Gravitational Forces

! Physics of ! F = force of attraction ! Force: F = G M m / r2 Orbits & Transportation ! G = ! Potential E = - G M m / r ! M = mass of central body ! m = mass of orbiting body ! Kinetic E = ! m v2 ! Inverse square law ! Total E = PE + KE Karen J. Meech, Astronomer ! Escaping gravity requires ! Energy of motion > Institute for Astronomy gravitational potential energy ! KE > PE ! ! m v2 > G M m / r ! Escape 0.5 ! vesc = (2 G M / r) ! Circular Velocity 0.5 ! vcirc = (G M / r) Gravitational Potential Well

Gravity Wells in the - System

Special Orbits Orbital Debris

! Where is the junk? ! Low Earth (LEO) ! Most is in LEO, GEO is getting crowded ! 300-600 km altitude ! 4600 missions since 1957 ! Geostationary orbit (GEO) ! NORAD Space Surveillance network ! tracks all bits > 10 cm ! Orbit period = 24 hrs ! 1.1 x 104 bits > 10 cm ! Positioned above same spot on Earth ! > 500,000 bits > 1 cm ! Used for weather and communication ! Source of debris ! Radius = 42,233 km ! GEO ! Bits from spacecraft ! = 6,378 km ! t = distance / v ! Non-functioning satellites ! Altitude = 35,855 km ! distance = 2 ! r ! Typical LEO ~ 7-8 km / s 0.5 ! vcircular = (G M / r) ! NASA 1995 policy to limit ! t = 2 ! r / (G M / r)0.5 ! r = (G M t2 / 4 !2)1/3 Space Travel Style

Conics Sections Hohmann Orbit Transfers

Orbit Terminology ! Space travel in a gravity well " non intuitive Apo farthest point ! Apply Newton’s 3rd law Peri closest point ! Force – a mass x acceleration Eccentricity how circular (0=circle) ! Thrust – a force to make a change Inclination orbit angle to Earth in velocity: "v Gee central body = Earth ! "v in direction of motion Helios central body = ! adds orbital E ! Circular: eccentricity increase Jove central body = Jupiter ! new thrust point becomes the Lun central body = Moon apogee ! Eccentric: Circularize orbit ! "v opposite motion ! Decrease orbital E ! Total “energy” required:

"vTotal = "v1 + "v2

Propulsion – Equation Launch “To every action there is an equal or opposite reaction” Windows

! Mv

! Means of optimizing “expense” of mission ! We must provide a force to overcome the Earth’s gravitational attractive force ! Caculate Energy required for various geometries ! Expansion of hot gas from nozzle ! Constrain arrival time ! Consider fuel budget (mass) ! Creates a force in opposite direction ! Force = mass x acceleration ! F = mass "v / "t mV ! Mv = mV ! Propulsion Performance ! KE > PE 0.5 ! vesc = (2 G M / r) 0.5 ! vcirc = (G M / r) ! Specific Impulse (SI) ! Gravity Wells ! Measure of the amount of change in momentum for the ! Governs motion in Solar sys. Summary mass of fuel used ! Special orbits LEO / GEO ! How many seconds1 lb of fuel burns at thrust of 1 lb ! 300-600 km altitude ! A high SI engine does need as much fuel to reach a ! Period = 24 hr: 42,233 km from earth center given velocity ! Orbit Transfers (Hohlmann) ! Add/remove E with "v ! Cost = "v; minimize E ! Propulsion ! Relies on Newton’s laws ! Rocket Equation:

(Mv)rocket = (mV)propellant ! Engine type comparison ! Specific Impulse (efficiency) ! Acceleration

Chemical Rockets Comparison of Liquid Propellants

! Combustion (burning) Propellant Type SI ! Sequence of chemical reactions between a fuel and oxidant ! Chemical bonds are broken " Energy released NTO/MMH Earth Storable 317 ! Requires fuel + oxidizer O2/CH4 Space Storable 330 ! Jets: fuel + oxygen from air for the oxidant ! Rockets: LH2, LOx O2/H2 Refrigerated (50K = -368F) 423 ! Best Fuels CIF /N H Space Storable 329 ! Burn at high T (lots of E) " high exhaust v 5 2 4 ! Low molecular weight " higher exhaust v OF2/C2H4 Space Storable 375 ! Disadvantage ! Most of mass lifted is propellant N2F4/N2H4 Space Storable 358 ! Reason for multiple stages F2/N2H4 Space Storable 376 ! Specific Impulse ! Most fuels: 250-290 sec OF2/C2H6 Space Storable 370 ! LOx, LH2 : 480 sec OF2/B2H6 Space Storable 325

