What Is Standard Gravity?

In space dynamics, the standard gravity parameter of a celestial body is the product of the universal gravitational constant and its mass. ^[1]

In space dynamics, the standard gravity parameter of a celestial body is

In a more general case, where the objects are not necessarily large and small, we define:

The vector r is the position of one object relative to the other;

In the case of an elliptical orbit, the semi-major axis a is also defined;

(Two

Sum of the values); where:

Is the mass of two objects.

Then:

For circular orbits,

.

For elliptical orbits,

. (The unit of a is AU, the unit of T is year, and M is the total mass relative to the sun, we have

)

For parabolic orbits,

Is constant, equal to

.

For elliptical and hyperbolic orbits,

Is the half of the semi-major axis multiplied by the absolute value of the comparative orbital energy, which is defined as the total energy of the system divided by the reduced mass.

The standard gravity parameter of the earth is called the gravitational constant , which is equal to 398 600.441 8 ± 0.000 8 k ³ ms ^-2 . So the error is 1 to 500 000 000, which is much smaller than the error of G and M (1 to 7000).

The standard gravity parameter of the sun is called the heliocentric gravitational constant , which is equal to 1.32712440018 × 10m ³ s ^-2 .