In the Virgo Cluster there are galaxies measured to be...

In the Virgo Cluster there are galaxies measured to be traveling at about $1000 \mathrm{km} / \mathrm{sec}$ at a distance of $500 \mathrm{kpc}$ from the center of the cluster. If you apply the mass formula to this velocity and radius, what interior mass do you find?

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Key Concepts

Astronomical Unit Conversions

Astrophysical calculations often involve units like kilometers, seconds, and kiloparsecs. Converting these units to a consistent system, such as the SI system, ensures that constants like the gravitational constant are used correctly, thereby yielding accurate estimates of mass and other physical quantities.

Dynamical Mass Estimation

Dynamical mass estimation is a method used to determine the mass of a system by analyzing the motions of objects within it. By observing the velocity and distance of orbiting bodies, astronomers can infer the total mass—both visible and dark matter—contained within the system.

Newton's Law of Universal Gravitation

Newton's law states that every two masses attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This law provides the fundamental basis for understanding gravitational interactions in astrophysical systems.

Circular Orbital Motion

In the context of a body orbiting another in a circular path, the gravitational force acts as the centripetal force. This leads to the relationship v² = GM/r, which is used to determine the mass enclosed within the orbit by rearranging the formula to M = v²r/G, linking orbital velocity and radius to the central mass.

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