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The standard gravitational parameter can be determined using a pendulum oscillating above the surface of a body as: [13] μ ≈ 4 π 2 r 2 L T 2 {\displaystyle \mu \approx {\frac {4\pi ^{2}r^{2}L}{T^{2}}}} where r is the radius of the gravitating body, L is the length of the pendulum, and T is the period of the pendulum (for the reason of the ...
The product GM is the standard gravitational parameter and is often known to higher precision than G or M separately. The potential has units of energy per mass, e.g., J/kg in the MKS system. By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero.
Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: = = =, where = is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center. As an object in an escape trajectory moves outward, its ...
The gravitational potential energy is the potential energy an object has because it is within a gravitational field. The magnitude of the force between a point mass, M {\displaystyle M} , and another point mass, m {\displaystyle m} , is given by Newton's law of gravitation : [ 3 ] F = G M m r 2 {\displaystyle F={\frac {GMm}{r^{2}}}}
= (+) is the standard gravitational parameter of the bodies; h {\displaystyle h\,\!} is the specific relative angular momentum of the same body referenced [ 2 ] to the center of mass. In other context h is used in the sense of a total for two bodies expressed as relative angular momentum of the system divided by the reduced mass, giving the ...
The quantity GM —the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter (also denoted μ). The standard gravitational parameter GM appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of ...
The product GM is the standard gravitational parameter and is often known to higher precision than G or M separately. The potential has units of energy per mass, e.g., J/kg in the MKS system. By convention, it is always negative where it is defined, and as x tends to infinity, it approaches zero.
Water is the chemical substance with chemical formula H 2 O; one molecule of water has two hydrogen atoms covalently bonded to a single oxygen atom. [26] Water is a tasteless, odorless liquid at ambient temperature and pressure. Liquid water has weak absorption bands at wavelengths of around 750 nm which cause it to appear to have a blue color. [4]