Astronomy & space · Advanced university
Enclosed mass from an idealized rotation speed
Assume circular motion about a spherically symmetric mass distribution; this is not valid for all geometries.
Method and conditions
Assume circular motion about a spherically symmetric mass distribution; this is not valid for all geometries.
M = v²r/G
Worked examples
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
In compatible model units G=2, circular speed v=2, and orbital radius r=25. Assuming spherical symmetry, calculate enclosed mass. Round the final result to 4 decimal places if needed.
Set v²/r=GM/r², giving M=2²×25/2.
50
Try it
In compatible model units G=2, circular speed v=4, and orbital radius r=20. Assuming spherical symmetry, calculate enclosed mass. Round the final result to 4 decimal places if needed.
In compatible model units G=2, circular speed v=28, and orbital radius r=25. Assuming spherical symmetry, calculate enclosed mass. Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 160
Set v²/r=GM/r², giving M=4²×20/2.
- 9800
Set v²/r=GM/r², giving M=28²×25/2.
Further reading and review references
These are reference links, not copied exercises, institutional endorsement or proof of independent review.
AI-assisted preview; independent educational review required. Level labels describe prerequisites, not accreditation or official curriculum alignment.