Even the Tiniest Frog Can Become an Astronaut by Jumping From the Surface of a Mile-Size Asteroid
The OSIRIS-REx mission collected 70.3 grams of rocks and dust from the asteroid Bennu and delivered it back to Earth on September 24, 2023. Given its diameter of half a kilometer, the escape speed from the surface gravity of Bennu is 18 centimeters per second. This means that even the smallest frogs, shorter than a thumbnail, can easily escape from the surface of this asteroid to space through a single jump. This backdrop constitutes the easiest way of becoming an astronaut!
The muscle power responsible for the world record in high-jump, 2.45 meters on Earth, would enable a qualified athlete to escape from the surface gravity of a rock that is about 10 kilometers in diameter. This scale matches roughly the length of Manhattan island or the Chicxulub impactor which killed non-avian dinosaurs when it collided with Earth 66 million years ago.
However, it is impossible for the muscle power of any terrestrial animal to enable escape from much larger rocks. For example, the escape speed from the Moon is 2.4 kilometers per second. For Mars it doubles to 5 kilometers per second, whereas for Earth it doubles again to 11.2 kilometers per second. In all these cases, escape is however possible by boarding chemical rockets. The hot gas produced by burning rocket fuel achieves an exhaust speed of a few kilometers per second and the rocket equation allows a terminal payload speed that exceeds the exhaust speed by the natural logarithm of the ratio between the initial mass of the fuel plus payload divided by the final mass of the payload alone.
Escape from the solid surface of objects larger than Earth is more challenging. The escape speed from a rocky planet increases as mass to the power of 0.2–0.3 above the mass of Earth. Chemical propulsion is impractical above fifty Earth masses, since the mass in chemical fuel needs to exceed the payload mass by a factor larger than a thousand.
But there are even more massive objects with a solid surface. At the end of its life, the core of the Sun will cool to become a white dwarf, namely a metallic ball of roughly the radius of the Earth containing about 60% of the mass of the Sun. The escape speed from the surface of a white dwarf, roughly 5,000 kilometers per second, can only be achieved by a nuclear engine.
An even more compact object is a neutron star, formed as a result of the collapse of the core of a massive star with 8–25 times the mass of the Sun. Typically, neutron stars pack 1.4 solar masses within a 12-kilometer radius, comparable to the size of the Chicxulub impactor. The corresponding escape speed here is 180,000 kilometers per second, just above half the speed of light. Escape here is best served by light sails that are propelled to the speed of light by a powerful laser beam, similar to the concept of the Starshot initiative that I had been leading in recent years.
Finally, there is no way to escape from a black hole, irrespective of the propulsion scheme.
Given this cosmic perspective, we must be grateful for the coincidence that chemical propulsion allows astronauts to escape from Earth and from the habitable zone around the Sun towards interstellar space. The engineering challenge for civilizations that were born on more massive objects or closer to their host stars is larger. On this Thanksgiving holiday our space agencies should extend gratitude to mother nature for being so kind to earthlings.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He chairs the advisory board for the Breakthrough Starshot project, and is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. His new book, titled “Interstellar”, was published in August 2023.
