<p><a href="https://youtu.be/V2BqeXfLdhw" rel="nofollow noreferrer">This video</a> talks about how by sending a spacecraft to around 600 AU and beyond, we would could use the Sun as a gravitational lens and take clear detailed images of exoplanets light-years away.</p>
<p>What it doesn't say however is the exact resolution. An exoplanet 4 light-years away would obviously appear bigger and more detailed than one 100 light years away. But by how much?</p>
<p>Is there a direct formula showing the resolution for an exoplanet at x light-years? As in kilometers/pixel?</p>
<p><a href="https://i.sstatic.net/FHpzf.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/FHpzf.jpg" alt="screenshot from &quot;Using the Sun to Image Alien Planets&quot;" /></a></p>

CC BY-SA 4.0
2021-01-23T20:25:37.990Z
Possible duplicate of https://astronomy.stackexchange.com/questions/3644/using-the-sun-as-a-gravitational-lens?
WarpPrime
CC BY-SA 4.0
2021-01-23T21:13:56.783Z
@fasterthanlight No. I want to know the resolution of a planet at a certain distance by using the Sun's gravitational lensing. As in km/pixel. Not necessarily those units, but you know. Just how clear would the image be?
user177107
CC BY-SA 4.0
2021-01-23T23:38:17.663Z
@fasterthanlight where are you seeing anything about "...a direct formula showing the resolution for an exoplanet at x light-years?" I don't find the word "resolution" anywhere on that page. This is a different question needing a different answer.
uhoh
CC BY-SA 4.0
2021-01-24T04:21:39.703Z
@user177107 and uhoh: it does answer it someway : there is no way on earth, but you'd need to go to the kuiper belt or oort cloud to  start using it as a lens to focus the light of a single source
planetmaker
CC BY-SA 4.0
2021-01-24T09:58:13.290Z
The calculation you want is done here. https://astronomy.stackexchange.com/questions/33498/what-is-the-gravitational-lensing-focal-distance-of-a-white-dwarf-star
ProfRob
CC BY-SA 4.0
2021-01-24T23:18:30.317Z
@ProfRob you've worked out a substantial fraction of the necessary calculation there and it is disheartening that the sun is actually too strong to conveniently image an exoplanet without building something [at least a little bit like this](https://twitter.com/urbanfoxxxx/status/1112410477747990531) as a focal plane, but I'm thinking that resolution may have other factors as well.
uhoh
CC BY-SA 4.0
2021-01-24T23:24:53.103Z
@ProfRob In oder to obtain an image with a non-lens like this (i.e. $\theta \sim 1/r$ vs thin lens $\theta \sim r$) one needs some kind of annular restriction in angle to see the Einstein ring for a given feature on the exoplanet's surface. Does that restriction somehow also restrict resolution (e.g. diffraction)? See also the currently insufficiently answered Space SE question [What might the first deep space telescope using the Sun or Jupiter as a gravitational lens be like?](https://space.stackexchange.com/q/31815/12102)
uhoh
CC BY-SA 4.0
2021-06-20T23:36:20.360Z
The article here https://www.centauri-dreams.org/2020/12/16/jpl-work-on-a-gravitational-lensing-mission/   suggests a resolution of 10 to 25km, is that the sort of thing you're looking for?
Dave Gremlin
<observational-astronomy><gravitational-lensing><angular-resolution>
What exactly would the resolution of an exoplanet hypothetically imaged by using the Sun as a gravitational lens be?
user177107
# What exactly would the resolution of an exoplanet hypothetically imaged by using the Sun as a gravitational lens be?

(Asked by: username_0 on 2021-01-23)

[This video](https://youtu.be/V2BqeXfLdhw) talks about how by sending a spacecraft to around 600 AU and beyond, we would could use the Sun as a gravitational lens and take clear detailed images of exoplanets light-years away.

What it doesn't say however is the exact resolution. An exoplanet 4 light-years away would obviously appear bigger and more detailed than one 100 light years away. But by how much?

Is there a direct formula showing the resolution for an exoplanet at x light-years? As in kilometers/pixel?

[![screenshot from ](https://i.sstatic.net/FHpzf.jpg)](https://i.sstatic.net/FHpzf.jpg)

**Tags:** observational-astronomy, gravitational-lensing, angular-resolution
> **Comments:**
> **username_1**: Possible duplicate of https://astronomy.stackexchange.com/questions/3644/using-the-sun-as-a-gravitational-lens?  
> **username_0**: @fasterthanlight No. I want to know the resolution of a planet at a certain distance by using the Sun's gravitational lensing. As in km/pixel. Not necessarily those units, but you know. Just how clear would the image be?  
> **username_2**: @fasterthanlight where are you seeing anything about "...a direct formula showing the resolution for an exoplanet at x light-years?" I don't find the word "resolution" anywhere on that page. This is a different question needing a different answer.  
> **username_3**: @user177107 and uhoh: it does answer it someway : there is no way on earth, but you'd need to go to the kuiper belt or oort cloud to  start using it as a lens to focus the light of a single source  
> **username_4**: The calculation you want is done here. https://astronomy.stackexchange.com/questions/33498/what-is-the-gravitational-lensing-focal-distance-of-a-white-dwarf-star  
> **username_2**: @ProfRob you've worked out a substantial fraction of the necessary calculation there and it is disheartening that the sun is actually too strong to conveniently image an exoplanet without building something [at least a little bit like this](https://twitter.com/urbanfoxxxx/status/1112410477747990531) as a focal plane, but I'm thinking that resolution may have other factors as well.  
> **username_2**: @ProfRob In oder to obtain an image with a non-lens like this (i.e. $\theta \sim 1/r$ vs thin lens $\theta \sim r$) one needs some kind of annular restriction in angle to see the Einstein ring for a given feature on the exoplanet's surface. Does that restriction somehow also restrict resolution (e.g. diffraction)? See also the currently insufficiently answered Space SE question [What might the first deep space telescope using the Sun or Jupiter as a gravitational lens be like?](https://space.stackexchange.com/q/31815/12102)  
> **username_5**: The article here https://www.centauri-dreams.org/2020/12/16/jpl-work-on-a-gravitational-lensing-mission/   suggests a resolution of 10 to 25km, is that the sort of thing you're looking for?  

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## 0 answers

