The fantasy of rising above the surface of the Earth and flying out among the stars is as old as the human imagination itself. After Marco Polo brought back Chinese gunpowder to the 13th century Europeans, they were able to militarize it into firearms, and the technology of chemically-propelled ballistics took off so that by the early 20th century rockets intended to fully penetrate Earth’s atmosphere and drift out into Outer Space were being visualized and tested.
William Leitch in 1861 and Konstantin Tsiolkovsky in 1903 expressed the idea of using rockets to enable human spaceflight. From 1920 Robert Goddard proposed improvements to rocket design, and in 1926 built and launched the first modern rocket. That modernity was marked by the first use of a converging-diverging exhaust tube — known as a de Laval nozzle — which enabled the hot exhaust gases emitted by the combusting rocket fuel to convert their heat energy into outward unidirectional motion at supersonic speed: thrust!
But with the exception of tinkerers like Goddard, rockets were used as military weapons — artillery — most dramatically by Nazi Germany from 1943 with its V2 ballistic missile rocket-bombs. The American space program began in 1945 with the use of captured German V2 rockets to send cameras and scientific probes into the upper atmosphere. The USSR’s independent space program began in the 1950s, making a dramatic breakthrough — shocking Americans — with the lofting of Sputnik 1, the first artificial Earth satellite, which was launched into an elliptical low Earth orbit on 4 October 1957. It orbited for three weeks before its batteries died and then orbited silently for two months before it fell back into the atmosphere on the 4th of January 1958.
The major thrust of both American and Soviet rocket development throughout the 1950s and 1960s was to construct intercontinental ballistic missiles that could carry nuclear warheads, and have such capability presented as a threat display to deter aggression by other technologically advanced and militarily powerful adversaries: the Cold War. Putting men as the payloads in such large rockets and blasting them into Earth orbit, and eventually out to the Moon, was primarily a flagrant display to all, signaling the possession of awesome military power. Science exploration was a minor byproduct of the space race, but ultimately some of that scientific curiosity yielded the most beneficial results from the entire rocketry endeavor.
Now, 52 years after Neil Armstrong first set a human foot on the Moon, propelled by American public funding, at least three of our attention-seeking Billionaire Boys are competing to burn up disposable bundles of their money to launch themselves into space joyrides, and to then exploit the technology they have paid to have built as the basis of “space tourism” businesses.
On Tuesday, 20 July 2021, Jeff Bezos and three others were blasted in his rocket up to an elevation of 106 km above the surface of the Earth, for a two-way trip totaling 10 minutes and 10 seconds. To some this is a laudable achievement of the free market system, while to others it is a pathetic expansion of conspicuous consumption to a new exorbitant level. Many ask: could the billions extracted from the labor of Bezos’s exploited and precarious workforce not have been better spent to alleviate hunger and homelessness?, and could the massive amount of chemical energy expended to pull off this stunt not have been better used with much greater efficiency to power broadly beneficial purposes on the surface of the Earth? But such questions mistake applying standards of human solidarity and social responsibility to seek understanding billionaire’s egotistical behavior. Here, I will provide one answer to the energy question.
The minimum energy needed to loft any mass up to 106 km above the surface of the Earth is 1,022,842.066 Joules per kilogram (J/kg). So, for the total energy expenditure in any specific case, multiply the mass of the fully loaded rocket (in kg) by 1,022,842.066 Joules/kg. One joule is the energy required to lift a medium-sized tomato up 1 meter (3 ft 3 in), assuming the tomato has a mass of 101.97 grams (3.597 oz). Lofting a mass up to 106 km above the surface of the Earth requires as much energy as lifting it only 1 meter above the Earth’s surface 104,265 times.
Outer Space is considered to begin at elevation 100 km, which is called the Von Karman Line (after a renowned aerodynamicist). Satellites in Low Earth Orbit have elevations between 180 km and 2,000 km; in Mid Earth Orbit, 2,000 km to 35,780 km elevation; in Geosynchronous Orbit at 35,780 km elevation; in High Earth Orbit beyond 35,780 km; and the Orbit of the Moon occurs at a distance of 378,032 km from the Earth’s surface.
It requires 9.81 Joules of energy to lift a 1 kg mass 1 meter above the surface of the Earth (or 9.81 of those 3.597 ounce tomatoes, all at once). In terms of “g’s” pulling a mass “down” toward the center of the Earth, the g-force at the surface of the Earth is 1g, the g-force at 106 km is 0.968g, the g-force at 180 km is 0.946g, the g-force at 2,000 km is 0.579g, the g-force at 35,780 km is 0.023g, and the g-force at 378,032 km (the distance to the Moon) is negligible at 0.0002747g.
Satellites in stable orbits around the Earth need an additional energy to accelerate them up to an orbital velocity, and it is this boost to lateral momentum, in combination with the “centrifugal” (radial) pull by Earth’s gravity, that results in the curved trajectory that describes the satellite’s stable orbit, which can be either circular or elliptical.
I do not know the weight of Bezos’s rocket (I have not seen it published), but IF I assume it weighed as much as a fully loaded Boeing 707 jet airplane, 150,000 kg, then the total (minimum) energy to lift it up to 106 km would have been 1.534×10^11 Joules = 153.4 gigajoules (GJ). Whatever the actual weight was, lofting it to an elevation of 106 km requires at least 1.023 megajoules/kilogram (MJ/kg).
I am guessing that small rockets, perhaps comparable to Bezos’s, could weigh half as much (or less) as a Boeing 707 airplane (~10s of thousands of kg), and I am certain that Bezos’s rocket was much smaller than the the Saturn V rockets that lofted the Apollo Moon missions, and which initially weighed about 2.8 million kg.
The real issue is that blasting stuff up into space — away from Earth and against its gravity — is immensely energy intensive. Given that one has that energy in the first place, why use/waste inordinate amounts of it to loft small payloads into space? For a few items like weather and GPS satellites, space telescopes, and tiny robotic planetary probes, I think it is worthwhile for the expansion of scientific knowledge and the physical improvement of social conditions. But for almost all else, and most especially manned space flight, it is the total waste of space junk littering militarism and propaganda.
And now, symptomatic of our dysfunctional economics, manned space flight has also become just another item of supremely exclusive and very showy personal conspicuous consumption. As Eeyore would gloomily intone in the Winnie-the-Pooh books: “Pathetic.”
Here’s a short report in PDF form is freely available to anyone interested in the details of my calculations.