Is it possible to observe Pluto from the window of an apartment in a big city?
This planet dwarf planet was discovered in 1930 with a large telescope at the Lowell Observatory, where light pollution was likely not a problem. One might then think that it is impossible to see Pluto from an apartment, at least not without very sophisticated equipment. However, almost a century later, good lenses are widely available, images can be recorded effortlessly with the sensors in digital cameras, and computers allow us to post-process these images, in order to separate signal from background.
So perhaps it is possible to image Pluto.
Let us then compare the Moon, Jupiter and Pluto:
Obviously from Earth we do not see them with the relative sizes shown above. Based on their diameters and distances from us, these three bodies have approximate/mean angular sizes of 31'~0.5° (the Moon), 40''~0.01° (Jupiter) and 0.1''~0.00003° (Pluto). I am using here the standard units to measure angles: a full circle in the sky, like the horizon seen from a flat area, has 360 degrees (°), each degree can be subdivided into 60 arc-minutes ('), and in turn each arc-minute can be further subdivided into 60 arc-seconds ('')
. Therefore along the horizon one can fit roughly 700 Moons, 30 000 Jupiters and 10 000 000 Plutos.
Jupiter compared to the Moon looks as follows:
Jupiter's apparent size is significantly smaller than the Moon's, and it cannot be distinguished from a point with the naked eye. However, in the night sky it is seen as a very bright dot, which is viewable even in very light polluted skies. But Pluto is much smaller than Jupiter, and it also more distant from us. So, from our vantage point, Pluto looks tiny even compared with Jupiter's Giant Red Spot:
Pluto's small size is not the only problem. Because it orbits the Sun at a much greater distance than the Moon and Jupiter, its surface brightness (due to reflected sunlight) is lower. In fact, the Moon's surface brightness is 5 to 6 times larger than Jupiter's, and around 260 larger than Pluto's. If we were to magnify Pluto and Jupiter such that they would have the same size in the sky as the Moon, they would look like this:
Actually, this is not quite true: In this picture Pluto was brightened by a factor of 500%, otherwise we would see only blackness.
So it is extremely small and dark.
As a consequence, Pluto is very faint in the night sky. Astronomers use magnitudes to discuss an object's brightness. The magnitude scale is logarithmic: an object with magnitude $x$ is $\sqrt[5]{100}\approx2.5$ times brighter than a magnitude $x+1$ object. For example, seen from Earth, a star with an apparent magnitude 2 is 2.5 times brighter than one with magnitude 3 and approximately $2.5\times2.5\approx6.3$ times brighter than a magnitude 4 star.
Sirius, the brightest star in the sky after the Sun, has an apparent magnitude of -1.46. Some planets such as Venus (-4.2) and Jupiter (-2.94 to -1.66) are even brighter. The full Moon can reach magnitude -12.9 and the Sun has a relatively constant magnitude of around -26.7 (sunlight is therefore around $2.5^{14}\approx400000$ times more intense than moonlight).
It is often said that the faintest objects viewable with the naked eye under very dark skies have magnitudes close to 6. That means that under excellent conditions it is possible to see stars and planets from magnitude -4.2 to 6 (a range of around 10 magnitudes).
Pluto's brightness changes over decades because its distance from us varies significantly. In 2019, its magnitude was about 14.3
, which is well beyond what can be seen with the naked eye.
How many photons coming from Pluto hit our eyes? We receive on Earth around 1360 Joules of solar energy per second and per square meter of area. Using Plank's radiation distribution law for a black body with temperature T=5800 K, we find that the Sun's photon's have an average energy of $\sim3\times10^{-19}\textrm{J}$, so we receive from the Sun roughly $4\times 10^{21}$ photons per second and per square meter of surface area perpendicular to the Sun's rays.
Let us assume that the spectrum of Pluto is the same as the Sun's. Since the Sun is around $2.5^{14.3-(-26.7)}\approx3\times10^{16}$ brighter than Pluto (as seen from Earth) and the pupil of a human eye is around 5mm wide, we conclude that only 3 or 4 seconds photons coming from Pluto hit each of our eyes every second.
