To ensure our calculated values and units are consistent with astronomical science, we use conventional values. Using a fixed, agreed-upon set of units and constants—even if they're not the "most accurate measurement"—keeps all calculations, papers, and research on the same page. So when we are using convensional value we are not being 'imprecice' but standards-compliant. Organizations like the International Astronomical Union (IAU) define these values so that the entire scientific community can be in sync. This saves from a constant cycle of updates and alot of wasted energy as accuracy improoves.
For those who want to dive deeper:
The gravitational constant is a fundamental quantity that determines the strength of gravity. While its value is still being refined, for high-precision calculations, it is often more accurate to use the gravitational parameter (GM)—the product of G and a body's mass (M)—because this product can be measured with much higher precision from a satellite's orbit.
These are the IAU's fixed, nominal radii used to standardize units like "Earth radii" for exoplanet discovery.
The bellow units are fictitious, included for comparison purposes / are derived from conventional radiuses above (via C=2πR). We use units deriving from conventional values, for internal consistency.
TIP: You can always switch to SI to compare the result. In the logs you will find accurate results in SI without any rounding.
We use the standard gravitational parameter (GM), which can be measured with extreme precision from a satellite's orbit.
Derived from the conventional (IAU) radii.
⚠️Attention: Conventional values (like the official IAU nominal Earth constant bellow) often involve rounding. The rounding and number of digits is respected as part of the convension.
These are derived from the conventional mass and volume values.
These values represent the standard gravitational forces for each planet.
These values are standard, conventional figures for the minimum speed needed to escape each planet's gravitational pull.
The use of conventional values ensures consistency with astronomy, but may result to oddities for starters.
Using conventional values means our units are consistent with those used in scientific papers. For example, if a paper states an exoplanet is 5.4 Earth radii (R⊕), Exocalc will convert the value to the same measurement in meters that a professional astronomer would use.
Oddities can arise when applying these units to the same planets that defined them: A common point of confusion is using 1 R⊕ to describe Earth's mean radius. This is incorrect. 1 R⊕ is the IAU's nominal equatorial radius (~6,378 km), which is about ~7 km more than Earth's mean radius (~6,371 km).
TIP: To accurately define Earth's shape as an oblate spheroid, use both the equatorial (6378.137 km) and polar (6356.752 km) conventional measurements. The calculator will then correctly compute a mean radius of approximately 6,371 Kilometers and 87cm or so.. which is basicaly the non rounded version of the popular textbook value.
But even with this level of precision in your geometry, the mean surface gravity will slightly exceed 1 g⊕. This can be highly confusing, as many sources state Earth's surface gravity is exactly 1 g.
Here's the explanation ⚠️Warning Technical wall of text incoming::
1 g⊕ is a conventionally defined constant (exactly 9.80665 m/s²). It represents the average gravity that we feel at 45° latitude and accounts for the effects of Earth's spin and its non-spherical shape. Our mean radius calculation, however, does not include these factors, leading to a slightly higher theoretical value. (Actually the 1g is not a 'calculated value', but an agreed upon value)
On top of that the 'inverse square law' that we use so far for gravity is NOT the most precise method (Yes you heard me right) as it hypothesizes that all mass is uniform or consetrated in one point. Spherical harmonics on the other side take in account: Oblatness, lattitude, height, and most importantly the mass distribution. Applying this advanced method for an angle of 45° on Earth at 50m height, yields ~1g. Spherical harmonics equations, are unique for each planet.
Ultimately, the conventional values are not here to demosntrate the most accurate measurements, also some may seem conflicting, 1ER does not yield 1EV. But that`s nothing compared to the benefits. A world without conventional values would resemble the Babels Tower. Imagine having to change all references in all books because a unit became more accurate.
Mean Radius (R_mean) in Exocalc is the Volumetric Mean Radius. Mean radius hypothesizes a "spherical equivalent" of the oblate version of a planet (The second is closer to the shape of a real planet). The model relates the two shapes assuming constant volume based on an idealized Maclaurin Spheroid.
You will notice that when you adjust the oblateness (flattening) of a planet in this calculator, the volume remains constant by design. This reflects the physical reality that while flattening redistributes mass and tends to increase the surface area, the total amount of space the planet occupies (its volume) is preserved for the purpose of our mean radius calculation.
Author Aris T.