Editing Orbital period (section)

===Effect of central body's density===
For a perfect sphere of uniform [[density]], it is possible to rewrite the first equation without measuring the mass as:

:<math>T = \sqrt{\frac{a^3}{r^3} \frac{3 \pi}{G \rho}}</math>

where:
* ''r'' is the sphere's radius
* ''a'' is the orbit's semi-major axis,
* ''G'' is the gravitational constant,
* ''ρ'' is the density of the sphere.

For instance, a small body in circular orbit 10.5 [[centimetre|cm]] above the surface of a sphere of [[tungsten]] half a metre in radius would travel at slightly more than 1 [[millimetre|mm]]/[[second|s]], completing an orbit every hour. If the same sphere were made of [[lead]] the small body would need to orbit just 6.7 [[millimetre|mm]] above the surface for sustaining the same orbital period.

When a very small body is in a circular orbit barely above the surface of a sphere of any radius and mean density ''ρ'' (in kg/m<sup>3</sup>), the above equation simplifies to 

:<math>T = \sqrt{ \frac {3\pi}{G \rho} }</math>

(since ''r'' now nearly equals ''a''). Thus the orbital period in low orbit depends only on the density of the central body, regardless of its size.

So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5,515&nbsp;kg/m<sup>3</sup>,<ref>{{citation |url=http://www.wolframalpha.com/input/?i=density+of+the+earth |title=Density of the Earth |publisher=wolframalpha.com}}</ref> e.g. [[Mercury (planet)|Mercury]] with 5,427&nbsp;kg/m<sup>3</sup> and [[Venus]] with 5,243&nbsp;kg/m<sup>3</sup>) we get:
:''T'' = 1.41 hours

and for a body made of water (''ρ''&nbsp;≈&nbsp;1,000&nbsp;kg/m<sup>3</sup>),<ref>{{citation |url=http://www.wolframalpha.com/input/?i=density+of+water |title=Density of water |publisher=wolframalpha.com}}</ref> or bodies with a similar density, e.g. Saturn's moons [[Iapetus]] with 1,088&nbsp;kg/m<sup>3</sup> and [[Tethys (moon)|Tethys]] with 984&nbsp;kg/m<sup>3</sup> we get:

:''T'' = 3.30 hours

Thus, as an alternative for using a very small number like ''G'', the strength of universal gravity can be described using some reference material, such as water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes. Conversely, this can be used as a kind of "universal" [[time standard|unit of time]] if we have a unit of density.{{cn|date=March 2025}}{{or|date=March 2025}}