Astronomy & space · Advanced university
Enclosed mass from an idealized rotation speed · formula reference
Assume circular motion about a spherically symmetric mass distribution; this is not valid for all geometries.
Formula
Assume circular motion about a spherically symmetric mass distribution; this is not valid for all geometries.
M = v²r/G
Worked example
In compatible model units G=2, circular speed v=15, and orbital radius r=16. Assuming spherical symmetry, calculate enclosed mass. Round the final result to 4 decimal places if needed.
Set v²/r=GM/r², giving M=15²×16/2.
1800
Prerequisites and checking
Algebra and the topic definitions. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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