A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. (a) One of these stars is believed to be in an approximätely circular orbit with a radius of about 1.50 x 10" AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting.

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Chapter1: Units, Trigonometry. And Vectors
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A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a
clue to the size of this black hole.
(a) One of these stars is believed to be in an approximātely circular orbit with a radius of about 1.50 x 10° AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is
orbiting.
kg
(b) What is the speed of this star?
V
star
m/s
How does it compare with the speed of the Earth in its orbit?
V star
VEarth
How does it compare with the speed of light?
V
star
Transcribed Image Text:A massive black hole is believed to exist at the center of our galaxy (and most other spiral galaxies). Since the 1990s, astronomers have been tracking the motions of several dozen stars in rapid motion around the center. Their motions give a clue to the size of this black hole. (a) One of these stars is believed to be in an approximātely circular orbit with a radius of about 1.50 x 10° AU and a period of approximately 30 yr. Use these numbers to determine the mass of the black hole around which this star is orbiting. kg (b) What is the speed of this star? V star m/s How does it compare with the speed of the Earth in its orbit? V star VEarth How does it compare with the speed of light? V star
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