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The standard gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be expressed as G ( m 1 + m 2 ) , or as GM when one body is much larger than the other: μ = G ( M + m ) ≈ G M . {\displaystyle \mu =G(M+m)\approx GM.}
The gravitational field of the Moon has been measured by tracking the radio signals emitted by orbiting spacecraft. The principle used depends on the Doppler effect, whereby the line-of-sight spacecraft acceleration can be measured by small shifts in frequency of the radio signal, and the measurement of the distance from the spacecraft to a station on Earth.
μ = G(M + m), a gravitational parameter, [note 2] where G is Newton's gravitational constant, M is the mass of the primary body (i.e., the Sun), m is the mass of the secondary body (i.e., a planet), and; p is the semi-parameter (the semi-latus rectum) of the body's orbit. Note that every variable in the above equations is a constant for two ...
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. This quantity gives a convenient simplification of various gravity-related formulas.
Gravitational parameter: m 3/ s 2: 1.327×10 20: ... but that its shape became "frozen in" and did not change as it spun down due to tidal forces from its moon Weywot
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 Sun's gravitational effect on the Moon is more than twice that of Earth's on the Moon; consequently, the Moon's trajectory is always convex [26] [27] (as seen when looking Sunward at the entire Sun–Earth–Moon system from a great distance outside Earth–Moon solar orbit), and is nowhere concave (from the same perspective) or looped.
Despite being the only moon in the Solar System with a substantial magnetic field, it is the largest Solar System object without a substantial atmosphere. Like Saturn's largest moon Titan, it is larger than the planet Mercury, but has somewhat less surface gravity than Mercury, Io, or the Moon due to its lower density compared to the three. [18]