// This program draws the effects of a rocket changing an orbit. // All of the burns use the same change in speed but burn in // 4 different directions. // /** This file demonstrates how thrust in a rocket changes an orbit. White: Typical orbit Red: Stop: Slows down rocket Green: Go: Speeds up rocket Blue: Down: Burns downward toward planet Yellow: Up: Burns upward away from planet Each velocity change is regarded as instantaneous and occurs at the "top" of the diagram. */ [orbitalHeight, dv] = eval[input["Enter orbital changes",[["Height above ground", "1000 km"], ["Velocity change", "1000 mph"]]]] y = earthradius + orbitalHeight x = 0 miles vy = 0 m/s // Calculate horizontal velocity for a circular orbit. // This is derived sybolically by orbit.frink. It's amazing. Check it out. vx = G^(1/2) earthmass^(1/2) (earthradius + orbitalHeight)^(-1/2) println["vx = " + (vx -> "mph")] // Calculate circular orbital period. // This is derived sybolically by orbit.frink. It's amazing. Check it out. period = 2 pi vx^-1 (earthradius + orbitalHeight) println["Period is " + (period -> HMS)] g = new graphics g.backgroundColor[0,0,0] g.color[0,0,.5] g.fillEllipseCenter[0, 0, 2 earthradius/mile, 2 earthradius/mile] g.color[1,1,1] drawOrbit[g, x, y, vx, vy, period] // White: Nominal orbit g.color[0,0,1] // Blue: down: Accelerate towards earth. drawOrbit[g, x, y, vx, vy-dv, period] g.color[1,1,0] // Yellow: up: Accelerate up drawOrbit[g, x, y, vx, vy+dv, period] g.color[1,0,0] drawOrbit[g, x, y, vx-dv, vy, period] // Red: stop: Backwards (slow down) g.color[0,1,0] drawOrbit[g, x, y, vx+dv, vy, period] // Green: go: Forwards (speed up) g.show[] drawOrbit[g, x, y, vx, vy, period=120 min] := { p = new polyline timestep = period/1000 for t = 0 min to period step timestep { dsqr = x^2 + y^2 a = G earthmass / dsqr theta = arctan[y,x] ax = - a cos[theta] ay = - a sin[theta] vx = vx + timestep ax vy = vy + timestep ay x = x + timestep vx y = y + timestep vy p.addPoint[x/mile,-y/mile] } g.add[p] }