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Showing posts with the label math

Throwing Stuff In Space

In my last post about the Russian space program I said that cosmonauts regularly throw stuff in space so it will burn up and not result in permanent space junk. A reader asks whether you can actually do this.. Man, way to ask a hard question. Orbital mechanics says "if a space vehicle comes within 120 to 160 km of the Earth's surface, atmospheric drag will bring it down in a few days, with final disintegration occurring at an altitude of about 80 km", and we can work out how much delta-v a cosmonaut has to impart to get the semi-major axis of the orbit of the debris below 160 km. dVA = sqrt(GM*(2.0/rA - 1.0/((rA + rB) / 2.0))) - sqrt(GM/rA) where rB = 160km + roE where rA = 278km + roE to 460km + roE where roE = 6378.1km where GM = 6.67300 * 5.9742 * 10^24 * 10^-11 with the ISS at 278km the delta-v retrograde is 34.684365m/s or 77.5867148 mph, which is major league baseball. with the ISS at 428km the delta-v retrograde is 77.243278m/s or 172.788292 mph, with is sp...

Coding Orbital Mechanics

I forget what inspired me, probably discussions about propellant depots, but after an hour of two playing around in the great spaceflight simulator Orbiter I decided to give the old orbital mechanics another go. I've written dynamic physics simulators before which have really nice accuracy and can handle the big numbers required for orbital simulations, including three body problems, but I never managed to tackle the classical orbital mechanics - too much Greek terminology I guess - until today. I set myself a somewhat difficult task: Given a position vector r and a velocity vector v , somewhere above a reference (say, a planetary body) calculate all the required classical orbital elements: a - semi-major axis e - eccentricity i - inclination l - longitude of the ascending node w - argument of periapsis t - true anomaly There's others, but they can be derived from these. You'll also note I haven't used any Greek letters that my keyboard doesn...

Hating On Propellant Depots

Dan Adamo is a retired flight dynamics officer for the Shuttle program and does space mission trajectory, design and operations in his sleep. I recently saw him put together a design reference mission for a human mission to the moons of Mars, for fun , using only well understood technology. Back in February he did a Space Show Classroom where he discussed many topics and once again demonstrated his effortless grasp of orbital dynamics. A listener asked about propellant depots and Adamo answered with what I think is the most articulate objection to the concept of low earth orbit propellant depots. He went on to talk more favorably about propellant depots at Lagrangian points and on the surface of destinations such as the Moon and Mars, but I think his objections are more interesting. Starting from the ground up, here's where I have problems with propellant depots, in low Earth orbit. Once you establish the depot, it can be empty for all I care at this point, but once you...