Midterm 2 Study Guide
Midterm 2 Study Guide 0087
Popular in Basics of Space Flight
verified elite notetaker
Popular in Astronomy
This 16 page Study Guide was uploaded by Austin Frownfelter on Tuesday November 3, 2015. The Study Guide belongs to 0087 at University of Pittsburgh taught by Dr. Regina Schulte-Ladbeck in Summer 2015. Since its upload, it has received 32 views. For similar materials see Basics of Space Flight in Astronomy at University of Pittsburgh.
Reviews for Midterm 2 Study Guide
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 11/03/15
Read chapters 57: http://reslscience.weebly.com/freestuff.html Review Lecture notes: Weeks 69 will be attached to the end of this guide Review/Reanswer homework Review the questions at end of each chapter Applying Newton’s laws Use this practice quiz: h ttp://tinyurl.com/oupw58t Find more Newton’s laws problems Tuesday’s review: Newton’s laws (Chapter 5): 1. Inertia (remain in motion/at rest) 2. F=ma 3. Equal and opposite reactions Force is in Newtons (N). Examples: Gravitational force is weight Normal force is force ground pushes up on object Centripetal force is circular force Lift is upward force from wings Thrust is forward force from rockets Acceleration is in : s Gravity is acceleration Centripetav −vceleration a = Δv= f i Δt tf−i Questions to Consider: Chapter 5: 1, 3, 5, 10, 12, 16, 17, 20, 24, 26 Chapter 6: 1, 3, 4, 5, 6, 7, 9, 11, 13, 16, 19, 22, 25 Chapter 7: 1, 2, 4, 5, 6, 8, 10, 11, 12, 13, 14, 19, 20 Previous topics to keep in mind: Kepler’s laws from Chapter 3 Coordinate Systems from Chapter 4 Newton’s laws from Chapter 5 Necessary for test: Pitt ID PeopleSoft number #2 Pencil Good Eraser Week 6 Astrodynamics How do airplanes fly? Forces Thrust Force in direction of motion Drag Force in opposite direction of motion Weight/Gravity Force directed toward Earth Lift Force pulling aircraft upward In level flight Thrust must be greater than Drag Lift must be equal to Weight In Ascent/Takeoff Thrust must be greater than Drag Lift must be greater than Weight In Descent/Landing Thrust must be greater than/equal to Drag Lift must be less than W eight What is a Force? Push or Pull as a result of an interaction between objects “F” is the term for Force Vector (it’s applied in a direction) In units of “Newtons” or “N” 2 1N = 1 kg x 1 m/s 1N = 0.225 lbs Newton’s laws 1st law: Inertia “An object at rest will stay at rest until a force acts upon it” “An object in motion will stay in motion until a force acts upon it” Example: Ball rolling on floor will experience friction and slow down 2nd law: F=m*a Force is equal to mass times the acceleration a = acceleration, also a vector If force is constant: A Larger mass will have a smaller acceleration A smaller mass will have a larger acceleration 3rd law: Equal and Opposite Reactions If an object exerts a force on an object, that second object exerts an equal and opposite force on the first object. Week 6 Rocketeers call acceleration “Delta V” or Δν v i initial velocity v = final velocity f ti f= time z i f position zf−zi Δv = v −vf= i tf−i Δv Δz m a = Δt = (Δt) → s2 Δv = a Δ* Δv F = m a =*m Δt In a rocket, as propellant is expelled, the mass of the rocket changes over time Δm = m − m f i Negative value, as the final mass is less than the initial mass Δm Δt Δt= burn time F = Δm Δv Δt * m × v = p ==> Momentum Thrust depends on mass flow rate through the engine and the exhaust velocity ↑ T = Δm↑ ↑ = Δv ↑ Δt↓ Example: Throwing vs. Shooting a piece of chalk F = Δp Δt FΔt = Δp = I Changing the momentum of an object requires an impulse. Increasing the Δt will decrease the I , decreasing the “hurt” of an Lift Drag Can be understood from the 3rd law Object needs to be moving 2 size, shape, inclination, air density, v Week 6 Newton’s Law of Gravity Law: The