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Published equation contexts

CMR2\frac{C}{MR^2}

Why this formula appears here

Gravity. A planet’s external gravity field is not sensed with a gravimeter sitting on the planet; it is read off the motion of an orbiting or flying-by spacecraft, whose trajectory bends in response to mass distribution beneath it. In practice this means tracking the spacecraft’s radio carrier signal from Earth and measuring its Doppler shift with extreme precision as the spacecraft accelerates and decelerates along its orbit. A denser, non-uniformly distributed interior produces small, characteristic deviations from a simple point-mass orbit, expressed as gravity harmonics ( J2J_2 , C22C_{22} , and higher terms) layered on top of the dominant 1/r2r^2 term. From those harmonics and the body’s known…

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How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction.

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Published contexts (1)

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CMR2,\frac{C}{MR^2},

Equation 4 · Space Science

How Planetary Science and Exploration Actually Work

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

Gravity. A planet’s external gravity field is not sensed with a gravimeter sitting on the planet; it is read off the motion of an orbiting or flying-by spacecraft, whose trajectory bends in response to mass distribution beneath it. In practice this means tracking the spacecraft’s radio carrier signal from Earth and measuring its Doppler shift with extreme precision as the spacecraft accelerates and decelerates along its orbit. A denser, non-uniformly distributed interior produces small, characteristic deviations from a simple point-mass orbit, expressed as gravity harmonics ( J2J_2 , C22C_{22} , and higher terms) layered on top of the dominant 1/r2r^2 term. From those harmonics and the body’s known…

Meanings in this article

  • CC: the polar moment of inertia.
  • MM: the mass.
  • R2R^2: the square of R; the mean radius.
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