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Questions and Answers
Calculate the approximate mass of the Milky Way Galaxy from the fact that the Sun orbits the galactic center every 230 million years at a distance of 27,000 light-years. (As discussed in Chapter 15, this calculation actually tells us only the mass of the galaxy within the Sun's orbit.) Express your answer to two significant figures and include the appropriate units.
Calculate the approximate mass of the Milky Way Galaxy from the fact that the Sun orbits the galactic center every 230 million years at a distance of 27,000 light-years. (As discussed in Chapter 15, this calculation actually tells us only the mass of the galaxy within the Sun's orbit.) Express your answer to two significant figures and include the appropriate units.
To calculate the approximate mass of the Milky Way Galaxy within the Sun's orbit, we need to use the relationship between orbital period, distance, and mass. According to Kepler's Third Law of Planetary Motion, the equation is given by: $$M = \frac{{4\pi^2d^3}}{{G(T^2)}}$$ where M is the mass of the galaxy within the Sun's orbit, d is the distance between the Sun and the galactic center, T is the period of the Sun's orbit, and G is the gravitational constant. Plugging in the values, we have: $$M = \frac{{4\pi^2(27000\text{ light-years})^3}}{{G(230\text{ million years})^2}}$$ Calculating this equation will give us the approximate mass of the Milky Way Galaxy within the Sun's orbit.
What is the information given in the text?
What is the information given in the text?
The Sun orbits the galactic center every 230 million years at a distance of 27,000 light-years.
What does the calculation in the text actually tell us?
What does the calculation in the text actually tell us?
The calculation tells us only the mass of the galaxy within the Sun's orbit.
What is the approximate mass of the Milky Way Galaxy within the Sun's orbit?
What is the approximate mass of the Milky Way Galaxy within the Sun's orbit?
Study Notes
Key Information Given
- The Sun orbits the Milky Way's galactic center every 230 million years.
- The distance of the Sun from the galactic center is approximately 27,000 light-years.
Nature of the Calculation
- The calculation reveals the mass of the Milky Way Galaxy within the Sun's orbit, rather than the total mass of the galaxy.
- The orbital period and distance provide the basis for calculating gravitational effects and mass.
Approximate Mass of the Milky Way Galaxy
- The mass of the Milky Way within the Sun's orbit is approximately 1.5 trillion solar masses (1.5 x 10^12 M☉).
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Description
Test your knowledge of galactic mass with this quiz! Calculate the approximate mass of the Milky Way Galaxy using the Sun's orbit and distance from the galactic center. Express your answer to two significant figures and don't forget the units!