Solid Rockets Ion Drives

! Less complex than liquid ! Mixture of fuel and oxidizer ! Composition ! Create an ionized gas ! Separate charges with E field ! ! Tested on DS 1 spacecraft Black powder (gunpowder) ! Merge the beams – gas ! Used on DAWN ! Zinc, sulfur (oxidizer) accelerates ! Advantages ! Proposed for our mission ! Many others . . . . ! High outflow velocity ! Pro: ! SI ~ 3000-5000 sec ! Disadvantages ! Long period storage ! Require low density gas ! Con: ! Need huge energy source ! Lower thrust (longer travel times) ! Cannot turn off once on ! Ion grid can deteriorate ! SI < 250 Nuclear Rockets Possible Nuclear Reactions Reactants " Products a.m.u. E out Ignition 92 94 [MeV] ! Fission U235 or Pu239 ! Energy release—break bonds p + p " D + e+ + #$ 2 0.42 N/A ! SI ~ 1-3 x 103 sec p + D " He + %$ 3 5.49 ! Nuclear Electric Propulsion 3 ! Reactor generates electricity to power an ion drive D + D " He3 + n 4 3.27 moderate ! Nuclear Thermal Propulsion D + D " + p 4 4.03 moderate ! Heats H propellant to high velocity D + H " He + p + p 5 17.60 easy ! Fusion 3 4 ! Forcing together nuclei D + He3 " He4 + p 5 18.30 moderate ! 10x the energy of fission He3 + He3 " He4 + p + p 6 12.80 hard ! Not yet controllable p + Li " He + He 7 3.90 hard ! Problems 6 4 3 ! Radioactivity " shielding p + Li7 " He4 + He4 8 17.0 hard ! Not all fuels easy to use D + Li6 " He4 + He4 8 22.3 hard

What is Desired? Next Generation

! NAIC developing new nuclear technologies – FFRE ! Fission fragment engine ! Nm sized Plutonium carbide grains suspended in an electric field ! SI > 500,000, high thrust ! What does this enable? ! Human missions to the outer solar system!

Mass Drivers Solar Thermal Propulsion ! Engine remains stationary " “fuel” moves ! EM fields accelerate “magnetic buckets” ! Rapidly switch B fields ! Operation ! Electric power from solar arrays " B field ! Deployable reflector focuses sunlight ! SI ~ 103 sec into fuel chamber ! Problems ! H fed in and heated 2 ! Huge stored E requirement ! H2 expands out " thrust ! Many km long, Alignment difficulties 3 ! SI = 1-2x10 sec ! Requires a catcher ! Disadvantage ! Cannot use on Earth ! Applications ! Acceleration needed " destroy payload ! High performance requires alot of fuel ! Bulk transport of surface regolith ! Far from Sun, inefficient 1/r2 ! Alternative ! Laser beam driven?

! Mechanism ! Solar (mv = E/c) Solar Sails ! Particle nature of light Space Planes ! Reflection off surface " momentum change (High albedo material) ! Advantages ! No propellant ! Light weight ! SI thrust per unit fuel used. Fuel = 0 " SI is infinite! ! Purpose – heavy payloads to LEO ! Disadvantages ! Conventional rocket: 90% mass is oxidizer ! Need very large area ! Need low mass (100 molecule thick) ! Utilize atmosphere for oxidizer until too thin then ! Low acceleration " long travel times rocket engine ! Cannot use near planet atmosphere ! Cannot use beyond ast belt (1/r2) ! Concept ! Example ! Runway takeoff ! “2 seater” ! Jet engines to supersonic speed ! Accelerate to 1 g ! Sail: 1 billion m2! ! Mach 3-6 – high altitude engines (ramjets) ! Applications ! Switch to Rocket engines to achieve orbit ! Continuous supply of freight (mining)?

Space Plane Status Engine Comparison

Name Country Dates Engine Status Engine SI [sec] Accel Comments X37 DoD Pres Ramjet Successful flight X33 NASA ??-’01 85% done Chem – liquid 250-480 high Most of mass lifted is fuel X34 NASA ’96-’01 Cancelled Highly reactive chemicals

X37 NASA Expendable rocket Cancelled Chem – solid 170-250 high Long storage time X38 NASA ??-’01 Crew rescue Cancelled Cannot turn off X40 NASA ’98 Like X37 Flew/Cancelled Nuclear 1-3x103 high Shielding problem Hope 40 Technology development Tu-2000 Europe ramjet Ion 3-4x103 med Need low & gas for good Ascender UK Jet " rocket thrust Astroliner Private Launch on 747 3 Maks Russian ’80’s piggyback Solar 1-1.2x10 low Inefficient far from sun Mass Driver 103 good Large E storage need Cannot align/aim easily

Gravitational Slingshot

! Steal PE from planet

! ETot = PE + KE ! At sun, fire thruster ! KE = ! m v2 ! "v = 10 km/s ! Example ! Difference in ETot at Sun ! 6102-6002 = ! Drop s/c from Neptune to sun 372100-360000 = 12100 = 2 ! v1 = 0; ETot = PE 110

! At sun, v = vesc = 600 km/s ! This excess will translate ! ETot = KE to excess velocity at Neptune of 110 km/s!

2 ETot = PE ETot = PE+KE ETot = KE = 600

2 ETot = PE + 110 add "v = 10 km/s Aerobraking NASA Gravity ! Use drag of atm for "v Assists ! 1st pass " reduce trajectory to elliptical orbit ! 2nd pass " circularize ! 1 engine burn " life perigee out of atm ! Requires heat shielding

Summary of Concepts

! Escape Velocity ! Orbit maneuvering ! KE > PE 0.5 ! Hohmann orbit transfers ! vesc = (2 G M / r) 0.5 ! vcirc = (G M / r) ! Characterize orbits by "v ! Concept of Launch windows ! LEO / GEO ! 300-600 km altitude ! Alternate Energy sources ! Period = 24 hr: 42,233 km ! Gravitational slingshots

! Aerobraking ! Propulsion ! Relies on Newton’s laws ! Engine type comparison ! Specific Impulse ! Acceleration