Energy on this world and elsewhere Instructor: Gordon D. Cates Office: Physics 106a, Phone: (434) 924-4792 email: cates@virginia.edu Course web site available at www.phys.virginia.edu, click on classes and find Physics 1110. or at http://people.virginia.edu/~gdc4k/phys111/fall17/home.html Lecture #27 November 30, 2017
Energy Elsewhere
Issues when living in space Artificial gravity - probably necessary for long-term habitation. Radiation shielding - important issue for anything other than low-earth orbit. All this leads to structures that are large enough to have artificial gravity, and massive enough to have radiation shielding. We will see, however, that the structures cannot be too big or they will tear themselves apart.
Issues when living in space
In the absence of artificial gravity, exercise is necessary to avoid negative effects
In the absence of artificial gravity, exercise is necessary to avoid negative effects
In the absence of artificial gravity, exercise is necessary to avoid negative effects
In the absence of artificial gravity, exercise is necessary to avoid negative effects
Artificial gravity Spin the spacecraft so that the centrifugal force causes artificial gravity. If you ve ever been on certain amusement park rides, you know this is not always a good idea. Quote from O Neill s book.
Artificial gravity in the movie 2001 Rotation period as a function of radius r and acceleration: T =2 r/a Something as small as this would need to spin way too fast. If we assume a 10 meter radius, the period of rotation would be around 6 seconds.
Artificial gravity in the movie 2001 Rotation period as a function of radius r and acceleration: T =2 r/a Something as small as this would need to spin way too fast. If we assume a 10 meter radius, the period of rotation would be around 6 seconds.
One thought was that early habitats could be built out of the shuttle s external fuel tanks
O Neill s Island One Spherical living space is one mile in circumference (radius of around 256 meters). If spun with a rotation period of 30 seconds, the artificial gravity would feel like earth s along the equator. Living space is shielded against radiation. Agriculture conducted in unshielded toruses. Zero-g industry at each end. Solar collectors provide energy. Radiators dissipate excess heat. So something around 250 meters is the smallest size that is safe against motion sickness.
O Neill s Island One Would house around 10,000 people
Constructing Island I Mass ~ 3 x 10 9 kg Mass of USS George Washington (Aircraft carrier): 1.1 x 10 6 kg Island I is x28 bigger!!! From the surface of the Earth Days of Oil = (251 MJ/kg)(3x10 9 kg) (6000 MJ/barrel)(19x10 6 barrels/day) = 6.6 days From the surface of the Moon Days of Oil = (7.1 MJ/kg)(3x10 9 kg) (6000 MJ/barrel)(19x10 6 barrels/day) = 0.19 days = 4.5 hours Even launching from the Earth s surface, at $100/barrel, the energy cost would be $12.5 billion. Clearly, energy is not the dominant cost for constructing something like Island I.
Cost of Constructing Island I Mass ~ 3 x 10 9 kg Mass of USS George Washington (Aircraft carrier): 1.1 x 10 6 kg Island I is x28 bigger!!! Cost of oil, if sending everything up from the Earth: $12.5 Billion Cost using current market price for payloads heading to GEO: $180 Trillion Cost if payload costs go down by factor of 100: $1.80 Trillion Maybe launching from the moon isn t so crazy. Need to imagine a whole new way to develop extraterrestrial construction projects, perhaps self-replicating construction robots?
The Stanford Torus Diameter of 1.9 km This gives a rotation period of 1 minute for 1 g (Earth gravity) Was imagined to house between 10,000 and 140,000 inhabitants. One of many ringshaped space stations imagined over the years.
Inside the Stanford Torus
Could we go smaller? Before the first people went into orbit, people wondered whether humans could even survive weightlessness. Mars is just over 1/3 Earth gravity. Could we live with this long term? If so, the required radius could drop by around a factor of three. gravity is proportional to radius (all other things remaining equal) Volume, or total mass, could be down by 3 3 =27! Perhaps a mass reduction of 100? More?
What limits the size of space colonies with artificial gravity? Answer: tensile strength Required tensile strength = Radius x (density of material) x g artificial The strength of the material out of which the space habitat is constructed rises linearly with the radius of the spinnig structure.
What limits the size of space colonies with artificial gravity? Island Three contains two cylinders, each with a diameter of 4 miles (radius of 3,220 m) and a length of 20 miles. land area up to 250 mi 2!! Required Tensile strength = 3,220 m 2710 kg/m 3 9.81 m/s 2 = 86x10 6 N/m 2 Density of aluminum Acceleration of gravity on earth Aluminum starts to deform around 95x10 6 N/m 2 - still (marginally) possible with Al!
It appears that colonizing space within our solar system is (marginally) within the energy scales of our current civilization.
What about star travel?
Island I as a starship Mass ~ 3 x 10 9 kg Assume travel at 1/4 speed of light. Let s compute the kinetic energy this represents. Kinetic energy = 1/2 m v 2 = (1/2)( 3 x 10 9 kg)(0.25 x 3 x 10 8 m/s) 2 = 8.4 x 10 24 Joules What is this in days (or years) of U.S. oil consumption? 8.4 x 10 24 Joules) Days of Oil = (6000 MJ/barrel)(19x10 6 barrels/day) = 7.4 x 10 7 days = 200,000 years Even if you assume a starship 100 times less massive, this is still 2000 year s worth of U.S. oil consumption. The bottom line? Interstellar travel will take absolutely huge energy consumption.
What is the right energy scale for a starship? Earth has radius of 6.37x10 6 meters. Intensity of the sun above atmosphere is roughly 1.4x10 3 W/m 2. The above two bullets imply that the Earth receives around 1.78 x 10 17 J/s. For 8.4 x 10 24 J (the kinetic energy of Island I traveling at 0.25 times the speed of light), this is 545 days worth of sunlight! Whether we imagine a starship as large as Island I, or a starship 100 times less massive, the energy needed is at the scale of the energy that falls on the entire Earth for somewhere between 1 day and 1 year!
So.. What is the most the human race might be able to do to provide itself with energy?
Paper by Freeman Dyson in Science, vol. 131, pg. 1667 (1960)
Paper by Freeman Dyson in Science, vol. 131, pg. 1667 (1960) Dyson then examines the available energy (that coming from the star), the available material (he considers the mass of Jupiter as being typical), and the time it would take, from an energy perspective, to disassemble Jupiter and rearrange the solar system. He then concludes that:
Paper by Freeman Dyson in Science, vol. 131, pg. 1667 (1960)
Paper by Freeman Dyson in Science, vol. 131, pg. 1667 (1960)
Dyson Spheres A solid spinning object would tear itself apart. Instead, a system of many orbiting objects could be used.
Dyson Spheres have inspired science fiction... Larry Niven s Ringworld, similarly the world of Halo, spinning to achieve artificial gravity, would actually not work. A system of objects, however, could be feasible.
Even Star Trek episodes... This is a YouTube clip of a Star Trek episode along with some commentary...
Even Star Trek episodes... This is a YouTube clip of a Star Trek episode along with some commentary...
Dyson Spheres Dyson himself states: I do not argue that this is what will happen in our system; I only say that this is what may have happened in other systems.