<p>According to <a href="https://link.springer.com/article/10.1007/s10569-009-9203-8" rel="nofollow noreferrer">E. V. Pitjeva &amp; E. M. Standish</a>, it is (on average) +/- 3 meters.  The measurement was made with over half a million observations of different types in 2008.  Generally using the positions of planets, asteroids, etc, and spacecraft and modeling the gravitational effects of all bodies.</p>
<p><a href="https://www.iau.org/static/resolutions/IAU2012_English.pdf" rel="nofollow noreferrer">IAU 2012 Resolution B2</a> adopts the value of the AU to be 149,597,870,700m exactly.  Mostly just to have an exact value to work with, not because the measurement is exact.</p>

CC BY-SA 4.0
2022-05-03T03:43:33.510Z
2022-05-03T03:55:37.737Z
2022-05-03T03:55:37.737Z
Greg Miller
<p>This is a partial answer too long for a comment, but it may help to get the ball rolling...</p>
<p>Starting from <a href="https://space.stackexchange.com/q/22948/12102">this answer</a> we can see that the standard gravitational parameter of the Sun used by JPL in their development ephemerides is <code>1.32712440040944E+20</code>. While that doesn't mean we know the Earth's orbit to 1 part in <span class="math-container">$10^{14}$</span> it hints that it's believed to be known surprisingly well!</p>
<p>It's possible that something like this might shed some light on the subject, but it's not an easy question to answer. <a href="https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf" rel="nofollow noreferrer">The Planetary and Lunar Ephemeris DE 430 and 431, IPN Progress Report 42-196 (February 2014)</a>  Part of the problem is that we don't know exactly where the solar system barycenter is with respect to the Sun because there may be bodies far away we haven't detected yet. That's only a small effect on the Sun-Earth orbit. If I had to guess, I'd say it's somewhere between 1 and 100 meters uncertainty between the Earth and <em>the center</em> of the Sun. Where <a href="https://astronomy.stackexchange.com/q/32727/7982">the edge of the Sun falls</a> is a <a href="https://youtu.be/5T6umD9Z8HA" rel="nofollow noreferrer">horse of a different color!</a></p>

CC BY-SA 4.0
2020-02-16T14:01:39.717Z
The second paragraph is not correct. From the link you yourself provided, "The mass parameter of the Sun was defined by $GM_{\odot} = k^2$, where Gauss’s constant k = 0.01720209895 is a defined value. ... For DE430 and DE431, $GM_{\odot}$ has been set to $k^2$ since our current estimate is consistent with this value given the current value of the au."
David Hammen
CC BY-SA 4.0
2020-02-17T03:38:38.943Z
@DavidHammen I'll have a look thanks! My "stack" is overflowing right now so it may take a day or so...
uhoh
CC BY-SA 4.0
2022-04-02T23:04:11.860Z
FWIW, https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=Sun gives 132712440041.93938 $\rm{km^2/s^3}$ for $GM_\odot$, which equates exactly to $k^2$ using standard 53 bit double precision arithmetic.
PM 2Ring
CC BY-SA 4.0
2022-04-02T23:04:32.880Z
High precision [Gauss k from GM](https://sagecell.sagemath.org/?z=eJxNjz2PwjAMQHf_CksMtAyHk5RrO9yAkMp0C4i1Umh7UpQ2uasTJP79JUxMtuz3_LHBs47MaOFuAuMXNgSXLsXLpOfOTPNY5EYJsMHzN_ofvEaHxqFderXnXsISrxnviq1Qshayqogq8dGqVjXbl3fksHrnFzPoGW_OhOwvoGPyRNUe2rqpqSbK7Mm7x7SGNB6DRx3BykTlHTssBBHhPlXLXr2xo35ypnkavBsZbH7jM52RHP5bQ2FlCb-rcSkr_wE1eUK-&lang=sage)
PM 2Ring
CC BY-SA 4.0
2022-04-02T23:07:57.207Z
@PM2Ring I wrote "This is a partial answer too long for a comment, but it may help to get the ball rolling..." in hopes that someone with a better understanding would write a proper answer. Of course you are welcome to edit this one but I'd kinda hoped a new answer would be posted at which time (if it was good) I'd just delete this.
uhoh
CC BY-SA 4.0
2022-04-02T23:15:57.977Z
Sorry, I don't really have a better answer either.
PM 2Ring
CC BY-SA 4.0
2020-02-12T14:41:02.820Z
2022-04-02T23:06:43.283Z
2022-04-02T23:06:43.283Z
uhoh
<p>How precisely can the distance to the Sun be measured? Wikipedia says the distance to the Moon can be measured upto millimeter precision. But Wikipedia article on distance to the Sun says only about Astronomical Unit and nothing on the precision of the measurement of the distance to the Sun. I am certainly aware that we now use radar to measure the distance to the Sun, and I remember reading the precision in its measurement somewhere on the Internet, but I can't find it anymore. When I try to find the relevant information on the Internet, all I find is educational articles on things such as parallax, which is certainly superceded by radar measurements, or articles on lunar distance, which I am not looking for. Relevant references will highly be appreciated.</p>

