The GM Product
The quantity GM—the product of the gravitational constant and the mass of a given astronomical body such as the Sun or the Earth—is known as the standard gravitational parameter and is denoted . Depending on the body concerned, it may also be called the geocentric or heliocentric gravitational constant, among other names.
This quantity gives a convenient simplification of various gravity-related formulas. Also, for celestial bodies such as the Earth and the Sun, the value of the product GM is known more accurately than each factor independently. Indeed, the limited accuracy available for G often limits the accuracy of scientific determination of such masses in the first place.
For Earth, using M⊕ as the symbol for the mass of the Earth, we have
Calculations in celestial mechanics can also be carried out using the unit of solar mass rather than the standard SI unit kilogram. In this case we use the Gaussian gravitational constant k, where
If instead of mean solar day we use the sidereal year as our time unit, the value of ks is very close to 2π (k = 6.28315).
The standard gravitational parameter GM appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler's laws of planetary motion, and in the formula for escape velocity.
Read more about this topic: Gravitational Constant
Famous quotes containing the word product:
“Everything that is beautiful and noble is the product of reason and calculation.”
—Charles Baudelaire (18211867)