Question: Rockets If there were no launch pad beneath the space - PDF document

Rockets 1 Rockets 2 Question: Rockets If there were no launch pad beneath the space shuttle at lift-off, the upward thrust of its engines would be • approximately unchanged. • approximately half as much. • approximately zero. Rockets 3 Rockets 4 Observations About Rockets Momentum Conservation • Plumes of flame emerge from rockets • A rocket’s momentum is initially zero • Rockets can accelerate straight up • Momentum is redistributed during thrust – Ship pushes on fuel; fuel pushes on ship • Rockets can go very fast – Fuel acquires backward momentum • The flame only touches the ground initially – Ship acquires forward momentum • Rockets operate well in empty space • Rocket’s total momentum remains zero • Rockets usually fly nose-first Rockets 5 Rockets 6 Rocket Propulsion Question: • Neglecting gravity, then If there were no launch pad beneath the space shuttle at lift-off, the upward thrust – rocket’s total momentum is always zero + = of its engines would be momentum momentum 0 fuel ship • approximately unchanged. • The momentum of the ship is opposite • approximately half as much. • the momentum of the ejected fuel • approximately zero. – or, equivalently, • the velocity of that fuel and • the mass of that fuel •1

Rockets 7 Rockets 8 Rocket Engines Stability and Orientation • Chemical reactions produce hot, high- • On ground, rocket needs static stability pressure gas • In air, rocket needs aerodynamic stability • Gas speeds up in nozzle – Center of dynamic pressure behind c.o.m. • Gas reaches sonic speed • In space, rocket is a freely rotating object in throat of de Laval nozzle – Orientation governed by angular momentum • Beyond throat, supersonic – Rocket’s orientation doesn’t affect its travel gas expands to speed up further Rockets 9 Rockets 10 Ship’s Ultimate Speed Gravity, Part 1 • Increases as • The earth’s acceleration due to gravity is only constant for small changes in height – ratio of fuel mass to ship mass increases – fuel exhaust speed increases • When the distance between two objects changes substantially, the relationship is: • If fuel were released with rocket at rest, mass = ⋅ fuel speed speed ultimate exhaust ⋅ ⋅ mass gravitational constant mass mass ship 1 2 force = • Because rocket accelerates during thrust, 2 (distance between masses) ultimate speed is less than given above Rockets 11 Rockets 12 Gravity, Part 2 Gravity, Part 3 • An object’s weight is only constant for • Even far above earth, an object has weight small changes in height • Astronauts and satellites have weights • When its height changes significantly, the – weights are somewhat less than normal relationship is: – weights depend on altitude • Astronauts and satellites are in free fall ⋅ ⋅ gravitational constant mass mass object earth weight = (distance between centers of object and earth) 2 •2

Rockets 13 Rockets 14 Orbits, Part 1 Orbits, Part 2 • An object that has a • An object that begins to fall sideways velocity from rest falls directly follows a trajectory toward the earth called an orbit • Acceleration and velocity • Orbits can be closed are in the same direction or open, and are ellipses, parabolas, and hyperbolas Rockets 15 Rockets 16 Current Rocket Technology Summary About Rockets • X-Prize Rockets • Rockets are pushed forward by their fuel • Single State to Orbit Rockets • Total rocket impulse is the product of exhaust speed times exhaust mass • Improbable Dreams • Rockets can be stabilized aerodynamical – Rockets that rarely require refueling – Rockets that can land and leave large planets • Rockets can be stabilized by thrust alone – Rockets that can turn on a dime in space • After engine burn-out, rockets can orbit •3