<p>I don't know if this is what most astronomers use, but it is certainly a method that <em>could</em> be used. It also makes for some interesting photos.</p>

<p><a href="https://en.wikipedia.org/wiki/Gravitational_lens" rel="nofollow">Gravitational lensing</a> was one of the great predictions of Einstein's theory of general relativity, and was actually one of the first pieces of evidence for it - see the solar eclipse of 1919. Gravitational lensing is the bending of light by a massive object. Because mass and energy warp space-time, we know that if you can calculate how much the light is bent, you can calculate the mass of the body bending it. Wikipedia gives the following formula:</p>

<p>$$\theta=\frac{4GM}{rc^2}$$</p>

<p>where $M$ is mass, $r$ is the distance the object is from the light, and $G$ and $c$ are, of course, constants. So if you can measure how much light is bent by an object, you can calculate its mass. It's hard, and you would need good conditions for it to work, but it could work, nonetheless.</p>

CC BY-SA 3.0
2014-10-08T01:04:06.963Z
2014-10-08T01:04:06.963Z
HDE 226868
<p>they use Newton's law of universal gravitation, example gravity interaction between moon and earth , jupiter Jupiter and its moons, or sun and planets, 
you can find <a href="http://en.wikipedia.org/wiki/Gravitational_constant" rel="nofollow">here</a> , play with m1 and m2, G and r , to calculate , the key is r and G , get m1 for earth and m2 for any body in free fall , after get distance between earth and sun, and get m for the sun , if they required most exact I guess that they use relativity and Lorenz transformations.  </p>

CC BY-SA 4.0
2021-01-10T06:59:43.957Z
I thought if m2 was significantly smaller than m1 then m2 is canceled out and you only need to use m1 to workout trajectory and acceleration. Ergo you would not be able to work out the mass of a small (e.g planet, asteroid) celestial body, just from its movements
DarcyThomas
CC BY-SA 3.0
2014-10-07T23:48:05.453Z
How will they measure the acceleration of objects on the planet due to acceleration ($g_p$)?
HDE 226868
CC BY-SA 3.0
2014-10-08T00:13:41.297Z
when they get G and m of sun, and distance between sun and planets , you can find more information [here](http://imagine.gsfc.nasa.gov/YBA/cyg-X1-mass/mass-of-sun.html)
Adrian R
CC BY-SA 3.0
2014-10-08T00:14:30.753Z
But how do they measure the mass of the Sun, as this question asks?
HDE 226868
CC BY-SA 3.0
2014-10-08T00:31:46.000Z
they use m from earth and distance between earth and sun to get G and m of sun, more information , [link] (http://zebu.uoregon.edu/~soper/Sun/mass.html)
Adrian R
CC BY-SA 3.0
2014-10-08T00:34:42.047Z
Nice (hadn't thought of that), but the question asks about a general celestial body.
HDE 226868
CC BY-SA 3.0
2014-10-08T00:49:00.507Z
for celestial body in general, they get positions in lapse times, and get velocity and acelerations, f=m*a
Adrian R
CC BY-SA 3.0
2014-10-07T23:31:28.923Z
2014-10-07T23:31:28.923Z
Adrian R
<p>How do astronomers find out the correct weight of a planet even though there isn't any direct means to weigh them? What technique do they use? Just curious!</p>

CC BY-SA 4.0
2020-09-15T11:39:40.117Z
People are answering the mass of a celestial body;
user2617804
CC BY-SA 3.0
2014-10-08T06:50:38.073Z
http://lasp.colorado.edu/education/outerplanets/math/extrasolar_masses.pdf
Aaron
<star><planet><astrophysics><mass>
Weight of a celestial body
Devgeet Patel
# Weight of a celestial body

(Asked by: username_0 on 2014-08-13)

How do astronomers find out the correct weight of a planet even though there isn't any direct means to weigh them? What technique do they use? Just curious!

**Tags:** star, planet, astrophysics, mass

> **Comments:**
> **username_2**: http://lasp.colorado.edu/education/outerplanets/math/extrasolar_masses.pdf  
> **username_1**: People are answering the mass of a celestial body;  

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## 2 answers

### Answer by username_3 on 2014-10-08. Score: 2

I don't know if this is what most astronomers use, but it is certainly a method that *could* be used. It also makes for some interesting photos.

[Gravitational lensing](https://en.wikipedia.org/wiki/Gravitational_lens) was one of the great predictions of Einstein's theory of general relativity, and was actually one of the first pieces of evidence for it - see the solar eclipse of 1919. Gravitational lensing is the bending of light by a massive object. Because mass and energy warp space-time, we know that if you can calculate how much the light is bent, you can calculate the mass of the body bending it. Wikipedia gives the following formula:

$$\theta=\frac{4GM}{rc^2}$$

where $M$ is mass, $r$ is the distance the object is from the light, and $G$ and $c$ are, of course, constants. So if you can measure how much light is bent by an object, you can calculate its mass. It's hard, and you would need good conditions for it to work, but it could work, nonetheless.


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### Answer by username_4 on 2014-10-07. Score: 0

they use Newton's law of universal gravitation, example gravity interaction between moon and earth , jupiter Jupiter and its moons, or sun and planets,
you can find [here](http://en.wikipedia.org/wiki/Gravitational_constant) , play with m1 and m2, G and r , to calculate , the key is r and G , get m1 for earth and m2 for any body in free fall , after get distance between earth and sun, and get m for the sun , if they required most exact I guess that they use relativity and Lorenz transformations.

> **Comments:**
> **username_3**: How will they measure the acceleration of objects on the planet due to acceleration ($g_p$)?  
> **username_4**: when they get G and m of sun, and distance between sun and planets , you can find more information [here](http://imagine.gsfc.nasa.gov/YBA/cyg-X1-mass/mass-of-sun.html)  
> **username_3**: But how do they measure the mass of the Sun, as this question asks?  
> **username_4**: they use m from earth and distance between earth and sun to get G and m of sun, more information , [link] (http://zebu.uoregon.edu/~soper/Sun/mass.html)  
> **username_3**: Nice (hadn't thought of that), but the question asks about a general celestial body.  
> **username_4**: for celestial body in general, they get positions in lapse times, and get velocity and acelerations, f=m*a  
> **username_5**: I thought if m2 was significantly smaller than m1 then m2 is canceled out and you only need to use m1 to workout trajectory and acceleration. Ergo you would not be able to work out the mass of a small (e.g planet, asteroid) celestial body, just from its movements  

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