<p>The <a href="https://en.wikipedia.org/wiki/Solar_gravitational_lens" rel="nofollow noreferrer">solar gravitational lens</a> was first proposed by Einstein in 1936. Although gravitational lensing gives excellent magnification and light amplification, there are various practical difficulties in utilising the Sun (or another star) as a gravitational lens.</p>
<p>The gravitational deflection of a light (or radio) ray just skimming the <a href="https://en.wikipedia.org/wiki/Solar_radius" rel="nofollow noreferrer">nominal solar radius</a> <span class="math-container">$R_\odot$</span> is ~<span class="math-container">$1.7512$</span> arcsecs. The deflection is approximately inversely proportional, so a ray passing the Sun at <span class="math-container">$2R_\odot$</span> gets deflected by ~<span class="math-container">$1.7512/2$</span> arcsecs. The nominal solar radius is defined to be the distance where the optical depth of the Sun's photosphere is <span class="math-container">$2/3$</span>, so for lensing purposes, we need to use a somewhat larger radius, at least <span class="math-container">$1.001 R_\odot$</span>. As the radius increases we get less interference from the solar atmosphere, but we also get less deflection.</p>
<p>The focal distance <span class="math-container">$d$</span> of a gravitational lens is given by
<span class="math-container">$$d = b / \tan(\theta)$$</span>
where <span class="math-container">$b$</span> is the <a href="https://en.wikipedia.org/wiki/Impact_parameter" rel="nofollow noreferrer">impact parameter</a> and <span class="math-container">$\theta$</span> is the deflection angle. (For small angles, <span class="math-container">$\tan(\theta) \approx \theta$</span>, in radians). The impact parameter is the minimal distance from the ray to the centre of the lensing body if there were no deflection; the deflection angle is the angle between that path and the actual path. (FWIW, I have some diagrams of strong photon deflection in the vicinity of a black hole <a href="https://physics.stackexchange.com/a/810981/123208">here</a>).</p>
<p>For a ray at <span class="math-container">$R_\odot$</span>, <span class="math-container">$\theta = 1.7512$</span> arcsecs and <span class="math-container">$d \approx 547.756$</span> au (<a href="https://en.wikipedia.org/wiki/Astronomical_unit" rel="nofollow noreferrer">astronomical units</a>). At <span class="math-container">$1.001 R_\odot$</span>, <span class="math-container">$\theta = 1.7494$</span> arcsecs and <span class="math-container">$d \approx 548.853$</span> au. A satellite with such a large orbital radius moves slowly. The period of a solar orbit of semi-major axis <span class="math-container">$547.756$</span> au is ~<span class="math-container">$12820$</span> (Julian) years, with <span class="math-container">$548.853$</span> we get ~<span class="math-container">$12858.6$</span> years. Our gravitational telescope can only focus on the region of the sky directly behind the Sun. To look in another direction it has to wait for its orbit to take it there (unless it has fuel to fly to a new location). Conversely, if our telescope is on a mission to study a particular exoplanet, it has a limited time window to gather data while the exoplanet is properly aligned with the Sun. After that, it has to wait for a new target to come into alignment.</p>
<p>It takes a while to get to <span class="math-container">$548$</span> au. Voyager 2 was launched almost 47 years ago, and its current distance from the Sun is only ~<span class="math-container">$137.3$</span> au. There's virtually no solar power available at <span class="math-container">$548$</span> au, so the satellite would need an <a href="https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_generator" rel="nofollow noreferrer">RTG</a> based on an isotope with a long half-life, or have a nuclear reactor.</p>
<hr />
<p>Sending a probe to the Sirius system is hard. Perhaps a tiny laser propelled probe could reach Sirius in a reasonable time frame, but such a probe will be travelling at a significant fraction of light speed, and it's not clear how to slow it down when it reaches its destination. But let's ignore those technical problems...</p>
