/* MJ-5 Unit I: longitude, correction, vector and period checks. */
kill(all)$

mean_longitude:40+360*50/225$
mean_longitude_check:mean_longitude-120$

epsilon:8/100$
correction_rad:epsilon*sin(%pi/3)$
correction_deg:correction_rad*180/%pi$
correction_check:radcan(correction_rad-sqrt(3)/25)$
corrected_longitude_check:radcan((mean_longitude+correction_deg)-(120+36*sqrt(3)/(5*%pi)))$

exact_correction_deg:atan2(epsilon*sin(%pi/3),1+epsilon*cos(%pi/3))*180/%pi$
exact_correction_check:radcan(tan(exact_correction_deg*%pi/180)-sqrt(3)/26)$

planet_sun:[(1/2)*cos(2*%pi/3),(1/2)*sin(2*%pi/3)]$
planet_earth:[1,0]+planet_sun$
planet_distance:sqrt(planet_earth[1]^2+planet_earth[2]^2)$
planet_vector_check:
    radcan((planet_earth[1]-3/4)^2+(planet_earth[2]-sqrt(3)/4)^2)$
planet_distance_check:radcan(planet_distance-sqrt(3)/2)$

synodic:1/abs(1/(2247/10)-1/(36525/100))$
synodic_check:ratsimp(synodic-1094289/1874)$

minimum_rate:1/2-2*(2/5)$
minimum_rate_check:minimum_rate+3/10$

parallax_rad:6371/384400$
parallax_deg:parallax_rad*180/%pi$
parallax_check:384400*parallax_rad-6371$

print("mean_longitude_check =",mean_longitude_check)$
print("correction_check =",correction_check)$
print("corrected_longitude_check =",corrected_longitude_check)$
print("exact_correction_check =",exact_correction_check)$
print("planet_vector_check =",planet_vector_check)$
print("planet_distance_check =",planet_distance_check)$
print("synodic_check =",synodic_check)$
print("minimum_rate_check =",minimum_rate_check)$
print("parallax_check =",parallax_check)$
print("correction_deg =",float(correction_deg))$
print("exact_correction_deg =",float(exact_correction_deg))$
print("synodic_days =",float(synodic))$
print("parallax_rad =",float(parallax_rad))$
print("parallax_deg =",float(parallax_deg))$