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In this video, we're going to be doing a quick example, working with orbital motion.
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Okay, what we have is we found a small planet, and it's an orbit around a star, and it's orbital distance.
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Okay, so the radius of the orbit r equals one a, u, so one astronomical unit.
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And the period of orbit t equals 2 .0 years.
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Okay, and what we want to find is the.
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Mass of the star relative to the sun.
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Okay? so we don't know this.
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How do we find this? i have a relationship between orbital radius, period, and mass for a given system.
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And that relationship is period squared over r cubed equals 4 pi squared over g.
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That's a gravitational constant.
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Times the mass of the larger body.
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Okay, so that will be the body that the smaller object is orbiting.
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For the earth, this mass would be the mass of the sun.
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For people on the new planet that we found, that would be the mass of our new star.
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Okay, so let's put numbers into this equation for both the earth and the new star.
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Okay, so for the earth, i have t squared is one year.
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Year squared over one a u cubed...