<p>Sirius A is more massive than the Sun, but it also has a larger radius. According to the data on Wikipedia <a href="https://en.wikipedia.org/wiki/Sirius" rel="nofollow noreferrer">Sirius</a>, its mass is ~<span class="math-container">$2.063 M_\odot$</span> (solar masses) and its radius is ~<span class="math-container">$1.711 R_\odot$</span>. Its light deflection angle at that radius is ~<span class="math-container">$2.111$</span> arcsecs, and its focal distance is ~<span class="math-container">$777.3$</span> au.</p>
<p>However, Sirius B is a white dwarf, so the light deflection at its surface is <em>much</em> larger. its mass is ~<span class="math-container">$1.018 M_\odot$</span> (solar masses) and its radius is only ~<span class="math-container">$0.0084 R_\odot$</span>. Its light deflection angle is huge: ~<span class="math-container">$212.334$</span> arcsecs, and its focal distance is only ~<span class="math-container">$0.037957$</span> au = <span class="math-container">$5678300$</span> km. That <em>sounds</em> great, but Sirius B is <em>very</em> hot. Its luminosity is only ~<span class="math-container">$5.6$</span>% of the solar luminosity, but its surface temperature is ~<span class="math-container">$25000$</span> K, so it's probably <em>not</em> a good idea to orbit it at <span class="math-container">$5678300$</span> km. Besides, the orbital period is <span class="math-container">$64.25$</span> hours, so the satellite wouldn't have much time to view its target, assuming it can deal with all the heat and light coming from the star.</p>
<p>Now, the telescope doesn't <em>have</em> to be located at the minimum distance from Sirius B. It could be placed in a larger orbit, where the deflection is smaller. The orbital period of Sirius A + B is ~<span class="math-container">$50.13$</span> years. The mean orbit radius is ~<span class="math-container">$19.782$</span> au. The eccentricity is ~<span class="math-container">$0.592$</span>, so their separation varies between ~<span class="math-container">$8.08$</span> au and ~<span class="math-container">$31.48$</span> au. Finding large stable orbits around Sirius B may not be easy.</p>
<p>Out at <span class="math-container">$777.3$</span> au, a satellite would be orbiting both the stars. Its orbital period would be ~<span class="math-container">$13119$</span> years.</p>
<p>So it doesn't seem like there would be any benefit in locating a gravitational lens telescope in the Sirius system. In fact, Sirian astronomers (if they existed, which is unlikely, given the age and history of the system) would possibly want to place such a telescope in <em>our</em> system. ;)</p>
<hr />
<p>Here's the SageMath <a href="https://sagecell.sagemath.org/?z=eJx9VN1u2zYYvddTHKgX%2DplmkZJsSUZVLEOSbQGGBcmK3QwpaIu2iOjHJakumZE9U5%2DhTzZQdBK7KHojiB8Pz%5Fd7Ptd1cbbbyeFBdExz7JpBDz1qvmn5WouhB%2Du3LXcA4C%2DhG2wl%2DyQ0M1esRct7hc2wZi1qoTTr1xZ61qoBg1wJzVrsuBRDbSmk0Jr3WD3i%2DnckN6LfIiFJNiPJjJIJ8n5XM83rg7mY0cRxXddxVkIrVFhkzs0lKtxw1l4K3ta%2DuQgcp%2DZbY770aUEQYycCh8m14mvzKl0QghA13zrOG5wpLYd%2D6ISJ%2D30vtMNGVKBZOS%5FzIic5IQb2y0mqOyZZxzWXyunG24OrNMlpkmWEZHSW5GVGywAhKLkrnW68sKC0LBaEzLJ0Pif5y%5FUaFZKyzMskmxeOZLVBL9K8mNE0N2fjYlHOp1h%2DEr3mkq21U%5FPNUXN8%5FaCrX3XX%5Fjw8%2DN7bJn13%5Fe3%2DvY2b9J1ktRgVRI%5F7zgsiB%2DiqW25wg%5FR9vxtvI3i3Y%2D8FEfxuvIjgXTCpGy8IIrRsxdvK65hSGHuhvQjq8PaDftzxyjP0w4GXKVXRCNZjZbKJwEY9fBin7laXrFU8WE4NN%2DBnqK2YsQSR%2DbPWwJmA0lwnYRdOQcRY3yWIQQmxg7OTote%2De7tu%5FmHyX7VuRFsfaJeg02s3glQRPJO%5FpZSonl3HkOqIaOPesFocDfYS2Eu5nKWbJxvK3j58wn3nWrqVYZMIoT5K7UuJGOb7I2hwANx3qLBC%2DLWv37odW%2DvXIVtivzp2tbrv7PHFl25MNV485DTO0%2DCE8%5FxlCJbY6%2DZpSpT1yv0uLDyoZjmjyeYJ9uQeWrCpTfj3HWJo1vu6OaW6PNkES%2Dw39TTvxCiSjTaDSWv7TX2Uz0TyBn82HFzKQZoZ1Q0HW6mhHfWzlSttt5RQ%2DI%5FMkvmXz2DaNjF5rWk9lYamlM5jmpZZGvq0pKGU%2DAE0yYqiyILYz%5FI8LRYklPIuNR1KSjKn9pwYIElSkpVpaPtXFnlBstNs%5F%2D7PTuJbYl8f12%2DxfS6fSdhc1Xz79OXzV%5FW%5F4S3T4tMJSayb5WzBn0xtzlGhWGSEOFeHhbKYz5J54GihW44Knuc5Rvt%5FnOzbSfLOJBXRQw0tk3hR76vgRA82OobidMlYkpMFM%5Fn7lr7pd8Q9RpBHqkaIac%2D8ahuhCWCaaIszndwJY39VEmJ0Y4AY5yelu56CNGMbX9lxuhpbwXo8cmZ1o625Zo9m7P8Ht4QH%2DA==&amp;lang=sage" rel="nofollow noreferrer">script</a> that I used for the calculations. You can type expressions into the input boxes, eg <code>1.711 * radS</code> to enter the radius of Sirius A into the Photon Deflection panel.</p>

