Exploring the Black Hole in Interstellar and Its Size

One of the most intriguing elements in the sci-fi film Interstellar is the depiction of the black hole known as 'Gargantua.' This essay delves into the actual size of the black hole in Interstellar and compares it with real-world black holes, such as the one at the center of our Milky Way galaxy, Sagittarius A*, and M87.

sizes of black holes in Interstellar

In Interstellar, the black hole 'Gargantua' is portrayed as having a mass of 100 million solar masses. To understand just how massive this is, we must compare it with real-world black holes. The black hole at the heart of our Milky Way, Sagittarius A*, has a mass of only 4.3 million solar masses. Therefore, 'Gargantua' is about 23 times larger than Sagittarius A*.

However, albeit impressive, 'Gargantua' is far from being the largest black hole we know. For example, the black hole M87, recently imaged by the Event Horizon Telescope (EHT), has a mass of 6.5 billion solar masses. M87 is itself not the largest known black hole, as there are larger ones with even more remarkably high masses.

Dimensions of a 100 Million Solar Mass Black Hole

The size of a black hole is primarily determined by its event horizon, which can be calculated using Schwarzschild's radius. The Schwarzschild radius (Rs) for a black hole of mass M is given by the formula:

Rs 2GM/c^2

For a 100 million solar mass black hole, the Schwarzschild radius would be:

Rs 2G x (100 x 10^6) M_☉ / c^2

Where G is the gravitational constant (6.6743 x 10^-11 m^3/kg.s^2), M_☉ is the mass of the Sun (1.99 x 10^38 kg), and c is the speed of light in a vacuum (3 x 10^8 m/s). Substituting the values, we get:

Rs 2 x 6.6743 x 10^-11 m^3/kg.s^2 x 100 x 10^6 x 1.99 x 10^38 kg / (3 x 10^8 m/s)^2

Rs 2.66743 x 10^28 m^3.s^2 / 9 x 10^16 m^2.s^2

Rs 2.96 x 10^11 meters

This means the event horizon of a 100 million solar mass black hole would be approximately 2.96 x 10^8 kilometers, or about 184 million miles. In terms of astronomical units (AU), this event horizon would extend to about 1.97 AU from the center of the black hole.

For comparison, the distance between the Sun and the Earth is 1 AU, which is approximately 150 million kilometers or about 93 million miles. The event horizon of Gargantua would be roughly two times the distance from the Sun to the Earth, which explains why it stretches beyond the orbit of Mars, which is located at 1.52 AU from the Sun.

While 'Gargantua' in Interstellar is a highly dramatized and artistic representation of a black hole, it serves as a fascinating point of discussion for both science and entertainment. The giant Schwarzschild radius of such a black hole challenges our understanding of relativity and the behavior of gravity on an astronomical scale.

Conclusion

Understanding the size of a black hole like 'Gargantua' in Interstellar provides a unique perspective into the vast scale of the universe. It highlights the remarkable difference between dramatized cinematic depictions and the scientifically accurate models of black holes.

With advancements in technologies such as the Event Horizon Telescope, the scientific community continues to unravel the mysteries of these fascinating celestial bodies. As we learn more, we can continue to refine our understanding and better appreciate the wonders of the universe.