To find the mass of a galaxy given its radius, we would typically use a formula that takes into account the galaxy's radius and the rotational velocity at the edge of the galaxy. For a galaxy in equilibrium, the mass $M$ within a radius $r$ can be estimated by using the following formula derived from Newton's law of gravitation and circular motion:

$M = \frac{v^2 r}{G}$

where:

• $M$ is the mass of the galaxy within the radius $r$,
• $v$ is the orbital velocity of objects (e.g., stars) near the edge of the galaxy,
• $G$ is the gravitational constant, approximately $6.674 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2}$,
• $r$ is the radius of the galaxy.

However, since only the radius $r = 61$ is provided, we need more information, specifically the rotational velocity $v$ at this radius, to calculate the mass accurately.

If you can provide the rotational velocity at the edge of the galaxy, I can proceed with the calculation.

Would you like to proceed with this approach or do you have additional information?

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Here are some follow-up questions:

1. Do you have the rotational velocity of the galaxy?
2. Is the radius provided in light-years, kilometers, or another unit?
3. Are there any assumptions about the galaxy's density distribution?
4. Would you like a brief explanation of why this formula applies to galaxies?
5. Are you looking for an approximate or exact mass calculation?

Tip: For galactic mass calculations, obtaining precise measurements of the rotational velocity is crucial for accuracy.