<p>Planets are satellites of the Sun. Most planets have satellites.
Whenever you find a parent body with satellites, you get first good results about their masses and distances by applying <a href="https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion">Kepler's laws</a>.
A second approach is using <a href="https://en.wikipedia.org/wiki/Stellar_parallax">parallax measurements</a> for distance estimates.
The distance to some of the planets can be measured very accurately by radar, e.g. for <a href="http://www.astroevents.no/distance.html">Venus</a>.
The known planets of our solar system have been visited by probes. Using <a href="http://blogs.esa.int/mex/2012/08/05/time-delay-between-mars-and-earth/">signal travel times</a>, you can calculate the distance of the probe to Earth. One of the methods to determine the distance between probe and the planet is by <a href="https://en.wikipedia.org/wiki/Photogrammetry">photogrammetry</a>.
Apply the measured data to the according <a href="https://en.wikipedia.org/wiki/Simultaneous_equations">system of equations</a>. Usually more data than needed are available. Then you get an <a href="https://en.wikipedia.org/wiki/Overdetermined_system">overdetermined system</a>. A best solution can be found by <a href="https://en.wikipedia.org/wiki/Ordinary_least_squares">minimizing appropriate squares</a>.</p>

<p><a href="https://en.wikipedia.org/wiki/Perturbation_theory#Beginnings_in_the_study_of_planetary_motion">Subtle deviations from Kepler's law</a> can be used to infer masses of planets which are hard to measure in a more direct way.
Once you know the distance of a planet, use its apparent diameter(s) to <a href="https://en.wikipedia.org/wiki/Trigonometry">calculate the actual diameter(s)</a>, and then <a href="https://en.wikipedia.org/wiki/Sphere#Enclosed_volume">the volume of a sphere</a> or a <a href="https://en.wikipedia.org/wiki/Spheroid">spheroid</a>.
With mass and volume you know the mean <a href="https://en.wikipedia.org/wiki/Density">density</a> of the planet.</p>

<p>Within our solar system, for very distant objects the apparent size of which cannot be determined you may estimate the surface <a href="https://en.wikipedia.org/wiki/Albedo">albedo</a> together with distance (by Kepler after knowing the mass of the Sun) and <a href="https://en.wikipedia.org/wiki/Apparent_magnitude">apparent magnitude</a> to obtain a rough estimate of the size of the object.</p>

<p>Better size estimates for objects of small apparent size can be obtained by <a href="https://en.wikipedia.org/wiki/Occultation">stellar occultations</a>, meaning measuring the time a star is occulted by the object. Together with the <a href="https://en.wikipedia.org/wiki/Angular_velocity">angular velocity</a> of the object you get data about its angular size.</p>

CC BY-SA 3.0
2016-01-27T17:33:56.250Z
Wow, thank you so much. This is actually really cool. I've been slowly iterating through your links and finding out lots of new information. Awesome!
voice
CC BY-SA 3.0
2016-01-27T12:45:10.130Z
2016-01-27T12:45:10.130Z
Gerald
<p>When I go to the wikipedia page for any planet in our solar system, the exact mass and volume are reported. How is it possible to do this with them being so far away? I suppose after hundreds of years we can observe them going around the sun, but this doesn't really give any information since we need both the mass and distance from the sun for it to be of any use.</p>

CC BY-SA 3.0
2016-01-26T19:01:24.290Z
You don't need to observe a full revolution of a planet to calculate its orbital period, but that doesn't really matter, since its period doesn't depend on its mass. But did you try [googling](https://www.google.dk/#q=how+do+you+measure+the+mass+of+a+planet) the answer?
pela
CC BY-SA 3.0
2016-01-26T19:02:38.103Z
Yes, but so much goes unexplained when I google it.
voice
CC BY-SA 3.0
2016-01-26T21:20:23.240Z
@LeChosenOne Is there anything specifically that confuses you about the results from Google?
HDE 226868
<planet>
How is the mass of solar system objects calculated?
voice
# How is the mass of solar system objects calculated?

(Asked by: username_0 on 2016-01-26)

When I go to the wikipedia page for any planet in our solar system, the exact mass and volume are reported. How is it possible to do this with them being so far away? I suppose after hundreds of years we can observe them going around the sun, but this doesn't really give any information since we need both the mass and distance from the sun for it to be of any use.

**Tags:** planet
> **Comments:**
> **username_1**: You don't need to observe a full revolution of a planet to calculate its orbital period, but that doesn't really matter, since its period doesn't depend on its mass. But did you try [googling](https://www.google.dk/#q=how+do+you+measure+the+mass+of+a+planet) the answer?  
> **username_0**: Yes, but so much goes unexplained when I google it.  
> **username_2**: @LeChosenOne Is there anything specifically that confuses you about the results from Google?  

---

## 1 answers

### Answer by username_3 on 2016-01-27. Score: 6 | Accepted answer

Planets are satellites of the Sun. Most planets have satellites.
Whenever you find a parent body with satellites, you get first good results about their masses and distances by applying [Kepler's laws](https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion).
A second approach is using [parallax measurements](https://en.wikipedia.org/wiki/Stellar_parallax) for distance estimates.
The distance to some of the planets can be measured very accurately by radar, e.g. for [Venus](http://www.astroevents.no/distance.html).
The known planets of our solar system have been visited by probes. Using [signal travel times](http://blogs.esa.int/mex/2012/08/05/time-delay-between-mars-and-earth/), you can calculate the distance of the probe to Earth. One of the methods to determine the distance between probe and the planet is by [photogrammetry](https://en.wikipedia.org/wiki/Photogrammetry).
Apply the measured data to the according [system of equations](https://en.wikipedia.org/wiki/Simultaneous_equations). Usually more data than needed are available. Then you get an [overdetermined system](https://en.wikipedia.org/wiki/Overdetermined_system). A best solution can be found by [minimizing appropriate squares](https://en.wikipedia.org/wiki/Ordinary_least_squares).

[Subtle deviations from Kepler's law](https://en.wikipedia.org/wiki/Perturbation_theory#Beginnings_in_the_study_of_planetary_motion) can be used to infer masses of planets which are hard to measure in a more direct way.
Once you know the distance of a planet, use its apparent diameter(s) to [calculate the actual diameter(s)](https://en.wikipedia.org/wiki/Trigonometry), and then [the volume of a sphere](https://en.wikipedia.org/wiki/Sphere#Enclosed_volume) or a [spheroid](https://en.wikipedia.org/wiki/Spheroid).
With mass and volume you know the mean [density](https://en.wikipedia.org/wiki/Density) of the planet.

Within our solar system, for very distant objects the apparent size of which cannot be determined you may estimate the surface [albedo](https://en.wikipedia.org/wiki/Albedo) together with distance (by Kepler after knowing the mass of the Sun) and [apparent magnitude](https://en.wikipedia.org/wiki/Apparent_magnitude) to obtain a rough estimate of the size of the object.

Better size estimates for objects of small apparent size can be obtained by [stellar occultations](https://en.wikipedia.org/wiki/Occultation), meaning measuring the time a star is occulted by the object. Together with the [angular velocity](https://en.wikipedia.org/wiki/Angular_velocity) of the object you get data about its angular size.

> **Comments:**
> **username_0**: Wow, thank you so much. This is actually really cool. I've been slowly iterating through your links and finding out lots of new information. Awesome!  

---