force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. M×m Equation: F = G 2 d G = Gravitational constant Gravitational force: ● acts at a distance ● Has an infinite range ● inversesquare law ● is always attractive Weight and Mass: ● Different. Weight is a force! ● W = m × g Your weight on Earth? M ×m person F = G ⊕ r⊕2 How much do you accelerate by Earth? M ×m m × a = G ⊕ perso person ⊕ r⊕2 m a⊕= g ⊕, the gravitational acceleration by Earths2or 9.8 W = m × g ==> Weight on Earth ⊕ person ⊕ W on planetmperson gplanet==> Weight on any Planet Week 6 Gravity and Altitude ● Force gets weaker with altitude, h ● d = ⊕ + h M ● g = G ⊕ 2 ==> Weight gets smalle (⊕ +h) m Altitude (km) g s2] 0 (Earth surface) 9.81 9 (Mount Everest) 9.80 500 (Low Earth Orbit) 8.44 5000 3.08 9000 1.69 (similar to moon) ∞ 0 (truly weightless) Free Fal Object moves due to gravity alone ● Near surface of Earth, an object in free fall accelerates by gravity, independent of mass ● Two objects dropped from the same height hit ground at the same time (neglecting air resistance) Δv hammer Δvfeather g ⊕ Δv = Δt hammer feather m Gravity ≈ 10s m Δt [s] Δv[ s2 0 0 1 10 2 20 3 30 Apparent and True weightlessness ● Absence of weight/Gravity ○ Infinite distance is impossible ● Absence of net forces due to gravity ○ Position between 2 separate masses Week 7 Weight W = mg g = G 2 M r M⊕ compared to plane r⊕ planet M uranus 14.5M ⊕ ; uranus= 4r⊕ 14.5M⊕ (4r ) = 0.91 g * ⊕ ⊕ True Weightlessness? Be an infinite distance from all mass Place yourself directly between the gravitational influences to have them cancel out Lagrange points Hills sphere M ⊕ M m G 2 = G 2 d1 d2 If the left is greater, the spacecraft will fall toward Earth If the right is greater, the spacecraft will fall toward the Moon Astronauts on the space station experience Apparent Weightlessness, due to being in constant freefall around Earth. They do not fall to the surface because they are moving forward, so they are moving in a circular orbit. Energy To exert a force, you need energy Types of energy: Gravitational Potential Energy Energy of Position P = mgh ==> P is symbol for gravitational potential energy Kinetic Energy Energy of motion 1 2 K = 2v ==> K is symbol for Kinetic Energy Conservation Law : Energy cannot be created nor destroyed, rather it may change form Rockets, chemical energy into kinetic energy Week 7 Rocket Equation ti v i 0, propellant mass isΔm t , v = Δv,M = M − Δm 1 1 tf, vfis max, final mass ism f Action Δm Δm F = ma = Δt × ve ==> Δt is propellant mass flow rate Reaction F = ma =− m × Δv ==> m = rocket’s mass, Δv = rate of velocity (increases) Δt Δt Δm×v e Δv Δm Δt =− m * Δt ÷ m ==> Δv =− v e m The mass is continuously decreasing, which requires calculus to solve properly. We are skipping Calculus to make it simpler. Tsiolkovsky's rocket equation m i Δv = v le( ) m f ==> “Ideal rocket equation”, because there is no drag, lift or weight How can you make Δvlarge? 1. Make exhaust velocity large. 2. increase miratio. Problematic, means almost all propellant and little/no payload. mf Other way to write rocket equation: m i ve m f = e ==> To increase the change in velocity, the mass ratio will be exponentially larger. In other words, if you want to go faster, you need more propellant Mission Profile Any space mission has a number of distinct, sequenced phases (stages) which make up its mission profile. Example: Orion flight test, December 2014. Mission Velocity Escape Velocity: Velocity going straight up, high enough that it escapes Earth’s gravity. Example: New Horizons probe (it will never come back to Earth) Called a “steep ascent” Week 7 Orbital Velocity: Velocity going up and forward, enough to get into an orbit of Earth. Called a “flat ascent” Uses a “gravity turn” Gravity tilts the direction, giving a smooth curve to the direction Escape Velocity