Energy. on this world and elsewhere. Instructor: Gordon D. Cates Office: Physics 106a, Phone: (434)

Transcription

1 Energy on this world and elsewhere Instructor: Gordon D. Cates Office: Physics 106a, Phone: (434) Course web site available at click on classes and find Physics or at Lecture #26 November 28, 2017

2 Energy Elsewhere

3 Putting things in low Earth orbit (LEO) The object must be going fast enough that as it falls it follows the (circular) surface of the Earth. Virtually all of the energy must be put into making the object move SIDEWAYS. Almost no energy goes into overcoming the gravity well of the Earth. The necessary speed is roughly 7.9 x 103 m/s (17,672 mph)

4 Putting things in low Earth orbit (LEO) The object must be going fast enough that as it falls it follows the (circular) surface of the Earth. Virtually all of the energy must be put into making the object move SIDEWAYS. Almost no energy goes into overcoming the gravity well of the Earth. The necessary speed is roughly 7.9 x 103 m/s (17,672 mph)

5 So how much energy per kg? Energy = ½mv 2 Energy per unit mass = ½mv 2 /m E/kg = ½v 2 = ½(7.9 x 10 3 m/s) 2 E/kg = 31.2 x 10 6 J/kg This is for an orbit essentially skimming the Earth s surface.

6 The rocket equation (one way of quantifying the problem) V m mass = m(t) V(t) e (ΔV/Vm) = ~9.2 for low Earth orbit, and 21.4 for geosynchronous orbit.

7 That is why rockets are so huge!

8 That is why rockets are so huge!

9 To move to higher orbits, in addition to speed, you also need to overcome the potential energy trap GMm r The object at left has enough velocity to climb out of the Earth s gravitational well, but NOT enough to stay in orbit. For high orbits, you need kinetic energy equal to the depth of the potential well PLUS kinetic energy for orbital velocity.

10 To move to higher orbits, in addition to speed, you also need to overcome the potential energy trap GMm r The object at left has enough velocity to climb out of the Earth s gravitational well, but NOT enough to stay in orbit. For high orbits, you need kinetic energy equal to the depth of the potential well PLUS kinetic energy for orbital velocity.

11 Energies to move around the earth/moon system Plot includes both required speed and climbing out of a gravity well. One somewhat subtle point, it takes energy to move down as well as to move up.

12 The energy Budget to reach different places These include both the energy needed to climb the potential well as well as accounting for the right orbital speed.

13 Energy to go to GEO from earth This one is easy, its just 57.8 MJ/kg. It includes both: - the energy needed to climb out of the gravitational well - the energy needed to stay up there, in other words, the kinetic energy necessary to stay in orbit. What it does NOT include is wasted energy. It imagines that we just magically put our payload where we want it with perfect efficiency!

14 Energy that is necessarily wasted when using rockets V m mass = m(t) V(t) When a rocket fires exhaust out its back end, chemical energy is released in order to provide kinetic energy to the exhaust. The rocket thus acquires kinetic energy and moves forward. But the exhaust ALSO has kinetic energy. That energy also needed to come from the exhaust. Finally, the engine is not perfectly efficient. Some energy does not go into nice ORGANIZED movement of the exhaust traveling backwards. Some goes into random thermal energy (i.e. the exhaust is HOT). Also, some of the exhaust does not go straight backward. So... Energy needed to get to GEO = 57.8 MJ/kg x 2.17 x 2 = 251 MJ/kg Accounts for KE of exhaust. Accounts for efficiency of rocket engine.

15 O Neill s Answer for developing space more efficiently Build stuff in space. Don t launch using rockets!!

16 What is the minimum difference in energy getting to GEO from the moon instead of from Earth?

17 What is the minimum difference in energy getting to GEO from the moon instead of from Earth? 57.8 MJ/kg

18 What is the minimum difference in energy getting to GEO from the moon instead of from Earth? 2.9 MJ/kg 57.8 MJ/kg

19 What is the minimum difference in energy getting to GEO from the moon instead of from Earth? 62.0 MJ/kg MJ/kg = 4.2 MJ/kg 2.9 MJ/kg 57.8 MJ/kg

20 What is the minimum difference in energy getting to GEO from the moon instead of from Earth? 62.0 MJ/kg MJ/kg = 4.2 MJ/kg 2.9 MJ/kg 57.8 MJ/kg From this you would conclude that it is 57.2/( ) = 57.2/7.1 = 8.1 times easier to go from the moon.

21 What is the energy needed to go to GEO from Earth s surface when we include rocket inefficiencies The rocket s exhaust will have kinetic energy V m mass = m(t) V(t) The rocket s exhaust will also have heat energy Energy needed to get to GEO = 57.8 MJ/kg x 2.17 x 2 = 251 MJ/kg Accounts for KE of exhaust. Accounts for efficiency of rocket engine. So practically speaking, it doesn t take 57.8 MJ/kg, it takes more like 251 MJ/kg So really, it is 252/7.1 = 35.5 times easier to go from the moon.

22 Rockets can be avoided when launching from the surface of the moon by using mass drivers

23 Energy to go to GEO from the moon 2.9 MJ/kg to climb out of the moon s gravity well MJ/kg MJ/kg = 4.2 MJ/kg to move from the moon s orbit to GEO. You can assume almost perfect efficiency using the mass drivers on the moon. Result: energy needed (moon to GEO) = 2.9MJ/kg + 4.2MJ/kg = 7.1 MJ/kg So really, it is 252/7.1 = 35.5 times easier to go from the moon.

24 Demonstration of a small mass driver

25 Demonstration of a small mass driver

26 Okay, from an energy perspective, it is clearly easier to move stuff to GEO from the moon But is energy really what is driving costs?

27 Costs for going to GEO from Earth energy = 251 MJ/kg 1 gallon gasoline = 1.2 x 10 8 J Cost of 1 kg going to GEO = 251 x 106 J 1.19 x 10 8 J = 2.1 gallons of gas Can this possibly be right?

28 Costs for going to GEO from Earth Market cost to put 1 kg in GEO = ~$60,000 Market cost of 2.1 Gallons of gas = ~$6.00 Just a small discrepancy of a factor of 10,000!!! What s going on? That fact is that the cost is not in the energy, the cost is in the ROCKET.

29 Reusable rockets could drive cost way down!!! Eventually, the energy costs could end up dominating, and living and manufacturing in space could be the way to go, but at present, that is not the case.

30 Short/Medium-term reasons to develop human space flight Exploration, the search for extraterrestrial life, basic science. Space tourism Orbiting solar power stations Mining Asteroids (at least two companies already exist) Valuable metals such as gold, platinum, silver, iridium and others. Other elements that are in limited supply such as rare earth s Water, that could be converted into rocket fuel (hydrogen and oxygen) to enable refueling without launching fuel from the Earth. Space manufacturing where zero-gravity is an advantage. Eventually make satellites in space? Colonization

31 Video from the company Planetary Resources

32 Video from the company Planetary Resources

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