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Physics / Physics: Principles with Applications 6 / Chapter 5 / Problem 88GP

Physics: Principles with Applications | 6th Edition | ISBN: 9780321569837 | Authors: Douglas C. Giancoli

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The Sun rotates around the center of the Milky Way Galaxy (Fig. 5–46) at a distance of

Chapter 5, Problem 88GP

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QUESTION:

The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center $\left({1ly=9.5×{10}^{15}\ m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left({2×{10}^{30}\ kg}\right)$ , how many stars would there be in our Galaxy?

Figure 5-46 Problem 88. Edge -on view of our Galaxy

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QUESTION:

The Sun rotates around the center of the Milky Way Galaxy (Fig. 5-46) at a distance of about 30,000 light-years from the center $\left({1ly=9.5×{10}^{15}\ m}\right)$ . If it takes about 200 million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun $\left({2×{10}^{30}\ kg}\right)$ , how many stars would there be in our Galaxy?

Figure 5-46 Problem 88. Edge -on view of our Galaxy

ANSWER:

Solution 88 GP

Step 1 of 3

We have to estimate the mass of the Milky Way Galaxy.

The mass of the Milky Way Galaxy can be estimated by using the expressions for rotational speed (orbital velocity) of the Sun about the galactic centre.

$v=\sqrt{G\ \frac{{M}_{galaxy}}{{r}_{orbit}}}$

where,

$G=$ Universal gravitational constant

$=6.67\times{}1{0}^{-11}$ N $\cdot{}$ m2/kg2

${r}_{orbit}=$ radius of the Sun’s orbit around the

galactic centre = 30,000 light years

Thus,

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

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

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