CC BY-SA 4.0
2024-08-12T06:09:30.897Z
2024-08-13T09:25:51.393Z
2024-08-13T09:25:51.393Z
PM 2Ring
<p>For some time, the far-reaching and speculative idea of using the Sun as a gravitational lens has been floating around. This would require sending a spacecraft about ~550 AU of a distance away from Earth. Which seems very possible to happen in the next few decades.
But I am wondering, is there any plausibility to using other stars (like the Sirius A) for possibly even higher resolution or greater distance imaging due to the stars brightness and size?</p>
<p>Is there there enough parallax for this to be useful? How far away must a satellite go to be able to manipulate parallax to its advantage? Obviously let’s assume we have some type of interstellar propulsion system like laser propelled solar.</p>
<p>I'm curious if anyone can give useful feedback or calculations on the distance it can image and the quality of images it can capture, because in the far future if the solar gravitational lense work why not use other stars?!</p>

CC BY-SA 4.0
2024-08-11T19:18:53.823Z
Do you mean a mission to the focal point of Sirus A, which would be a few hundred AU from sirus A itself.  But Sirus is 500000 Au from the Earth, so  getting to the focal point of sirus is basically "can we do interstellar travel?",  It's much much further from us than the focal point of the sun. Whereas we could get to the sun's focal point in a few decades with no new tech, we have no practical means of travelling the 500000 au to Sirius.
James K
CC BY-SA 4.0
2024-08-11T19:42:59.277Z
That’s not my question yes, I’m aware this question requires interstellar travel im just curious the resolution and distance a solar gravitational lense can be if we used Sirius A. This is hypothetical
Michael Vargas
CC BY-SA 4.0
2024-08-11T20:25:41.803Z
Okay. I've not done the calculations, so I don't know, but I doubt the larger mass of sirius makes so much of a difference that it's worth a journey 1000 times longer.  But perhaps in a future in which we have human settlements on moons and planets on multiple systems, it might make sense to use focal points for, for example keeping in contact.  You could use the amplification at the focal point to make radio transmissions between star systems (but it's probably cheaper just to use a bigger dish) etc
James K
CC BY-SA 4.0
2024-08-12T08:20:03.320Z
Related https://astronomy.stackexchange.com/questions/33498/what-is-the-gravitational-lensing-focal-distance-of-a-white-dwarf-star
ProfRob
CC BY-SA 4.0
2024-08-19T09:58:07.453Z
What is a "FOCAL mission"? Who proposes them? Can you add a link for readers like me with below-average acronymological skills? *Thanks!*
uhoh
<telescope><interstellar>
Is it plausible to use Sirius A for a proposed FOCAL mission in the future?
Michael Vargas
# Is it plausible to use Sirius A for a proposed FOCAL mission in the future?

(Asked by: username_0 on 2024-08-11)

For some time, the far-reaching and speculative idea of using the Sun as a gravitational lens has been floating around. This would require sending a spacecraft about ~550 AU of a distance away from Earth. Which seems very possible to happen in the next few decades.
But I am wondering, is there any plausibility to using other stars (like the Sirius A) for possibly even higher resolution or greater distance imaging due to the stars brightness and size?

Is there there enough parallax for this to be useful? How far away must a satellite go to be able to manipulate parallax to its advantage? Obviously let’s assume we have some type of interstellar propulsion system like laser propelled solar.

I'm curious if anyone can give useful feedback or calculations on the distance it can image and the quality of images it can capture, because in the far future if the solar gravitational lense work why not use other stars?!

