What is the Schwarzschild radius of a black hole that has a mass equal to the average mass of a person (-70 kilograms)?

The gravitational constant, denoted as \(G\), is a key quantity in Newton's law of universal gravitation. It describes the strength of the gravitational force between two objects. The value of \(G\) is \(6.67430 \times 10^{-11} \ \text{m}^3/\text{kg}\text{·s}^2\).
This small number indicates that gravity, compared to other fundamental forces, is quite weak. The gravitational constant links mass and distance to the force of gravity. It's essential for calculating gravitational effects between celestial bodies, like the Earth and the Moon, or in our specific exercise, for computing the Schwarzschild radius of a black hole.

To see \(G\) in action, let's revisit our formula for the Schwarzschild radius: \( r_s = \frac{2GM}{c^2}\). Here, \(G\) helps us understand how tightly mass influences the curvature of spacetime, contributing to determining the event horizon of a black hole.

The speed of light, represented as \(c\), is crucial in both relativity and our formula for the Schwarzschild radius. It has a fixed value of \(3.00 \times 10^8 \ \text{m/s}\). This value is essential because nothing can travel faster than light in a vacuum.
In the context of black holes, the speed of light determines the escape velocity at which even light cannot escape the black hole's gravitational pull. This concept is central to the event horizon – the point beyond which nothing, not even light, can return.
Let's consider our formula again: \( r_s = \frac{2GM}{c^2}\). The term \(c^2\) in the denominator shows the immense speed light travels. It also shows how much energy is required to counter gravity at the Schwarzschild radius.
In simpler terms, the speed of light modulates how the immense mass of a black hole influences spacetime. The larger the mass, the more severe the warping, and hence, a larger event horizon.

Black holes are fascinating and mysterious objects in our universe. A black hole forms when a massive star collapses under its own gravity, compressing its mass into an incredibly small space. This leads to an extremely strong gravitational pull.
The Schwarzschild radius defines the size of a black hole’s event horizon, the point of no return. If an object crosses this boundary, it cannot escape the black hole’s gravity and will eventually be pulled in.
It's exciting to note how this applies to our exercise: the Schwarzschild radius of a black hole with a mass of 70 kg (the approximate mass of a person) is about \(1.04 \times 10^{-25} \text{m}\). Even though this radius is extremely tiny, it showcases the concept of how mass, no matter how small, can theoretically form a black hole if compressed into a sufficiently small space.
Thus, black holes aren't just about immense masses like stars, but rather about the density and how this mass warps the fabric of spacetime. This makes black holes such an intriguing topic in the study of astrophysics.