<p><strong>tl;dr:</strong> There's about a 1.4 mag oscillation due to <span class="math-container">$1/r^2$</span> effects and only a very tiny residual due to illumination angle.</p>
<hr />
<p>I went to JPL's <a href="https://ssd.jpl.nasa.gov/horizons/app.html#/" rel="noreferrer">Horizons</a> and extracted the distances between Jupiter and the Sun and the Earth, as well as various angles, illumination fraction, and the apparent magnitude of Jupiter as seen from the Sun.</p>
<p>It's pretty clear that the primary variation in brightness is due to <span class="math-container">$1/r^2$</span> and there's only a tiny effect related to illumination changes. While illumination fraction is only part of that effect, it's notable that it never drops below 99%.</p>
<p>In the first plot I show calculated apparent magnitude from Horizons' detailed modeling, and a simple expression based on only</p>
<p><span class="math-container">$$-2.5 \log_{10}\left(\frac{1}{r_{Sun-Jupiter}^2 \ r_{Earth-Jupiter}^2}\right) + C.$$</span></p>
<p>The value of <span class="math-container">$C$</span> is chosen to make the maximum equal to the Horizons maximum, and we see that the minima line up as well.</p>
<p>Of course at max and min the illumination fraction is 100% and the Sun-Jupiter-Earth angle is essentially zero.</p>
<p>The slight deviations at the half-way points are when this angle is maximum and the illumination fraction minimum (but still 99%).</p>
<p><a href="https://i.sstatic.net/l0gtz.png" rel="noreferrer"><img src="https://i.sstatic.net/l0gtz.png" alt="JPL Horizons Jupiter apparent magnitude from Earth vs simple model" /></a></p>
<p><a href="https://i.sstatic.net/HBUzC.png" rel="noreferrer"><img src="https://i.sstatic.net/HBUzC.png" alt="JPL Horizons Jupiter apparent magnitude from Earth and other things" /></a></p>

CC BY-SA 4.0
2023-12-30T23:30:04.977Z
Can I read from the last graph that "apparent magnitude" and "surface brightness" *increase* when the "distance to Sun" (and "distance to Earth") increases (I'd expect the opposite to be true), or is it just accidental?
U. Windl
CC BY-SA 4.0
2023-12-30T23:33:59.050Z
@U.Windl magnitudes are calculated using a negative sign in front of the logarithm (as shown in my expression). When the [apparent magnitude](https://en.wikipedia.org/wiki/Apparent_magnitude), and the surface brightness (apparent magnitude per arcsecond squared) values increase, it means they get dimmer, not brighter.
uhoh
CC BY-SA 4.0
2023-12-31T00:35:56.403Z
Thanks for explaining, and please forgive my lack of knowledge. I should have [looked it up](https://en.wikipedia.org/wiki/Apparent_magnitude).
U. Windl
CC BY-SA 4.0
2023-12-31T17:23:52.383Z
Here's a current Horizons plot of Jupiter's magnitude spanning 27 months https://i.sstatic.net/gwbfM.png created using my script at https://astronomy.stackexchange.com/a/53620/16685
PM 2Ring
CC BY-SA 4.0
2023-12-31T22:23:33.580Z
@U.Windl The way magnitudes are calculated is always confusing at first. Another place you find negative logarithm is in chemistry, pH 1 is very acidic (lots of H⁺ ions) and pH 9 is very basic (lots of OH⁻ but very little H⁺).
uhoh
CC BY-SA 4.0
2024-01-01T19:58:03.483Z
I think you mean pH 14 is very basic (drain cleaner).  pH =9 is slightly basic (baking soda)
James K
CC BY-SA 4.0
2024-01-01T22:48:28.847Z
@JamesK ya that's what I meant, thanks! I blame those gaffs on cosmic rays.
uhoh
CC BY-SA 4.0
2024-01-02T04:05:07.310Z
@JamesK update: and it seems that even 0-14 are not the limits, cf. https://chemistry.stackexchange.com/a/5738/16035 and https://chemistry.stackexchange.com/a/149638/16035
uhoh
CC BY-SA 4.0
2024-01-02T08:08:41.567Z
Yes, this was one of the great revelations in A-level chemistry.
James K
CC BY-SA 4.0
2023-12-30T23:13:22.600Z
2023-12-30T23:13:22.600Z
uhoh
<p>Jupiter appears particularly bright because it is close to Earth at the moment, it is also high in the sky (in the Northern Hemisphere). However its brightness doesn't vary that much.</p>
<p>Jupiter reached opposition in November (when it was directly opposite the sun) and the Earth has now (two months later) moved so that the angle between the sun and Jupiter is 116 degrees (value from Wolfram Alpha).  From our perspective (near to the sun) Jupiter is always close to 100% phase angle, we don't notice &quot;phases&quot; of Jupiter in the way that we notice them on the moon or Venus.</p>
<p>Jupiter is always very bright. At its brightest, it is nearly Magnitude -3, which is much brighter than any star. Moreover, when Jupiter's opposition occurs during the winter, it will be very high in the sky at midnight, and so appears impressively bright.  Jupiter is always brighter than magnitude -1.5, and so always a bright object, but when it is close to the sun or close to the horizon it can appear less impressive.</p>