**Tags:** telescope, interstellar

> **Comments:**
> **username_1**: Do you mean a mission to the focal point of Sirus A, which would be a few hundred AU from sirus A itself.  But Sirus is 500000 Au from the Earth, so  getting to the focal point of sirus is basically "can we do interstellar travel?",  It's much much further from us than the focal point of the sun. Whereas we could get to the sun's focal point in a few decades with no new tech, we have no practical means of travelling the 500000 au to Sirius.  
> **username_0**: That’s not my question yes, I’m aware this question requires interstellar travel im just curious the resolution and distance a solar gravitational lense can be if we used Sirius A. This is hypothetical  
> **username_1**: Okay. I've not done the calculations, so I don't know, but I doubt the larger mass of sirius makes so much of a difference that it's worth a journey 1000 times longer.  But perhaps in a future in which we have human settlements on moons and planets on multiple systems, it might make sense to use focal points for, for example keeping in contact.  You could use the amplification at the focal point to make radio transmissions between star systems (but it's probably cheaper just to use a bigger dish) etc  
> **username_2**: Related https://astronomy.stackexchange.com/questions/33498/what-is-the-gravitational-lensing-focal-distance-of-a-white-dwarf-star  
> **username_3**: What is a "FOCAL mission"? Who proposes them? Can you add a link for readers like me with below-average acronymological skills? *Thanks!*  

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## 1 answers

### Answer by username_4 on 2024-08-12. Score: 7

The [solar gravitational lens](https://en.wikipedia.org/wiki/Solar_gravitational_lens) was first proposed by Einstein in 1936. Although gravitational lensing gives excellent magnification and light amplification, there are various practical difficulties in utilising the Sun (or another star) as a gravitational lens.

The gravitational deflection of a light (or radio) ray just skimming the [nominal solar radius](https://en.wikipedia.org/wiki/Solar_radius) $R\_\odot$ is ~$1.7512$ arcsecs. The deflection is approximately inversely proportional, so a ray passing the Sun at $2R\_\odot$ gets deflected by ~$1.7512/2$ arcsecs. The nominal solar radius is defined to be the distance where the optical depth of the Sun's photosphere is $2/3$, so for lensing purposes, we need to use a somewhat larger radius, at least $1.001 R\_\odot$. As the radius increases we get less interference from the solar atmosphere, but we also get less deflection.

The focal distance $d$ of a gravitational lens is given by
$$d = b / \tan(\theta)$$
where $b$ is the [impact parameter](https://en.wikipedia.org/wiki/Impact_parameter) and $\theta$ is the deflection angle. (For small angles, $\tan(\theta) \approx \theta$, in radians). The impact parameter is the minimal distance from the ray to the centre of the lensing body if there were no deflection; the deflection angle is the angle between that path and the actual path. (FWIW, I have some diagrams of strong photon deflection in the vicinity of a black hole [here](https://physics.stackexchange.com/a/810981/123208)).

For a ray at $R\_\odot$, $\theta = 1.7512$ arcsecs and $d \approx 547.756$ au ([astronomical units](https://en.wikipedia.org/wiki/Astronomical_unit)). At $1.001 R\_\odot$, $\theta = 1.7494$ arcsecs and $d \approx 548.853$ au. A satellite with such a large orbital radius moves slowly. The period of a solar orbit of semi-major axis $547.756$ au is ~$12820$ (Julian) years, with $548.853$ we get ~$12858.6$ years. Our gravitational telescope can only focus on the region of the sky directly behind the Sun. To look in another direction it has to wait for its orbit to take it there (unless it has fuel to fly to a new location). Conversely, if our telescope is on a mission to study a particular exoplanet, it has a limited time window to gather data while the exoplanet is properly aligned with the Sun. After that, it has to wait for a new target to come into alignment.

It takes a while to get to $548$ au. Voyager 2 was launched almost 47 years ago, and its current distance from the Sun is only ~$137.3$ au. There's virtually no solar power available at $548$ au, so the satellite would need an [RTG](https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_generator) based on an isotope with a long half-life, or have a nuclear reactor.

---

Sending a probe to the Sirius system is hard. Perhaps a tiny laser propelled probe could reach Sirius in a reasonable time frame, but such a probe will be travelling at a significant fraction of light speed, and it's not clear how to slow it down when it reaches its destination. But let's ignore those technical problems...

Sirius A is more massive than the Sun, but it also has a larger radius. According to the data on Wikipedia [Sirius](https://en.wikipedia.org/wiki/Sirius), its mass is ~$2.063 M\_\odot$ (solar masses) and its radius is ~$1.711 R\_\odot$. Its light deflection angle at that radius is ~$2.111$ arcsecs, and its focal distance is ~$777.3$ au.

