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We use the following nomenclature throughout these pages:
= angle that first (larger) mirror makes to x-axis at distance from x-axis
= angle that tangent at k’th point on i’th mirror makes to x-axis (or 90° if or )
= magnification of mirror pair
= angle that stanchion makes to x-axis if mirror area element only has a single stanchion
= thickness of mirror
= drag coefficient of mirror arrangement
= angle that the line from to makes to x-axis
= energy per unit time available for thrust
= position along (negative) x-axis of the sun
= drag force per unit cross-sectional area perpendicular to the velocity vector
= also . Additional force (in cylindrical polar coordinates) per unit mirror area (area perpendicular to x-axis) provided by stanchions, = total force per unit mirror area (area perpendicular to x-axis) provided by stanchions in rotationally symmetric case, = component elements in equations linking and with and
= acceleration due to gravity (assumed to be 10ms-2 at the surface of the earth)
= effective acceleration due to thrust
= (also) iteration increment size for mirror positioning analysis (can be positive or negative)
= iteration step counter for mirror positioning analysis
= mass of launcher plus propellant at time
= rate of change of with respect to (is negative)
= . If or then k’th point of i’th mirror in xy-plane. If then object point of mirror pair, . If then image point, .
= mass of mirror
= upper limit on propellant ejection speed (if applicable)
= distance between and
, = arbitrary real numbers (positive or negative) defining the shape of the mirror layout
= radius of larger mirror
= density of material used to make larger mirror
= density of atmosphere
= , where is the angular velocity of the mirror
=
= time from commencement of solar-powered propulsion
= = Tension per unit cross-sectional area in mirror at , being the tension in the transverse direction and being the tension perpendicular to this and tangential to the mirror surface. = uniform tension whatever the direction (tangential to mirror) if ()
= rate of change of with respect to (for mirror defined with )
= vertically downward speed at which propellant is ejected (relative to launcher)
= velocity of launcher plus propellant at time
= rate of change of with respect to
= orbital speed (assumed to be 7800ms-1 for low earth orbit)
= horizontal speed at which propellant is ejected (relative to launcher)
, = distance between consecutive points in cross-sections of first and second mirrors respectively
= cylindrical polar coordinates corresponding to Cartesian coordinates
= a sign factor used in identification of mirror pair positioning
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