CC BY-SA 4.0
2023-12-31T14:58:22.360Z
uhoh's answer seems to say that Jupiter appears (much) brighter when it is close to the Sun, in fact that this is the dominating factor. You seem to contradict that. Can you resolve the contradiction?
Peter - Reinstate Monica
CC BY-SA 4.0
2023-12-31T15:10:53.043Z
@Peter-ReinstateMonica There's no contradiction. uhoh's answer says only that the brightness change is caused by "1/r^2 effects", but if you look at their graphs, you can see that the change in Jupiter-to-Earth distance is much larger than the change in Sun-to-Jupiter distance. So Jupiter's position in its orbit doesn't make that much difference to its brightness.
David
CC BY-SA 4.0
2023-12-31T15:17:18.230Z
Uhoh's answer is correct and detailed,  the variation is mostly due to the Earth Jupiter distance, and secondarily due to Jupiter sun distance and phase. Jupiter is brighter than average because the Earth is close to Jupiter. It appears especially bright in Germany because it is high in the sky.  It also happens to be quite close to the sun, and be at nearly 100% phase.
James K
CC BY-SA 4.0
2023-12-31T15:50:21.840Z
The answer briefly mentions winter, which might well be a big factor. A clear Northern Hemisphere winter night is a lot clearer than is a clear Northern Hemisphere summer night due to reduced absolute humidity. Another factor is the length of night. In Munich, it is quite possible in winter to go to work when it's still dark outside and to get home from work when it's once again nighttime. Yet another factor is light pollution from the stars themselves. The winter NH night sky faces a lightly populated region of the galaxy while the NH summer night sky faces a more densely populated region.
David Hammen
CC BY-SA 4.0
2024-01-01T16:59:35.770Z
@DavidHammen: Exactly. Also, the last 2 months have been really cloudy in southern Germany. We're not used to seeing the sun anymore, and there were very few clear nights. I was surprised how bright Jupiter was too, even though I often look at it.
Eric Duminil
CC BY-SA 4.0
2024-01-01T19:51:48.570Z
As @EricDuminil pointed out the sky was not that clear that day, and I might add that the time of observation was rather exactly on hour before "Astronomical Dawn" (still "Blue Hour").
U. Windl
CC BY-SA 4.0
2024-01-02T11:50:26.720Z
@U.Windl An hour before astronomical dawn? Are you sure you weren't looking at Venus rather than Jupiter?
David Hammen
CC BY-SA 4.0
2024-01-02T12:12:07.260Z
There is an inconsistency with "an hour before Astronomical dawn" and "Walking in the evening" (from the original question)  Venus is an impressively bright object in the early morning, low in the Eastern sky before dawn. But the photographs do appear to show Jupiter, as the stars of alpha and beta Aries are dimly visible, with beta Andromeda higher in the sky, and perhaps alpha cetus below. @U.Windl
James K
CC BY-SA 4.0
2024-01-03T09:06:13.230Z
@JamesK Actually I meant "dusk", not "dawn" (a typical "false friend": In German there is one word (Dämmerung) for both, and I thought it's similar in English, but there you have two different words. For clarity one can be specific in German "Morgendämmerung" (dawn) or "Abenddämmerung" (dusk)). Sorry for the confusion.
U. Windl
CC BY-SA 4.0
2023-12-30T22:27:06.570Z
2023-12-31T20:13:12.567Z
2023-12-31T20:13:12.567Z
James K
<p>When I was walking in the evening (2023-12-30) in the south of Germany (roughly 49°N 12°E) I noticed a single bright object in the sky, and (not being an astronomer) I wondered what it might be.
So I started Stellarium to point at the location to find out that it's Jupiter (you'll see the photo and the screenshot below).</p>
<p><a href="https://i.sstatic.net/qY2hDl.jpg" rel="noreferrer"><img src="https://i.sstatic.net/qY2hDl.jpg" alt="Part of the sky shot with my smartphone without tripod" /></a>
<a href="https://i.sstatic.net/ixiQOl.jpg" rel="noreferrer"><img src="https://i.sstatic.net/ixiQOl.jpg" alt="Screenshot of Stellarium showing the same part of the sky, including details of Jupiter" /></a></p>
<p>What made me wonder is the &quot;phase 0.99&quot;: Does it mean sun, earth and Jupiter are mostly in one line, so Jupiter will reflect as much light as possible back to the earth?</p>
<p>Wikipedia says Jupiter is about four times as far from sun than earth is, and it has about 11 times the size.
I wonder: What would be the brightest star in comparison, and how bright would it be (as a proportion)?</p>
<p>For reference, here's my attempt to &quot;gain up&quot; the photo:</p>
<p><a href="https://i.sstatic.net/oJ3srl.jpg" rel="noreferrer"><img src="https://i.sstatic.net/oJ3srl.jpg" alt="Part of the sky shot with my smartphone without tripod, &quot;gain up&quot; version" /></a></p>