From Earth is 11.2 km/s or 25,100 mph Derived from the conservation of energy v = 2GM => Works for any planet or object escape √ r 2 and G are constants Depends on the mass/distance relationship of the planet Mass of rocket is nowhere in the formula. Does not matter, the velocity is all that matters to escape the gravity. Orbital Velocity For earth is 7.8 km/s or 17,500 mph Motion in a circle An object wants to move tangentially, but inward acceleration keeps it moving in a circle. Centripetal Force/Centripetal Acceleration Angular Velocity, ω ° ω = 3P0 = Pπ 2πr v = P = ωr Centripetal Acceleration, a = v2 2 r F = m r Supplied by gravity 2 m r G r2 vorbit GMr √ Similar to Escape Velocity Dependent on Mass and radius of the planet. Mass of object in not necessary. Only difference is the “GM” is not multiplied by 2 Week 7 Launch Forces Forces on launchpad N = W Astronaut feels normal Earth weight Forces: Normal Force Weight (Gravity) Liftoff T > W ==> Liftoff “Thrust to Weight” ratio > 1 If in an atmosphere, there is a drag T > W + D Apparent Weight of astronaut increases Forces: Weight (Gravity) Thrust Drag In space, near Earth, on orbit No Trust, but moving forward (Inertia) No Drag, no atmosphere Apparent weight is 0 Gravitational weight No Normal force Forces: Weight (G Mm ) r Rocket Equation for a launch Δv = Δv −tΔv − wv − ΔvD steering Δv ⊕spin Δv t= Thrust Δv = Weight w Δv D Drag Δv steeringSteering losses Δv = Relative to Spin of Earth (+ if launching eastward, if westward) ⊕spin Week 8 Rocket Equation for Launch Δv = Δv − Δv − Δv − Δv ± Δv t W D steering ⊕spin Δv = Thrust t Δv W Weight Δv D Drag Δv steering Steering losses Δv ⊕spin Relative to Spin of Earth (+ if launching eastward, if westward) Typical Values: Δv − g = Δvw W ⊕ Δt g ⊕ 10 , 2t = 2min = 120s , ⇒ Δv ≈ 1.2 w km s s Δv D 1 − 1.5 ks km Δv steering 0.5 s Δv ≈ 0.4 km ⊕spin s Example: To get into orbit, Δv = 7.8 km s Δv T 7.8 ks + 1.2 sm + 1ks + 0.5 sm = 10.1 ks Approximately what we will need for a launch from the Kennedy Space Center to get into a low Earth orbit. Types of Propellants Classified by the “Specific Impulse” I sp ve (similar to miles per gallon g⊕ Solid Rocket Booster Liquid Rocket Cryogenics, freezing gas to use as as oxidizing agent Week 8 Differences: Solid Liquid Mixture of solid fuel and oxidizer Liquid Oxygen (oxidizer, “LOX”) Liquid fuels: Example: Petroleum Aluminum and aluminum perchlorate Cryogens (liquid gases) km km I sp200s, v ≈ 2e s Isp 400s, v ≈ e s Very low I , spt very simple Higher I , spt more complicated Limited Control, no “stop” once started Can stop and restart engine Valves, more chance of failure Cryogens are difficult to handle Staging To date, all launches from Earth have used multistage rockets Two types: Serial/Tandem Single line, back stage drops off, incrementally Parallel Center stage with stages strapped on the sides Advantage: Drop mass as fuel is lost (once burned out, the tank is useless.) Less mass to accelerate for each stage. Each stage can be designed differently Disadvantages: Complexity can lead to problems/failures. Stage separation is a point of failure Launch Alternative: Air launch to orbit Rocket is strapped to an airplane, and is released at a certain altitude Example: Stargazer aircraft and 3stage Pegasus rocket. Week 8 Landing General Concerns: Deceleration to v = 0 Type of body being landed on Gaseous Rocky Icy Solid Surface Atmosphere Aerobraking (uses drag of the atmosphere to slow down) Tremendous heat generated from air friction Heat shield Aerodynamics for descent and landing No atmosphere Needs rockets Week 9 Trajectories Flight paths through space Conic Sections Figure 8 (free return trajectories) Spiral (Electric propulsion solar sails) Suborbital trajectory Reach space, without completing a full orbit Example: For V2 with horizontal