Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 22: Problem 46

What is the Schwarzschild radius of a black hole whose mass is that of (a) the Earth, (b) the Sun, (c) the supermassive black hole in NGC 4261 (Section 22-5)? In each case, also calculate what the density would be if the matter were spread uniformly throughout the volume of the event horizon.

Short Answer

Expert verified
The Schwarzschild radius and density obtained depend on the mass of each celestial body. You obtain them using the described formulas in the steps provided above.

Step by step solution

01

Calculate Schwarzschild radius

For each of the given masses (Earth, Sun, supermassive black hole in NGC 4261), calculate the Schwarzschild radius using the formula \(r_s = \frac{2GM}{c^2}\). Note that the mass should be in kilograms, the gravitational constant G in \(m^3 kg^{-1} s^{-2}\) and the speed of light c in \(m s^{-1}\). The result will be in meters.
02

Calculate the volume

Next, calculate the volume of the sphere with radius \(r_s\) using the formula \(V = \frac{4}{3}πr_s^3\).
03

Calculate Density

Finally, calculate the density using the formula \(\rho = \frac{m}{V}\) where m is the mass of the black hole (in Kg) and V is the volume (in cubic meters).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You drop a ball inside a car traveling at a steady \(50 \mathrm{~km} / \mathrm{h}\) in a straight line on a smooth road. Does it fall in the same way as it does inside a stationary car? How does this question relate to Einstein's special theory of relativity?

What is a gamma-ray burster? What is the evidence that gamma-ray bursters are not located in the disk of our Galaxy or in a halo surrounding our Galaxy?

A twenty-third-century instructor at Starfleet Academy tells her students, "If someday your starship falls into a black hole, it'll be your own fault." Explain why it would require careful piloting to direct a spacecraft into a black hole.

How do astronomers locate supermassive black holes in galaxies?

If even light cannot escape from a black hole, how is it possible for black holes to evaporate?
See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Space Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Circular Motion and Gravitation

Read Explanation

Radiation

Read Explanation

Wave Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free