinguish them? In fact, you can tell a planet because it seems to ‘wander’ across the fixed background of stars over a period of day, weeks and months. Stars, on the other hand, stay in a fixed pattern on the sky. That whole pattern rotates once approximately every 24 hours (23 hours 56 minutes actually – look up the difference between a sidereal day and a solar day if you are interested…). However, you need to be reasonably familiar with the patterns of the stars to notice the wandering of the planets – like the hour hand of a clock, they move too slowly to see in real time. I’m a bit rusty, and had to refer to a map of Leo to find the ‘extra dot’ that had to be Saturn! Venus and Mercury can sometimes be found because they never ‘stray far’ from the Sun, but it requires a little experience to identify them from this fact.
Once we’ve discounted the colour and size (they are all fairly spherical, so we can ignore shape too!), and their behaviour, pretty much all we are left with is their brightness. In the picture, Saturn might be the brightest, but it’s not that much brighter than the other bright dot near it (‘down and left a bit’), which is Regulus, the brightest star in Leo. And Saturn certainly isn’t brighter than all stars – at its brightest it still looks fainter than Sirius and Canopus, the two brightest stars in the sky.
So how is it that such different objects are not so different in brightness?
One quick answer is that stars give off vastly more light than planets reflect, but stars are vastly further away, and these two effects tend to counteract one another. However, it isn’t clear at first sight that they should counteract each other quite as well as they seem to.
It would be a lot easier to distinguish a star from a planet if one were always much, much brighter than the other, but we’ve seen that isn’t the case. Why isn’t it the case? Well, let’s do a couple of back-of-the-envelope calculations (don’t worry – I’ll do them, and you can tag along for the ride), to estimate how much light gets to us from the brightest star, Sirius A, and the largest planet, Jupiter. We’ll need to make a whole host of assumptions and simplifications, but hopefully they won’t distort the picture too much… What we need to know is the ‘intensity’ of the light from Sirius, that is, the number of joules of energy hitting a square metre on Earth every second. Then we can calculate the light intensity at Earth from Jupiter, and compare the two. We are going to ignore completely the fact that the sensitivity of the human eye depends on the wavelength (colour) of the light, and focus purely on the energy content of the light.
Sirius A
Sirius A, thanks to the nuclear reactions at its core, throws out 3.9×1026 Joules of energy every second (or watts – a watt is a power of 1 joule per second). That’s a lot of watts – Sirius is about 25 times more powerful than the Sun. But how many of those watts hit a square metre here on Earth? Well, those watts of power radiate out in all directions. You can think of light from Sirius as spreading out in an expanding ‘bubble’. The surface area of the bubble is the surface area of a sphere, 4πr2, where r is the radius of the sphere (the distance the light has travelled from Sirius). The distance from Sirius to Earth is 8.6 light years = 8.1×1016 m, so the surface area of the bubble of light at that distance is 8.2×1034 m2.
Dividing the power output from Sirius between all those square metres will tell us the intensity of light on Earth from Sirius. That is, how much light energy per second hits a single square metre of Earth. It works out to be about (3.9×1026 W) ÷ (8.2×1034 m2) ≈ 5×10-9 W/m2 (watts per square metre). This does assume that none of the light has been absorbed on the way by interstellar dust and gas, but hey, you do want to get home tonight, right?
Jupiter
This one is a bit more involved, because Jupiter is reflecting sunlight rather than shining upon us directly. We are going to:
- Find the intensity of sunlight at Jupiter
- Estimate how much gets reflected
- Estimate how much of the reflected light hits a square metre of Earth
Now, whereas Sirius always appears the same brightness, the brightness of Jupiter depends upon where it and Earth are in their orbits. For simplicity, we’ll assume that Jupiter is ‘at opposition’. That is, there is a direct straight line from the Sun, through Earth to Jupiter, as in the diagram below. That will make it as close to Earth as it will ever get, and will ensure that it is a ‘full planet’ like a full moon, with the whole side facing us illuminated by the Sun.
The Earth-Sun distance is called 1 astronomical unit (1 A.U.). Jupiter is about 5.2 A.U. from the Sun, on average. (Planets don’t orbit the Sun in perfect circles. Their orbits are slightly elliptical, so their distance from the Sun varies. We’ll ignore this effect, as one of the simplifications we are making, to improve our chances of ever getting to the end of this post…). Now, the solar constant on Earth is approximately 1360 W/m2. This is a measure of the intensity of light from the Sun (just as we worked out for Sirius). We can use the inverse-square law to find the intensity of the Sun’s light at Jupiter. That means that if Jupiter is 5.2 times further away (it is – check the diagram), the intensity will be a fraction 1/(5.22) of the Earth’s solar constant. The inverse-square law is a consequence of the same ‘light spreading out over a bubble of surface area effect’ that we have already seen. Therefore, the intensity of sunlight at Jupiter is 1360 × 1/(5.22 ) ≈ 50 W/m2.
How much light does Jupiter receive from the Sun in total? Well, Jupiter’s radius is approximately 35 000 km. The cross-sectional area of the disc of Jupiter, as seen by the sun, is then πr2 = 3.85 × 1015 m2. And it therefore collects from the Sun 50 W for every square metre over 3.85×1015 m2, or a total of 1.9×1017 W.
There is an astronomical quantity called a body’s albedo, which is the fraction of incident light that it re-radiates/reflects. Let’s say Jupiter’s albedo is 0.5 (that’s pretty close). Then it re-radiates about 1017 W. This is yet another gross simplification, in that Jupiter really isn’t a flat disc all facing the Sun, but is a sphere, with much of it at an oblique angle. But again, for back-of-the-envelope purposes, let’s continue. We already need quite a large envelope…
Our question now is: of the 1017 W of sunlight re-radiated by Jupiter, how much of it hits a square metre of Earth? Well, we will use the (now familiar) argument that the 1017 W spreads out over an expanding bubble. Earth is 4.2 AU away (see diagram above), which is approximately 6.3 x 1011 m. The bubble at this distance has area 4π × (6.3×1011 m)2, or 5×1024 m2. And so the amount of light from Jupiter hitting a single one of those square metres is (1017 W) ÷ (5×1024 m2) = 2×10-8 W/m2.
Comparison
Let’s take stock. Admittedly, our calculations have been much-simplified, but our estimates are that the light intensity at Earth are:
- From Sirius A: 5×10-9 W/m2
- From Jupiter: 2×10-8 W/m2
That’s only a factor of four difference! The light from Jupiter is four times as intense as that from Sirius. Not 0.0004, not 40 000, but 4. Our eyes see 4× difference quite similarly – a 15 W bulb and a 60 W bulb look different, sure, but not that different. The eye is sensitive to light over approximately 10 orders of magnitude of brightness, so a factor of four can’t look that spectacular! And besides, there’s far more than a factor of 4 brightness variability within different stars, within different planets and even within the same planet as its brightness varies during its orbit. Added to which, these calculations were based on Jupiter being at a position that makes it at its brightest. A lot of the time it will be even more similar to Sirius!
No wonder stars and planets are easily confused. How amazing that the numbers we calculated are so similar, considering the difference in light generating methods and distances. If the answers were 40 000 times different, which wouldn’t seem unreasonable, we would never confuse planets and stars in the sky!
Is any of this important? Well, it won’t help you file your tax return or learn how to drive. But if you are out at night, and you look up and wonder whether any planets are visible, thinking about this might just brighten your evening.