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Ch 15: Oscillations
Chapter 15, Problem 13

Nothing can escape the event horizon of a black hole, not even light. You can think of the event horizon as being the distance from a black hole at which the escape speed is the speed of light, 3.00 ✕ 10⁸ m/s, making all escape impossible. What is the radius of the event horizon for a black hole with a mass 5.0 times the mass of the sun? This distance is called the Schwarzschild radius.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Event Horizon

The event horizon is the boundary surrounding a black hole beyond which no information or matter can escape. It represents the point at which the escape velocity equals the speed of light, making it impossible for anything, including light, to break free from the gravitational pull of the black hole.
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Schwarzschild Radius

The Schwarzschild radius is the radius of the event horizon for a non-rotating black hole. It is directly proportional to the mass of the black hole and can be calculated using the formula r_s = 2GM/c², where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.
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Escape Velocity

Escape velocity is the minimum speed needed for an object to break free from the gravitational attraction of a celestial body without any additional propulsion. For a black hole, this speed reaches the speed of light at the event horizon, illustrating the extreme gravitational forces at play.
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Related Practice
Textbook Question

Two Jupiter-size planets are released from rest 1.0 x 10¹¹ m apart. What are their speeds as they crash together?

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Textbook Question
Two stars, one twice as massive as the other, are 1.0 light year (ly) apart. One light year is the distance light travels in one year at the speed of light, 3.00 ✕ 10⁸ m/s . The gravitational potential energy of this double-star system is ─8.0 ✕ 10³⁴ J. What is the mass of the lighter star?
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Textbook Question
The Parker Solar Probe, launched in 2018, was the first spacecraft to explore the solar corona, the hot gases and flares that extend outward from the solar surface. The probe is in a highly elliptical orbit that, using the gravity of Venus, will be nudged ever closer to the sun until, in 2025, it reaches a closest approach of 6.9 million kilometers from the center of the sun. Its maximum speed as it whips through the corona will be 192 km/s. (b) The probe's highly elliptical orbit carries it out to a maximum distance of 160 Rₛ with a period of 88 days. What is its slowest speed, in km/s?
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Textbook Question
What is the escape speed from Jupiter?
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Textbook Question
A rocket is launched straight up from the earth's surface at a speed of 15,000 m/s. What is its speed when it is very far away from the earth?
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Textbook Question
A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?
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