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The Sun rotates about the center of the Milky WayGalaxy (Fig. 29$)$ at a distance of about $30,000$ light-yearsfrom the center $\left(11 y=9.5 \times 10^{15} \mathrm{m}\right) .$ If it takes about 200million years to make one rotation, estimate the mass of our Galaxy. Assume that the mass distribution of ourGalaxy is concentrated mostly in a central uniformsphere. If all the stars had about the mass of our Sun$\left(2 \times 10^{30} \mathrm{kg}\right),$ how many stars would there be in ourGalaxy?

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$3 \times 10^{41} k g$$2 \times 10^{11} s t a r s$

Physics 101 Mechanics

Chapter 6

Gravitation and Newton's Synthesis

Physics Basics

Newton's Laws of Motion

Applying Newton's Laws

Gravitation

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03:43

In physics, dynamics is the branch of physics concerned with the study of forces and their effect on matter, commonly in the context of motion. In everyday usage, "dynamics" usually refers to a set of laws that describe the motion of bodies under the action of a system of forces. The motion of a body is described by its position and its velocity as the time value varies. The science of dynamics can be subdivided into, Dynamics of a rigid body, which deals with the motion of a rigid body in the frame of reference where it is considered to be a rigid body. Dynamics of a continuum, which deals with the motion of a continuous system, in the frame of reference where the system is considered to be a continuum.

03:55

In physics, orbital motion is the motion of an object around another object, which is often a star or planet. Orbital motion is affected by the gravity of the central object, as well as by the resistance of deep space (which is negligible at the distances of most orbits in the Solar System).

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The Sun rotates around the…

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The Sun revolves around th…

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The Sun rotates about the …

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84. The Sun revolves aroun…

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The Sun, which is $2.2 \ti…

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The Sun, mass $2.0 \times …

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The Milky Way galaxy rotat…

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(II) Our Sun rotates about…

So here we simply want to find the mass of the galaxy and then the number of stars in the galaxy. So we can say that the velocity is going to be equal to the square root of thie gravitational, constant times the mass of the galaxy divided by the radius of thie Sun's orbit around the amount around the Milky Way. So we can say that the mass of the galaxy will be equal to the rate of the radius of the sun's orbit. Times V squared divided by G. Ah, we know that the is going to be equal to two pi times the radius of the sun's orbit divided by the period of tea. And so we can say that the mass of the galaxy is going to be equal to four Thai Square times. The radius of the sun's orbit cubed the radius of the sun's orbit Cube, divided by G. T. Squared my apologies. And so now we can solve, so we can simply say, four pi squared and then times the radius of the Sun's orbit is going to be 30,000 light years, so 30,000 times 9.5 times 10 to the 15th meters quantity squared, so this would be 9.5 times 10 to the 15th meters. That's how far light travels in one year. So we're trying. We're most playing one year, one light year by 30,000 Emery setting it to the third power. And then this will be divided by against 6.67 times 10 to the negative Elevens times the period of the sun. So 200,000,000 years. So 200 times 10 to the 60 years and then there are specifically three, 3.15 times, 10 to the seventh seconds per year. And then this will be quantity squared. And so we find that the mass of the galaxy is going to be equal. Tio 3.4552 times 10 to the 41st kilograms. So this would be one answer the mass of the galaxy. And then we want to find the number of stars so we can find a number of stars by most by dividing the mass of the galaxy by the mass of our own sun. And so this is assuming that most of the stars and the galaxy have the mass of our sun, so we have to make that assumption in order to find the number of stars. So this will be 3.452 times 10 to the 41st kilogram, divided by 2.0 times 10 to the 30th kilograms. And this is giving us 1.7226 times 10 to the 11 stars. We know that it's a little bit less than this because not all Nass in the Galaxy is because of stars. Most of it is because of stars. However, again, we have a lot of planets that orange stars and a lot of asteroids and comets and ah, lot of, of course, different types of mass that take up, of course, the mass of the galaxy. It's not just star, so it's going to be a little bit less than this. However, this is, Ah, asbestos, the prophet nation, as we can get with a simple algebra, that is the end of the solution. Thank you for watching

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