# How is the diameter of a gas giant calculated?

As we know atmospheres of celestial bodies don't just stop at a given distance. They gradually become less dense as you move away from the center.

I understand that the diameter of stars is typically given to be that of their photosphere (i.e. the boundary where a laser shined from behind the star toward an observer would just barely be visable).

I assumed that a similar method using optical depth also applied to gas giants. However wikipedia currently has the somewhat confusing explanation:

As Jupiter has no surface, the base of its atmosphere is usually considered to be the point at which atmospheric pressure is equal to 1 MPa (10 bar), or ten times surface pressure on Earth.

Which isn't quite the same thing as diameter, but it got me thinking: When wikipedia or a textbook or whatever lists a diameter for a gas giant how is that figure arrived at?

I won't argue with the wikipedia definition (although the NASA Jupiter fact sheet lists it as the radius at 1 bar), but just to point out that the scale height of the atmosphere of Jupiter is given by, $h \sim kT/m g$, where $T$ is the temperature, $m$ is the mean molecular mass and $g$ is local gravity. Putting in some numbers: $g \simeq 24.8 m/s^2$, $m \simeq 2.2 m_u$, $T \simeq 165K$, gives $h \simeq 25\ km$. Thus the pressure changes extremely rapidly compared with the actual radius of a gas giant,and is very small compared to the difference for instance between the polar and equatorial radius for a gas giant (like Jupiter) with significant rotation.
So, whether you give a planet's radius at 1 bar or 10 bar isn't going to make a lot of difference $<100\ km$.