Answered: Using the rotation curve above, fill in…

Astronomy

1st Edition

ISBN:9781938168284

Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff

Chapter25: The Milky Way Galaxy

Section: Chapter Questions

Problem 24E: The first clue that the Galaxy contains a lot of dark matter was the observation that the orbital...

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Transcribed Image Text:Radial velocity vs Radius from center Using Newton's gravity equation, we will be able to determine the gravitational mass profile of the galaxy. This is a plot that shows the redshifted portion of the galaxy (which is spinning away from us) with the velocities corrected for inclination angle. So, the velocities in this graph represent the true orbital velocities of the stars and gas at each point in the galaxy's disk. Radial velocity, v (km s-¹) 175 150 125 100 75 50 25 O 0 Best-fit line NGC 2742 data 8 1 2 3 Rotation curve for NGC 2742 Power law best-fit: v=aRb where a 94 km s-¹ and b=0.28 4 5 6 Radius from center, R (kpc) 7 8 9 10

Using the rotation curve above, fill in the rotational velocity for each indicated radius. Then, use
this equation to calculate gravitational mass (in solar masses) at each radius.
M = R where G = 4.31 10-6 kpc km²
Mos²
Your values for M should be quite large, since we are talking about the mass of a galaxy! So, please
express these large numbers in scientific notation.
A
Radius (kpc)
2
+
6
8
10
B
Rotational Velocity (km/s)
C
Gravitational Mass (Mo)
Sanity check: The mass should increase with larger radii, since you are calculating the total mass
enclosed within each widening orbit.

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