<p>To follow up on <a href="https://astronomy.stackexchange.com/a/57867/7982">@JamesK's excellent answer and observations</a> we can calculate the period of <em>apparent</em> oscillations due to the <a href="https://en.wikipedia.org/wiki/Aliasing" rel="noreferrer">aliasing</a> that arises from sampling at a frequency close to or below the actual oscillations.</p>
<p>If we assert that a &quot;day&quot; in this context is the recognized 24 hours or 86400 seconds, and that Mars' rotational period is 1.025957176 days, then if we observed Mars from a fixed distant point in space, <strong>the number of oscillations per year</strong> due to oscillations of the effective albedo of the side presented would be given by</p>
<p><span class="math-container">$$\text{ 365.25 × (1 - 1/1.025957176) = 9.24}$$</span></p>
<p>You can think of this as the difference in frequencies, cf. <a href="https://en.wikipedia.org/wiki/Moir%C3%A9_pattern" rel="noreferrer">moiré pattern</a> and <a href="https://en.wikipedia.org/wiki/Heterodyne" rel="noreferrer">heterodyne</a>.</p>
<p>But we're observing from Earth, not from infinity.</p>
<p>Since from Mars' perspective the Earth oscillates left and right with respect to the Sun, we can ignore that phase modulation and consider the frequency presented to Earth's average position - the Sun.</p>
<p>That means we need to use the average solar day of Mars instead.</p>
<p><span class="math-container">$$\text{ 365.25 × (1 - 1/1.02748843) = 9.77}$$</span></p>
<p>That's a good match to the apparent ~10 cycles per year in the plot.</p>

CC BY-SA 4.0
2024-06-10T05:44:32.833Z
Why doesn’t the same happen for say, ceres
Harrychink
CC BY-SA 4.0
2024-06-10T05:54:59.217Z
@Harrychink That's a good question! I think that "Why does Mars have such a large variation in albedo compared to other spherical solar system bodies, besides of course Earth?" could be a stand-alone question. I'll bet that the answer has to do with it being the only other rocky planet that's had an ocean, but that's just a guess. Of course you have to rule out asteroids that are non-spherical, and unusual moons like Ganymede and Enceladus which have nonuniform albedos for other reasons, and our Moon - unless of course you observe it from Mars.
uhoh
CC BY-SA 4.0
2024-06-10T20:11:49.270Z
Of the spherical bodies in the solar system, with a visible surface, having regions of different albedo is fairly common.  Earth. Mars, Moon, Pluto,  Ganemede, Io ...  Mercury, Calisto, Europa don't.... but since its pretty common both ways, I'm not sure a special explanation is needed except  "that's how it is". Geology tends to create regions, and Mars has been geologically active fairly recently.
James K
CC BY-SA 4.0
2024-06-10T04:31:46.623Z
2024-06-10T04:31:46.623Z
uhoh
<p>My first guess was that this was &quot;something to do with the moon&quot; since there seems to be roughly a monthly periodicity.  But looking more closely suggests that my first guess was wrong. The &quot;jaggedness&quot; doesn't match the length of a month.</p>
<p>Looking more carefully, this appears to be a result of the different albedo of Mars on different sides, and the fact that Mars's rotation is quite close to 24 hours.</p>
<p>The graph is plotted once every two days (probably at a 00:00 UTC), And each 48 hours, Mars rotates a bit less than 720 degrees.  So, just like a strobe effect, it seems that Mars is rotating very slowly.  As it rotates, different parts of the surface are visible from Earth, and some parts are darker than others.</p>
<p>I tested this by getting Nasa Horizons to generate the data for Mars in July -Jan 2023. The &quot;jaggedness&quot; was visible. I noted that on 19 July, Mars was dim.  I then asked Horizons to generate the data just for that day, and noted that over the course of one day, Mars shows the full range of brightness variations that are seen over the month. I conclude that this is a result of Mars rotating at just less than once every 24 hours, and having different brightness on different parts of its surface.</p>

