<p>There will hopefully be better answers based on equations for apparent magnitude which use albedo and phase angle (albedo is problematic for spacecraft because they can have big flat shiny surfaces that make them flare at certain times (<a href="https://space.stackexchange.com/questions/tagged/satellite-flare">1</a>, <a href="https://en.wikipedia.org/wiki/Satellite_flare" rel="nofollow noreferrer">2</a>)).</p>
<p>I think that the easiest, quickest way is to pick a satellite that's similar to yours, and look up on one of the websites that predict passes for a given location and get the distance and predicted magnitude for a few passes. Add to  them <span class="math-container">$2.5 \log_{10}(r/r_{pass})$</span> where <span class="math-container">$r_{pass}$</span> is the distance given in the prediction and <span class="math-container">$r$</span> is your distance.</p>
<p>If they don't give a distance, then choose an overhead pass, use the maximum brightness and use the orbital altitude. For example, if the Hubble Space Telescope passes overhead (say above 70 degrees) and will reach +1 magnitude, we know that the distance is roughly 540 kilometers.</p>
<p>If you want to observe it at 10 kilometers, add <span class="math-container">$2.5 \log_{10}(10/540) = -4.4$</span> to get a magnitude of -3.4.</p>
<p>There is some more information at <a href="https://astronomy.stackexchange.com/q/28744/7982">Calculating the apparent magnitude of a satellite</a> <strong>However I do not see it as a duplicate</strong> because you'd like something quick and easy to use to estimate, and there's a lot of information there, including <em>phase angle</em>, but it may not be very accessible.</p>

CC BY-SA 4.0
2024-08-12T07:48:51.653Z
Thank you for the answer, but unfortunately it is not exactly what I'm looking for. TBH I'm not looking for one specific satellite but for rough estimation to be able to calculate a lot of different satellites. But thanks for the contribution, it might be very usefull later.
jlipinski
CC BY-SA 4.0
2024-08-12T09:31:49.060Z
@jlipinski Yep, like I said in the first sentence: "There will hopefully be better answers based on equations for apparent magnitude which use albedo and phase angle..." Even then, you'll either have to approximate your satellite as a diffuse sphere with an average albedo, or do detailed modeling for all the reflective surfaces.
uhoh
CC BY-SA 4.0
2024-08-10T01:53:02.837Z
2024-08-10T01:53:02.837Z
uhoh
<p>I'm looking for a way to estimate an object's brightness as seen by an observer in space. I expect the estimation to depend on factors such as the distance to the Sun, the Sun-satellite-observer angle, the satellite's albedo (or reflectivity index, or something similar), the distance between the satellite and the observer, and the area of the satellite that reflects light.</p>
<p>Is there an easy way to estimate this (preferably in magnitude)? I've seen some papers that seem to address this problem, but all the integrals made my head hurt. I don't need such a complicated solution—just an estimation.</p>

<observational-astronomy><artificial-satellite><brightness>
How to estimate artificial satellite brightness as seen from another satellite?
jlipinski
# How to estimate artificial satellite brightness as seen from another satellite?

(Asked by: username_0 on 2024-08-09)

I'm looking for a way to estimate an object's brightness as seen by an observer in space. I expect the estimation to depend on factors such as the distance to the Sun, the Sun-satellite-observer angle, the satellite's albedo (or reflectivity index, or something similar), the distance between the satellite and the observer, and the area of the satellite that reflects light.

Is there an easy way to estimate this (preferably in magnitude)? I've seen some papers that seem to address this problem, but all the integrals made my head hurt. I don't need such a complicated solution—just an estimation.

**Tags:** observational-astronomy, artificial-satellite, brightness

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## 1 answers

### Answer by username_1 on 2024-08-10. Score: 2

There will hopefully be better answers based on equations for apparent magnitude which use albedo and phase angle (albedo is problematic for spacecraft because they can have big flat shiny surfaces that make them flare at certain times ([1](https://space.stackexchange.com/questions/tagged/satellite-flare), [2](https://en.wikipedia.org/wiki/Satellite_flare))).

I think that the easiest, quickest way is to pick a satellite that's similar to yours, and look up on one of the websites that predict passes for a given location and get the distance and predicted magnitude for a few passes. Add to them $2.5 \log\_{10}(r/r\_{pass})$ where $r\_{pass}$ is the distance given in the prediction and $r$ is your distance.

If they don't give a distance, then choose an overhead pass, use the maximum brightness and use the orbital altitude. For example, if the Hubble Space Telescope passes overhead (say above 70 degrees) and will reach +1 magnitude, we know that the distance is roughly 540 kilometers.

If you want to observe it at 10 kilometers, add $2.5 \log\_{10}(10/540) = -4.4$ to get a magnitude of -3.4.

There is some more information at [Calculating the apparent magnitude of a satellite](https://astronomy.stackexchange.com/q/28744/7982) **However I do not see it as a duplicate** because you'd like something quick and easy to use to estimate, and there's a lot of information there, including *phase angle*, but it may not be very accessible.

> **Comments:**
> **username_0**: Thank you for the answer, but unfortunately it is not exactly what I'm looking for. TBH I'm not looking for one specific satellite but for rough estimation to be able to calculate a lot of different satellites. But thanks for the contribution, it might be very usefull later.  
> **username_1**: @jlipinski Yep, like I said in the first sentence: "There will hopefully be better answers based on equations for apparent magnitude which use albedo and phase angle..." Even then, you'll either have to approximate your satellite as a diffuse sphere with an average albedo, or do detailed modeling for all the reflective surfaces.  

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