CC BY-SA 4.0
2023-12-30T21:57:53.180Z
Guten Abend! Yes, Jupiter is almost in straight line with the Earth and the Sun—the “perfect“ line was on November 3, 2023; it’s also called the “opposition.” Jupiter is brightest around opposition, but it’s generally a very bright “star” in the sky, so you probably just didn’t notice it before.
Pierre Paquette
CC BY-SA 4.0
2023-12-31T13:04:03.150Z
Minor not, regarding *roughly 45°N 12°E* -- that's central Italy, not southern Germany. Did you perhaps mean "roughly 48°N 12°E"? That is fairly close to Munich.
David Hammen
CC BY-SA 4.0
2024-01-01T19:45:01.373Z
That happens if you *think* you remember the numbers correctly; actually it should have been 49°N, sorry.
U. Windl
CC BY-SA 4.0
2024-01-02T01:06:09.893Z
@PierrePaquette does this mean (in layman's terms) it was "full Jupiter"? - i.e. sun lit up most/all of Jupiter as it's viewed from earth? If I understood correctly, you should make it an answer as that's probably the simplest explanation?
stevec
CC BY-SA 4.0
2024-01-02T02:13:27.300Z
@stevec The moon has strong phases (as seen from Earth) because Earth is sometimes looking at the night side (the one that faces away from the Sun, towards the outer solar system), and sometimes looking at the bright side (the Sun-facing one). This changes rapidly due to the Moon's orbit around Earth. But no matter where Earth is in its orbit relative to the "Jupiter side" of the solar system we're always looking fairly close to directly at its bright side; it's always close to "full Jupiter". We'd have to get out near or beyond Jupiter's orbit to see much of its night side.
Ben
CC BY-SA 4.0
2024-11-20T06:51:20.957Z
19, Nov. 2024-
Durango Co. Elevation 6,500 MSL. Clear skies. Light pollution minimum. I have been checking out Jupiter lately. The night sky is filled with the light from this planet! Here is the data. Magnitude
-2.63
Distance
4.13 AU
Radius
69911 Km
Ra/Dec
05h 10m32.3s +22°14'54.0"
Az/Alt
120°14'10.8" +64°54'09.9"
Phase
100%
Visibility
Rise: 18:09 Set: 08:38
AeroPuter
<jupiter><brightness>
Why was Jupiter so bright; is it the "phase"?
U. Windl
# Why was Jupiter so bright; is it the "phase"?

(Asked by: username_0 on 2023-12-30)

When I was walking in the evening (2023-12-30) in the south of Germany (roughly 49°N 12°E) I noticed a single bright object in the sky, and (not being an astronomer) I wondered what it might be.
So I started Stellarium to point at the location to find out that it's Jupiter (you'll see the photo and the screenshot below).

[![Part of the sky shot with my smartphone without tripod](https://i.sstatic.net/qY2hDl.jpg)](https://i.sstatic.net/qY2hDl.jpg)
[![Screenshot of Stellarium showing the same part of the sky, including details of Jupiter](https://i.sstatic.net/ixiQOl.jpg)](https://i.sstatic.net/ixiQOl.jpg)

What made me wonder is the "phase 0.99": Does it mean sun, earth and Jupiter are mostly in one line, so Jupiter will reflect as much light as possible back to the earth?

Wikipedia says Jupiter is about four times as far from sun than earth is, and it has about 11 times the size.
I wonder: What would be the brightest star in comparison, and how bright would it be (as a proportion)?