However, Sirius B is a white dwarf, so the light deflection at its surface is *much* larger. its mass is ~$1.018 M\_\odot$ (solar masses) and its radius is only ~$0.0084 R\_\odot$. Its light deflection angle is huge: ~$212.334$ arcsecs, and its focal distance is only ~$0.037957$ au = $5678300$ km. That *sounds* great, but Sirius B is *very* hot. Its luminosity is only ~$5.6$% of the solar luminosity, but its surface temperature is ~$25000$ K, so it's probably *not* a good idea to orbit it at $5678300$ km. Besides, the orbital period is $64.25$ hours, so the satellite wouldn't have much time to view its target, assuming it can deal with all the heat and light coming from the star.

Now, the telescope doesn't *have* to be located at the minimum distance from Sirius B. It could be placed in a larger orbit, where the deflection is smaller. The orbital period of Sirius A + B is ~$50.13$ years. The mean orbit radius is ~$19.782$ au. The eccentricity is ~$0.592$, so their separation varies between ~$8.08$ au and ~$31.48$ au. Finding large stable orbits around Sirius B may not be easy.

Out at $777.3$ au, a satellite would be orbiting both the stars. Its orbital period would be ~$13119$ years.

So it doesn't seem like there would be any benefit in locating a gravitational lens telescope in the Sirius system. In fact, Sirian astronomers (if they existed, which is unlikely, given the age and history of the system) would possibly want to place such a telescope in *our* system. ;)

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Here's the SageMath [script](https://sagecell.sagemath.org/?z=eJx9VN1u2zYYvddTHKgX%2DplmkZJsSUZVLEOSbQGGBcmK3QwpaIu2iOjHJakumZE9U5%2DhTzZQdBK7KHojiB8Pz%5Fd7Ptd1cbbbyeFBdExz7JpBDz1qvmn5WouhB%2Du3LXcA4C%2DhG2wl%2DyQ0M1esRct7hc2wZi1qoTTr1xZ61qoBg1wJzVrsuBRDbSmk0Jr3WD3i%2DnckN6LfIiFJNiPJjJIJ8n5XM83rg7mY0cRxXddxVkIrVFhkzs0lKtxw1l4K3ta%2DuQgcp%2DZbY770aUEQYycCh8m14mvzKl0QghA13zrOG5wpLYd%2D6ISJ%2D30vtMNGVKBZOS%5FzIic5IQb2y0mqOyZZxzWXyunG24OrNMlpkmWEZHSW5GVGywAhKLkrnW68sKC0LBaEzLJ0Pif5y%5FUaFZKyzMskmxeOZLVBL9K8mNE0N2fjYlHOp1h%2DEr3mkq21U%5FPNUXN8%5FaCrX3XX%5Fjw8%2DN7bJn13%5Fe3%2DvY2b9J1ktRgVRI%5F7zgsiB%2DiqW25wg%5FR9vxtvI3i3Y%2D8FEfxuvIjgXTCpGy8IIrRsxdvK65hSGHuhvQjq8PaDftzxyjP0w4GXKVXRCNZjZbKJwEY9fBin7laXrFU8WE4NN%2DBnqK2YsQSR%2DbPWwJmA0lwnYRdOQcRY3yWIQQmxg7OTote%2De7tu%5FmHyX7VuRFsfaJeg02s3glQRPJO%5FpZSonl3HkOqIaOPesFocDfYS2Eu5nKWbJxvK3j58wn3nWrqVYZMIoT5K7UuJGOb7I2hwANx3qLBC%2DLWv37odW%2DvXIVtivzp2tbrv7PHFl25MNV485DTO0%2DCE8%5FxlCJbY6%2DZpSpT1yv0uLDyoZjmjyeYJ9uQeWrCpTfj3HWJo1vu6OaW6PNkES%2Dw39TTvxCiSjTaDSWv7TX2Uz0TyBn82HFzKQZoZ1Q0HW6mhHfWzlSttt5RQ%2DI%5FMkvmXz2DaNjF5rWk9lYamlM5jmpZZGvq0pKGU%2DAE0yYqiyILYz%5FI8LRYklPIuNR1KSjKn9pwYIElSkpVpaPtXFnlBstNs%5F%2D7PTuJbYl8f12%2DxfS6fSdhc1Xz79OXzV%5FW%5F4S3T4tMJSayb5WzBn0xtzlGhWGSEOFeHhbKYz5J54GihW44Knuc5Rvt%5FnOzbSfLOJBXRQw0tk3hR76vgRA82OobidMlYkpMFM%5Fn7lr7pd8Q9RpBHqkaIac%2D8ahuhCWCaaIszndwJY39VEmJ0Y4AY5yelu56CNGMbX9lxuhpbwXo8cmZ1o625Zo9m7P8Ht4QH%2DA==&lang=sage) that I used for the calculations. You can type expressions into the input boxes, eg `1.711 * radS` to enter the radius of Sirius A into the Photon Deflection panel.


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