CC BY-SA 4.0
2024-06-10T10:02:56.427Z
What a wonderful example of "aliasing"!
kruemi
CC BY-SA 4.0
2024-06-10T11:22:17.327Z
Why does the same pattern appear on the predicted data.
Harrychink
CC BY-SA 4.0
2024-06-10T13:26:18.630Z
What predicted data are you referring to? But in any case, this seems like a very regular and explainable cycle, so I'd probably expect any competent prediction to take it into account.
Darth Pseudonym
CC BY-SA 4.0
2024-06-10T17:10:02.090Z
Because the predicted data uses the known variation in albedo of Mars to make its prediction.
James K
CC BY-SA 4.0
2024-08-11T07:08:53.437Z
@darth I meant why wouldn’t the predicted data have a more fine jaggedness corresponding to the actual rotational period of mars
Harrychink
CC BY-SA 4.0
2024-08-11T07:49:20.177Z
The predicted data are generated every two days, so the jaggedness can't be any quicker than that.  And due to the "aliasing" effect, it looks like slow changes.  In fact mars's brightness increases and decreases every 1.026 days.  You can't see that "fine jaggedness" in data points that are only calculated every two days.
James K
CC BY-SA 4.0
2024-06-09T16:36:18.140Z
2024-06-09T16:36:18.140Z
James K
<p>Caption:</p>
<blockquote>
<p>The following chart is the predicted light curve (visual magnitude as a function of time) of Mars, according to the most recent ephemeris data. Magnitude data is sampled with a 2 days interval and there might be inaccuracies for objects changing brightness very rapidly during the course of a few days. For comets there could be large discrepancies between the observed and predicted brightness because of their highly dynamic behaviour.</p>
</blockquote>
<p><a href="https://i.sstatic.net/82MOisIT.jpg" rel="noreferrer"><img src="https://i.sstatic.net/82MOisIT.jpg" alt="enter image description here" /></a></p>
<p>In addition to the large peak (from about +2 to -1 magnitude) around January 2025, I see a small wiggling behavior, about 10 oscillations per year, with an amplitude of about 0.1 magnitude.</p>
<p>Why is the light curve of Mars so jagged?</p>

CC BY-SA 4.0
2024-06-09T09:41:10.110Z
None of the other planets have such jagged light curves
Harrychink
CC BY-SA 4.0
2024-06-10T06:22:53.887Z
FWIW, I have a Horizons magnitude plotting script in this answer to a related question https://astronomy.stackexchange.com/a/53620/16685
PM 2Ring
<light><mars><light-curve>
Why does Mars have a jagged light curve?
Harrychink
# Why does Mars have a jagged light curve?

(Asked by: username_0 on 2024-06-09)

Caption:

> The following chart is the predicted light curve (visual magnitude as a function of time) of Mars, according to the most recent ephemeris data. Magnitude data is sampled with a 2 days interval and there might be inaccuracies for objects changing brightness very rapidly during the course of a few days. For comets there could be large discrepancies between the observed and predicted brightness because of their highly dynamic behaviour.

[![enter image description here](https://i.sstatic.net/82MOisIT.jpg)](https://i.sstatic.net/82MOisIT.jpg)

In addition to the large peak (from about +2 to -1 magnitude) around January 2025, I see a small wiggling behavior, about 10 oscillations per year, with an amplitude of about 0.1 magnitude.

Why is the light curve of Mars so jagged?

**Tags:** light, mars, light-curve
> **Comments:**
> **username_0**: None of the other planets have such jagged light curves  
> **username_1**: FWIW, I have a Horizons magnitude plotting script in this answer to a related question https://astronomy.stackexchange.com/a/53620/16685  

---

## 2 answers

### Answer by username_3 on 2024-06-09. Score: 41 | Accepted answer

My first guess was that this was "something to do with the moon" since there seems to be roughly a monthly periodicity. But looking more closely suggests that my first guess was wrong. The "jaggedness" doesn't match the length of a month.