For reference, here's my attempt to "gain up" the photo:

[![Part of the sky shot with my smartphone without tripod, ](https://i.sstatic.net/oJ3srl.jpg)](https://i.sstatic.net/oJ3srl.jpg)

**Tags:** jupiter, brightness
> **Comments:**
> **username_1**: Guten Abend! Yes, Jupiter is almost in straight line with the Earth and the Sun—the “perfect“ line was on November 3, 2023; it’s also called the “opposition.” Jupiter is brightest around opposition, but it’s generally a very bright “star” in the sky, so you probably just didn’t notice it before.  
> **username_2**: Minor not, regarding *roughly 45°N 12°E* -- that's central Italy, not southern Germany. Did you perhaps mean "roughly 48°N 12°E"? That is fairly close to Munich.  
> **username_0**: That happens if you *think* you remember the numbers correctly; actually it should have been 49°N, sorry.  
> **username_3**: @PierrePaquette does this mean (in layman's terms) it was "full Jupiter"? - i.e. sun lit up most/all of Jupiter as it's viewed from earth? If I understood correctly, you should make it an answer as that's probably the simplest explanation?  
> **username_4**: @stevec The moon has strong phases (as seen from Earth) because Earth is sometimes looking at the night side (the one that faces away from the Sun, towards the outer solar system), and sometimes looking at the bright side (the Sun-facing one). This changes rapidly due to the Moon's orbit around Earth. But no matter where Earth is in its orbit relative to the "Jupiter side" of the solar system we're always looking fairly close to directly at its bright side; it's always close to "full Jupiter". We'd have to get out near or beyond Jupiter's orbit to see much of its night side.  
> **username_5**: 19, Nov. 2024- Durango Co. Elevation 6,500 MSL. Clear skies. Light pollution minimum. I have been checking out Jupiter lately. The night sky is filled with the light from this planet! Here is the data. Magnitude -2.63 Distance 4.13 AU Radius 69911 Km Ra/Dec 05h 10m32.3s +22°14'54.0" Az/Alt 120°14'10.8" +64°54'09.9" Phase 100% Visibility Rise: 18:09 Set: 08:38  

---

## 2 answers

### Answer by username_8 on 2023-12-30. Score: 18 | Accepted answer

Jupiter appears particularly bright because it is close to Earth at the moment, it is also high in the sky (in the Northern Hemisphere). However its brightness doesn't vary that much.

Jupiter reached opposition in November (when it was directly opposite the sun) and the Earth has now (two months later) moved so that the angle between the sun and Jupiter is 116 degrees (value from Wolfram Alpha). From our perspective (near to the sun) Jupiter is always close to 100% phase angle, we don't notice "phases" of Jupiter in the way that we notice them on the moon or Venus.

Jupiter is always very bright. At its brightest, it is nearly Magnitude -3, which is much brighter than any star. Moreover, when Jupiter's opposition occurs during the winter, it will be very high in the sky at midnight, and so appears impressively bright. Jupiter is always brighter than magnitude -1.5, and so always a bright object, but when it is close to the sun or close to the horizon it can appear less impressive.

> **Comments:**
> **username_9**: uhoh's answer seems to say that Jupiter appears (much) brighter when it is close to the Sun, in fact that this is the dominating factor. You seem to contradict that. Can you resolve the contradiction?  
> **username_10**: @Peter-ReinstateMonica There's no contradiction. uhoh's answer says only that the brightness change is caused by "1/r^2 effects", but if you look at their graphs, you can see that the change in Jupiter-to-Earth distance is much larger than the change in Sun-to-Jupiter distance. So Jupiter's position in its orbit doesn't make that much difference to its brightness.  
> **username_8**: Uhoh's answer is correct and detailed,  the variation is mostly due to the Earth Jupiter distance, and secondarily due to Jupiter sun distance and phase. Jupiter is brighter than average because the Earth is close to Jupiter. It appears especially bright in Germany because it is high in the sky.  It also happens to be quite close to the sun, and be at nearly 100% phase.  
> **username_2**: The answer briefly mentions winter, which might well be a big factor. A clear Northern Hemisphere winter night is a lot clearer than is a clear Northern Hemisphere summer night due to reduced absolute humidity. Another factor is the length of night. In Munich, it is quite possible in winter to go to work when it's still dark outside and to get home from work when it's once again nighttime. Yet another factor is light pollution from the stars themselves. The winter NH night sky faces a lightly populated region of the galaxy while the NH summer night sky faces a more densely populated region.  
> **username_11**: @DavidHammen: Exactly. Also, the last 2 months have been really cloudy in southern Germany. We're not used to seeing the sun anymore, and there were very few clear nights. I was surprised how bright Jupiter was too, even though I often look at it.  
> **username_0**: As @EricDuminil pointed out the sky was not that clear that day, and I might add that the time of observation was rather exactly on hour before "Astronomical Dawn" (still "Blue Hour").  
> **username_2**: @U.Windl An hour before astronomical dawn? Are you sure you weren't looking at Venus rather than Jupiter?  
> **username_8**: There is an inconsistency with "an hour before Astronomical dawn" and "Walking in the evening" (from the original question)  Venus is an impressively bright object in the early morning, low in the Eastern sky before dawn. But the photographs do appear to show Jupiter, as the stars of alpha and beta Aries are dimly visible, with beta Andromeda higher in the sky, and perhaps alpha cetus below. @U.Windl  
> **username_0**: @JamesK Actually I meant "dusk", not "dawn" (a typical "false friend": In German there is one word (Dämmerung) for both, and I thought it's similar in English, but there you have two different words. For clarity one can be specific in German "Morgendämmerung" (dawn) or "Abenddämmerung" (dusk)). Sorry for the confusion.  