distance of 330 km, Δv = 1.6 km ≈ 3,580mph s Orbital Trajectories Kepler and Newton v = 2πr P v = GM √ r GM = 4π 22 r2 4π2 3 P = GM r Kepler’s 3rd law Video: https://www.youtube.com/watch?v=Am7EwmxBAW8 Planet is one of foci of the orbit Fastest point is at apogee, slowest point is at perigee Square of the Period of orbit is proportional to the cube of its semimajor axis Orbital Elements: a = semimajor axis = size e = eccentricity = shape i = inclination = tilt Ω = right ascension of ascending node = pin ω = argument of perigee = twist Week 9 v = mean anomaly = current position in orbit Burns: Posigrade burn = orbit raised everywhere except at burn point retrograde burn = orbit lowered everywhere except at burn point Hohmann transfer orbit Perigee at one orbit Apogee at other Uses the least fuel, most efficient, but time consuming Molniya orbit Change the eccentricity to increase coverage time of a certain area Sunsynchronous orbit The craft sees the same amount of time every orbit Orbital Perturbations Earth’s nonspherical shade and other bodies can modify an orbit Too much of a change requires more burn, else the craft will fall Postvideo: Characteristics Semimajor axis, or orbital altitude Low Earth Orbit Under 2000 km, or 1240 miles Medium Earth Orbit Between 2000 km and 35,786 km, or 122,236 miles High Earth Orbit Greater than 35,786 km Eccentricity Inclination Orbital Direction With spin of Earth (prograde orbit) Against spin of Earth (retrograde orbit) Synchronicity What multiple of the planet’s rotation period is the satellite’s orbital period 1:1 = synchronous, orbits once per day Special case: Geostationary orbit, satellite “hovers” over one point, always in zenith of observer underneath Week 9 Launch Window Time you can launch Affected by mission profile (all launch constraints) Time of day (sunlight) Weather/Visibility Launch Azimuth Direction of Launch Affected by mission profile Latitude of launch site (distance from equator) Safety constraints (cannot drop stages on land) Orbital inclination will always be greater than the latitude of the launch site, Except if azimuth is exactly west/east, which the inclination will be equal Orbital Maneuvers Need Δv thrust, propellant = money Changing orbital altitude Apogee will increase, except at burn point Orbital rendezvous “Target” and “Chaser” Chaser and Target must have the same inclination Must have the same altitude Chaser’s orbit must be synchronized with the target’s orbit If every part of the orbit is the same, then the phase angle (angle between the 2) will always stay the same. How do they catch up? Put the chaser in a phasing orbit. Increase the apogee (Δv), so when the chaser returns to its burn point (where the 2 orbits intersect), the angle is 0, and they meet. Requires 2 burns of the chaser, 1 to raise the phase orbit, the 2nd to return the orbit back “Proximity Operations” How do we do this with the least fuel? Hohmann transfer orbit, minimal Δv Used to get one circular orbit to another Used for Earth orbits and Interplanetary travel Week 9 For transferring planets, there is a small window of opportunity to make this transfer because of the planetary alignment Gravity Assist Add or subtract Δv using the gravity of a planet Because a planet is already in an orbit, you can use the gravity to pull it along, giving it more velocity. The same works to slow it down Example: Jupiter slingshot Voyager space probes used gravity assists of the planets to get farther in the solar system faster Freereturn trajectory Uses gravity to turn a spacecraft around “Free” meaning no burns required Analogy: Boomerang Constant Thrust Trajectory Depart from Earth orbit using constant, low thrust Engines: Ion engine Solar Sail Spiral orbit Example: Dawn to Vesta and Ceres
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'