<p>Edit: I just found out on Internet that we measure the distance to the Sun through distance to the Venus or Mercury. Anyway I want to know the precisions or errors in these measurements..</p>

CC BY-SA 4.0
2020-03-13T17:39:28.947Z
Can't we measure the distance to moon by just using laser time-of-flight?  Then we should know it very accurately.
Natsfan
CC BY-SA 4.0
2020-03-13T19:56:02.703Z
No, you know the distance to the mirror. @jmh
ProfRob
CC BY-SA 4.0
2020-03-13T20:43:46.770Z
Thanks. But won't laser light reflect off the surface of the moon and return to the earth with enough intensity to detect?  Or do we have to use a mirror?
Natsfan
CC BY-SA 4.0
2020-07-12T13:14:52.423Z
@jmh Why not use a mirror? That's what they got put there for, after all. ;) Rob's point is that using the laser timing info gives you the distance to the lunar surface, not to the centre of mass of the Moon, which is what you want for celestial mechanics calculations.
PM 2Ring
CC BY-SA 4.0
2021-10-17T18:55:13.483Z
Re *I am certainly aware that we now use radar to measure the distance to the Sun*: The Sun is one of the solar system bodies for which radar measurements of distance are essentially impossible. We could ping Pluto with radar (which we cannot yet do) before we could ping the Sun. See for example [this](https://physics.stackexchange.com/questions/335678) and [this](https://physics.stackexchange.com/questions/303659) at physics.SE.
David Hammen
<observational-astronomy><solar-system><ephemeris>
Precision in the measurement of the distance to the Sun
Youngsub Yoon
# Precision in the measurement of the distance to the Sun

(Asked by: username_0 on 2020-02-12)

How precisely can the distance to the Sun be measured? Wikipedia says the distance to the Moon can be measured upto millimeter precision. But Wikipedia article on distance to the Sun says only about Astronomical Unit and nothing on the precision of the measurement of the distance to the Sun. I am certainly aware that we now use radar to measure the distance to the Sun, and I remember reading the precision in its measurement somewhere on the Internet, but I can't find it anymore. When I try to find the relevant information on the Internet, all I find is educational articles on things such as parallax, which is certainly superceded by radar measurements, or articles on lunar distance, which I am not looking for. Relevant references will highly be appreciated.

Edit: I just found out on Internet that we measure the distance to the Sun through distance to the Venus or Mercury. Anyway I want to know the precisions or errors in these measurements..

**Tags:** observational-astronomy, solar-system, ephemeris

> **Comments:**
> **username_1**: Can't we measure the distance to moon by just using laser time-of-flight?  Then we should know it very accurately.  
> **username_2**: No, you know the distance to the mirror. @jmh  
> **username_1**: Thanks. But won't laser light reflect off the surface of the moon and return to the earth with enough intensity to detect?  Or do we have to use a mirror?  
> **username_3**: @jmh Why not use a mirror? That's what they got put there for, after all. ;) Rob's point is that using the laser timing info gives you the distance to the lunar surface, not to the centre of mass of the Moon, which is what you want for celestial mechanics calculations.  
> **username_4**: Re *I am certainly aware that we now use radar to measure the distance to the Sun*: The Sun is one of the solar system bodies for which radar measurements of distance are essentially impossible. We could ping Pluto with radar (which we cannot yet do) before we could ping the Sun. See for example [this](https://physics.stackexchange.com/questions/335678) and [this](https://physics.stackexchange.com/questions/303659) at physics.SE.  