---

### Answer by username_6 on 2023-12-30. Score: 23

**tl;dr:** There's about a 1.4 mag oscillation due to $1/r^2$ effects and only a very tiny residual due to illumination angle.

---

I went to JPL's [Horizons](https://ssd.jpl.nasa.gov/horizons/app.html#/) and extracted the distances between Jupiter and the Sun and the Earth, as well as various angles, illumination fraction, and the apparent magnitude of Jupiter as seen from the Sun.

It's pretty clear that the primary variation in brightness is due to $1/r^2$ and there's only a tiny effect related to illumination changes. While illumination fraction is only part of that effect, it's notable that it never drops below 99%.

In the first plot I show calculated apparent magnitude from Horizons' detailed modeling, and a simple expression based on only

$$-2.5 \log\_{10}\left(\frac{1}{r\_{Sun-Jupiter}^2 \ r\_{Earth-Jupiter}^2}\right) + C.$$

The value of $C$ is chosen to make the maximum equal to the Horizons maximum, and we see that the minima line up as well.

Of course at max and min the illumination fraction is 100% and the Sun-Jupiter-Earth angle is essentially zero.

The slight deviations at the half-way points are when this angle is maximum and the illumination fraction minimum (but still 99%).

[![JPL Horizons Jupiter apparent magnitude from Earth vs simple model](https://i.sstatic.net/l0gtz.png)](https://i.sstatic.net/l0gtz.png)

[![JPL Horizons Jupiter apparent magnitude from Earth and other things](https://i.sstatic.net/HBUzC.png)](https://i.sstatic.net/HBUzC.png)

> **Comments:**
> **username_0**: Can I read from the last graph that "apparent magnitude" and "surface brightness" *increase* when the "distance to Sun" (and "distance to Earth") increases (I'd expect the opposite to be true), or is it just accidental?  
> **username_6**: @U.Windl magnitudes are calculated using a negative sign in front of the logarithm (as shown in my expression). When the [apparent magnitude](https://en.wikipedia.org/wiki/Apparent_magnitude), and the surface brightness (apparent magnitude per arcsecond squared) values increase, it means they get dimmer, not brighter.  
> **username_0**: Thanks for explaining, and please forgive my lack of knowledge. I should have [looked it up](https://en.wikipedia.org/wiki/Apparent_magnitude).  
> **username_7**: Here's a current Horizons plot of Jupiter's magnitude spanning 27 months https://i.sstatic.net/gwbfM.png created using my script at https://astronomy.stackexchange.com/a/53620/16685  
> **username_6**: @U.Windl The way magnitudes are calculated is always confusing at first. Another place you find negative logarithm is in chemistry, pH 1 is very acidic (lots of H⁺ ions) and pH 9 is very basic (lots of OH⁻ but very little H⁺).  
> **username_8**: I think you mean pH 14 is very basic (drain cleaner).  pH =9 is slightly basic (baking soda)  
> **username_6**: @JamesK ya that's what I meant, thanks! I blame those gaffs on cosmic rays.  
> **username_6**: @JamesK update: and it seems that even 0-14 are not the limits, cf. https://chemistry.stackexchange.com/a/5738/16035 and https://chemistry.stackexchange.com/a/149638/16035  
> **username_8**: Yes, this was one of the great revelations in A-level chemistry.  

---

