What does a flat rotation curve imply about the distribution of total mass ($M$) as a function of radius ($r$) based on standard gravitational formulas?
Answer
The mass enclosed ($M$) must increase linearly with the radius ($r$).
If velocity ($v$) is constant, using the relationship $v^2 = GM/r$, it necessitates that the enclosed mass ($M$) must increase linearly with the radius ($r$) out to the edge of observation.
#Videos
Astrophysics: Galaxy Rotation Curves and Dark Matter - YouTube
Related Questions
What two parameters are plotted against each other to create a galaxy rotation curve?If a galaxy followed strict Keplerian expectations based only on visible matter, what should happen to orbital velocity far from the center?What observational tool allows astronomers to calculate the precise line-of-sight velocity of gas clouds?What key finding did Vera Rubin and Kent Ford discover when comparing measured rotation speeds to Keplerian predictions?What does a flat rotation curve imply about the distribution of total mass ($M$) as a function of radius ($r$) based on standard gravitational formulas?What is the unavoidable conclusion drawn from a galaxy rotation curve that refuses to drop off at large radii?What geometric structure is postulated to contain the vast majority of a galaxy's unseen mass?How can astronomers calculate the total mass ($M$) enclosed within a specific radius ($r$) using a known orbital velocity ($v$)?What alternative cosmological theory is mentioned that attempts to explain flat rotation curves by altering gravity rather than invoking unseen mass?How much greater can the dark matter mass be compared to the visible mass within a specific radius in many spiral galaxies?