Week 7 Notes
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This 4 page Class Notes was uploaded by Austin Frownfelter on Thursday October 15, 2015. The Class Notes belongs to 0087 at University of Pittsburgh taught by Dr. Regina Schulte-Ladbeck in Summer 2015. Since its upload, it has received 10 views. For similar materials see Basics of Space Flight in Astronomy at University of Pittsburgh.
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Date Created: 10/15/15
Spaceflight Week 7 Page 1 Weight W mg g G M M I compared to Laquot I I e planet Murcmus 145Mce ruranus 4re 145M 92 091 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 Earth r Spacecraft Mm if Ll l I kj39 m l l a MW 2 M G 6112 G 6122 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 fonNard 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 gt P is symbol for gravitational potential energy Kinetic Energy Energy of motion K mv2 gt 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 Spaceflight Week 7 Page 2 Rocket Equation t v O propellant mass is Am Pf EllE i i5 E l DUHEIZI t1 V1 AVDM M Am and Ihrual la generatet1 If vfiS max final mass is mf quot3933 Mass decreases item31y Hera355 Action Am Am 39 F ma Ti gtlt ve gt T IS propellant mass flow rate Reaction F ma m gtlt ATV gt m rocket s mass ATV rate of velocity increases AmXVe Q 4 Am N m At m gt Av ve m The mass is continuously decreasing which requires calculus to solve properly We are skipping Calculus to make it simpler Tsiolkovskv39s rocket equation Av ve gt Ideal rocket equation because there is no drag lift or weight How can you make Avlarge 1 Make exhaust velocity large 2 increase quot3 ratio Problematic means almost all propellant and littleno payload mf Other way to write rocket equation Av g eve gt 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 A lFEEtIIy Away Spaceflight Week 7 Page 3 Orbital Velocity Velocity going up and forward enough to get into an orbit of Earth Called a flat ascent t r g r v LL Uses a gravity turn 39 N i i U w Fled Gravity tilts the direction Earth p a a quot giving a smooth curve to the direction Escape Velocity From Earth is 112 kms or 25100 mph Derived from the conservation of energy Vescape gt Works for any planet or object 2 and G are constants Depends on the massdistance 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 78 kms or 17500 mph Motion in a circle An object wants to move tangentially but inward acceleration keeps it moving in a circle Centripetal ForceCentripetal Acceleration Angular Velocity m 360 2it P P 27rr v P mr Centripetal Acceleration a V72 Fm Supplied by gravity vi m mr G D GM Vorbz39t r 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 Spaceflight Week 7 Page 4 Launch Forces Forces on launchpad N W Drag Astronaut feels normal Earth weight I 1 Forces Normal Force Weight Gravity Liftoff T gt W gt Liftoff Thrust to Weight ratio gt 1 If in an atmosphere there is a drag T gt W D Apparent Weight of astronaut increases Forces ravity Th mat Thrust Drag In Space near Earth on orbit No Trust but moving forward Inertia No Drag no atmosphere Apparent weight is O Gravitational weight No Normal force Forces Weight G l weight Rocket Equation for a launch Av Avt Avw AVD Av Av Thrust Avw Weight AvD Drag Av Steering losses steering AVG I Relative to Spin of Earth if launching eastward if westward i AvB steering Spin
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