---

## 2 answers

### Answer by username_5 on 2022-05-03. Score: 1

According to [E. V. Pitjeva & E. M. Standish](https://link.springer.com/article/10.1007/s10569-009-9203-8), it is (on average) +/- 3 meters. The measurement was made with over half a million observations of different types in 2008. Generally using the positions of planets, asteroids, etc, and spacecraft and modeling the gravitational effects of all bodies.

[IAU 2012 Resolution B2](https://www.iau.org/static/resolutions/IAU2012_English.pdf) adopts the value of the AU to be 149,597,870,700m exactly. Mostly just to have an exact value to work with, not because the measurement is exact.


---

### Answer by username_6 on 2020-02-12. Score: 0

This is a partial answer too long for a comment, but it may help to get the ball rolling...

Starting from [this answer](https://space.stackexchange.com/q/22948/12102) we can see that the standard gravitational parameter of the Sun used by JPL in their development ephemerides is `1.32712440040944E+20`. While that doesn't mean we know the Earth's orbit to 1 part in $10^{14}$ it hints that it's believed to be known surprisingly well!

It's possible that something like this might shed some light on the subject, but it's not an easy question to answer. [The Planetary and Lunar Ephemeris DE 430 and 431, IPN Progress Report 42-196 (February 2014)](https://ipnpr.jpl.nasa.gov/progress_report/42-196/196C.pdf) Part of the problem is that we don't know exactly where the solar system barycenter is with respect to the Sun because there may be bodies far away we haven't detected yet. That's only a small effect on the Sun-Earth orbit. If I had to guess, I'd say it's somewhere between 1 and 100 meters uncertainty between the Earth and *the center* of the Sun. Where [the edge of the Sun falls](https://astronomy.stackexchange.com/q/32727/7982) is a [horse of a different color!](https://youtu.be/5T6umD9Z8HA)

> **Comments:**
> **username_4**: The second paragraph is not correct. From the link you yourself provided, "The mass parameter of the Sun was defined by $GM_{\odot} = k^2$, where Gauss’s constant k = 0.01720209895 is a defined value. ... For DE430 and DE431, $GM_{\odot}$ has been set to $k^2$ since our current estimate is consistent with this value given the current value of the au."  
> **username_6**: @DavidHammen I'll have a look thanks! My "stack" is overflowing right now so it may take a day or so...  
> **username_3**: FWIW, https://ssd.jpl.nasa.gov/api/horizons.api?format=text&MAKE_EPHEM=NO&COMMAND=Sun gives 132712440041.93938 $\rm{km^2/s^3}$ for $GM_\odot$, which equates exactly to $k^2$ using standard 53 bit double precision arithmetic.  
> **username_3**: High precision [Gauss k from GM](https://sagecell.sagemath.org/?z=eJxNjz2PwjAMQHf_CksMtAyHk5RrO9yAkMp0C4i1Umh7UpQ2uasTJP79JUxMtuz3_LHBs47MaOFuAuMXNgSXLsXLpOfOTPNY5EYJsMHzN_ofvEaHxqFderXnXsISrxnviq1Qshayqogq8dGqVjXbl3fksHrnFzPoGW_OhOwvoGPyRNUe2rqpqSbK7Mm7x7SGNB6DRx3BykTlHTssBBHhPlXLXr2xo35ypnkavBsZbH7jM52RHP5bQ2FlCb-rcSkr_wE1eUK-&lang=sage)  
> **username_6**: @PM2Ring I wrote "This is a partial answer too long for a comment, but it may help to get the ball rolling..." in hopes that someone with a better understanding would write a proper answer. Of course you are welcome to edit this one but I'd kinda hoped a new answer would be posted at which time (if it was good) I'd just delete this.  
> **username_3**: Sorry, I don't really have a better answer either.  

---