Nevertheless, despite the extremely low photon count, we must not forget that (a) we can use lenses with more than 5mm of aperture and (b) we can collect light over a long time period.
In August 2019, shortly after sunset one could see both Saturn (left) and Jupiter (right) over Prague:
Interestingly, both are very close to the galactic center. In fact, the Milky Way and it's central black hole are in the following positions:
The lines indicating the Milky Way's disk are very rough and, while the central black hole's position is accurate, its size here was increased by a factor of about $10^8$. The black hole's shadow is only ~50 micro arc-seconds wide (this is the so-called photon capture diameter) while the black hole itself (i.e. the event horizon) is even smaller by a factor of $\sqrt{27}/2\approx 2.6$. It is worth pointing that we do not have yet an image of this object; the picture above shows a simulation by the Event Horizon Telescope collaboration of what it might look like.
In any case, unlike Clyde Tombaugh in 1930, we now know where to find Pluto: In the photo above (August 2019) it is close to Saturn (6° to the left). This means that (a) it is close to the galactic disk, so it can be confused with many stars and (b) seen from Prague it was very close to the horizon after sunset, so clouds and light pollution were particularly problematic.
A small telescope with a 61mm aperture was used (William Optics Zenithstar 61 APO) together with a Nikon camera with a cropped sensor. The following is a 30 second exposure photo, with an ISO 400 setting (the full resolution image is viewable by clicking the picture):
Light pollution shows up as a fairly homogeneous brownish color across the whole image. This by itself is not a problem, as it can be removed with software:
We can also increase the brightness of the image in order to see faint objects, and it is here that the problem with light pollution appears: it increases the noise of the image, making it impossible to distinguish real objects in the sky (such as Pluto) from noise. Take a look at the above picture with the brightness increased by a factor of 50:
It is worth noting that the brightest star in the image (center-right) has a magnitude of around 5.6, so none of the stars in this patch of the sky are visible to the naked eye (except perhaps in an very dark location).
More importantly, the faintest stars which can be discerned (barely) from noise have a magnitude of around 13. This is not enough to see Pluto (magnitude 14.3). We must increase the signal (Pluto's light) to noise ratio. One way to do so is to collect more light.
That can be achieved by taking more photos, and afterwards aligning and stacking them all with software. Much can be said about the noise in photos; for the task at hand, it suffices to say that as we capture more light, both the signal (Pluto's light) and the background light pollution will grow linearly with the total exposure time $t$, but crucially the noise with only grow as $\sqrt t$ so the signal to noise ratio will grow as $t/\sqrt t=\sqrt t$.
On the night of the 23th to the 24th of July, I took 51 photos similar to the one above, hence it is expected that the signal to noise level will increase roughly by a factor $\sqrt{51}\approx7$ when compared to a single photo. This implies that objects up to 2 magnitudes fainter should be visible (the limiting magnitude will then be ~13+2=15).
That seems to be the case. After aligning and stacking the photos, the background light pollution was subtracted and the overall brightness of the resulting image was increased. The result is this:
The full resolution picture is viewable by click this image. Pluto appears as a small dot here:
Pluto was found in this image with the help of a sky chart. However, it would be nice to empirically establish that the dot marked above is not a star. To test the idea, 120 photos of the same patch of the sky were taken one day later. Due mostly to Earth's orbital motion around the Sun, Pluto's position in the night sky should change a little bit in 24 hours. And indeed, that is what happened, proving that the dot of light shown above is not a star. The Earth moves $2.6$ million kilometers every day: if this displacement was perpendicular to the axis Earth-Pluto, then Pluto's position would shift up to a maximum of 1.8 arc-minutes. In reality, for the time of the year when the photos were taken, the change in Plutos's position was about 1.4 arc-minutes:
Renato Fonseca
renatofonseca@gmail.com
or
renatofonseca@ugr.es
19 December 2024