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Show that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius, assuming the mass of the stars inside its orbit acts like a single mass at the center of the galaxy. You may use an equation from a previous chapter to support your conclusion, but you must justify its use and define all terms used.

from the above expression it can be said that the velocity of a star orbiting its galaxy in a circular orbit is inversely proportional to the square root of its orbital radius.

Physics 103

Chapter 34

Frontiers of Physics

Wave Optics

Particle Physics

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

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in this problem, we need to calculate the velocity often orbiting star in terms of its radius. To suppose this is the center of the galaxy and a star is orbiting around it. Now what are the forces that are acting on? It surfaced. You have the force of gravity, which is attractive, and that's acting in words. And then you have the centripetal force, which is acting outwards. Now the system is in a state of equilibrium orbit. So that means F C equals F G. Now what is the centripetal force it's given by m V squared over r r R is the distance to the center Force of gravity is given to be G times two to muss is divided Boy are square here small him is the star mass on capital M is the galaxy mass. So this is the galaxy mess. Now we solve for V So our councils one power off our cancels on the right side the small and cancel out and you get that the velocity is our velocity square is G m over our, which tells you that velocity is taking square with both sides. Is GM over our says square root. I'm sorry. So the velocity depends on the inverse square root off distance because it appears in the denominator under the square root.

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