Looking more carefully, this appears to be a result of the different albedo of Mars on different sides, and the fact that Mars's rotation is quite close to 24 hours.

The graph is plotted once every two days (probably at a 00:00 UTC), And each 48 hours, Mars rotates a bit less than 720 degrees. So, just like a strobe effect, it seems that Mars is rotating very slowly. As it rotates, different parts of the surface are visible from Earth, and some parts are darker than others.

I tested this by getting Nasa Horizons to generate the data for Mars in July -Jan 2023. The "jaggedness" was visible. I noted that on 19 July, Mars was dim. I then asked Horizons to generate the data just for that day, and noted that over the course of one day, Mars shows the full range of brightness variations that are seen over the month. I conclude that this is a result of Mars rotating at just less than once every 24 hours, and having different brightness on different parts of its surface.

> **Comments:**
> **username_4**: What a wonderful example of "aliasing"!  
> **username_0**: Why does the same pattern appear on the predicted data.  
> **username_5**: What predicted data are you referring to? But in any case, this seems like a very regular and explainable cycle, so I'd probably expect any competent prediction to take it into account.  
> **username_3**: Because the predicted data uses the known variation in albedo of Mars to make its prediction.  
> **username_0**: @darth I meant why wouldn’t the predicted data have a more fine jaggedness corresponding to the actual rotational period of mars  
> **username_3**: The predicted data are generated every two days, so the jaggedness can't be any quicker than that.  And due to the "aliasing" effect, it looks like slow changes.  In fact mars's brightness increases and decreases every 1.026 days.  You can't see that "fine jaggedness" in data points that are only calculated every two days.  

---

### Answer by username_2 on 2024-06-10. Score: 17

To follow up on [@JamesK's excellent answer and observations](https://astronomy.stackexchange.com/a/57867/7982) we can calculate the period of *apparent* oscillations due to the [aliasing](https://en.wikipedia.org/wiki/Aliasing) that arises from sampling at a frequency close to or below the actual oscillations.

If we assert that a "day" in this context is the recognized 24 hours or 86400 seconds, and that Mars' rotational period is 1.025957176 days, then if we observed Mars from a fixed distant point in space, **the number of oscillations per year** due to oscillations of the effective albedo of the side presented would be given by

$$\text{ 365.25 × (1 - 1/1.025957176) = 9.24}$$

You can think of this as the difference in frequencies, cf. [moiré pattern](https://en.wikipedia.org/wiki/Moir%C3%A9_pattern) and [heterodyne](https://en.wikipedia.org/wiki/Heterodyne).

But we're observing from Earth, not from infinity.

Since from Mars' perspective the Earth oscillates left and right with respect to the Sun, we can ignore that phase modulation and consider the frequency presented to Earth's average position - the Sun.

That means we need to use the average solar day of Mars instead.

$$\text{ 365.25 × (1 - 1/1.02748843) = 9.77}$$

That's a good match to the apparent ~10 cycles per year in the plot.

> **Comments:**
> **username_0**: Why doesn’t the same happen for say, ceres  
> **username_2**: @Harrychink That's a good question! I think that "Why does Mars have such a large variation in albedo compared to other spherical solar system bodies, besides of course Earth?" could be a stand-alone question. I'll bet that the answer has to do with it being the only other rocky planet that's had an ocean, but that's just a guess. Of course you have to rule out asteroids that are non-spherical, and unusual moons like Ganymede and Enceladus which have nonuniform albedos for other reasons, and our Moon - unless of course you observe it from Mars.  
> **username_3**: Of the spherical bodies in the solar system, with a visible surface, having regions of different albedo is fairly common.  Earth. Mars, Moon, Pluto,  Ganemede, Io ...  Mercury, Calisto, Europa don't.... but since its pretty common both ways, I'm not sure a special explanation is needed except  "that's how it is". Geology tends to create regions, and Mars has been geologically active fairly recently.  

---

