# Okay to post homework
# Ryan Badi, April 14 2024, Homework 22

Help := proc():
  printf("PlotBodies(t)\nObtain a plot of the sun, moon, and earth at time t to be displayed using Maple's display process.\nUsage: display(PlotBodies(0));\nUse this process for still images.\n\n"):
  printf("GetBodies()\nObtain an animation object for the sun, moon, and earth to be displayed using Maple's display process.\nUsage: display(GetBodies());\nUse this process for animations.\n"):
end:

# Tidal Force
# We begin with the knowledge that the tidadl force, F, is proportional to M / d^3 where M refers to the mass of the celestial body and d refers to the distance between its center and earth's.
# Because the moon's tidal force is stronger than the sun's, we have that F_m / F_s > 1.
# Also known to us due to trigonometric identities is that d = R / t where R is the radius of the celestial body and t is the angle we observe on earth.
# Substituting, we have that (M_m / d_m^3) / (M_s / d_s^3) = (M_m / R_m^3) / (M_s / R_s^3) > 1.
# Known to us due to geometry is that V = 4 / 3 * Pi * R^3 where V is the volume of the clestial body.
# Also known is that p = M/V where p is the densityof the celestial body. 
# Substituing further, we have that (M_m / R_m^3) / (M_s / R_s^3) = (M_m / V_m) / (M_s / V_s) = p_m / p_s > 1.
# Thus, we have proven that the moon is more dense than the sun.

# Project Progress
# So far, we have created a function to generate anagrams given a database, and we have also added two databases. We still need to create the functionality to interface with the user properly.
# The project and any further progress can be found here: https://github.com/AlexV-01/anagram-puzzle-book

with(plots):
trueToScale := false: # Set this to true if a realistic scale is desired. Doing so will result in an image that is difficult to see.

sunCenterX := proc(t): return 0: end:
sunCenterY := proc(t): return 0: end:
earthCenterX := proc(t): return bodies["sun"]["distance"]*cos(t): end:
earthCenterY := proc(t): return bodies["sun"]["distance"]*sin(t): end:
moonCenterX := proc(t): return earthCenterX(t) + bodies["moon"]["distance"]*cos(365*t): end:
moonCenterY := proc(t): return earthCenterY(t) + bodies["moon"]["distance"]*sin(365*t): end:

bodies := table(["sun" = table(["radius" = 696.*10^3, "distance" = 149.6*10^6, "centerX" = sunCenterX, "centerY" = sunCenterY, "color" = "yellow"]), "earth" = table(["radius" = 6378.1, "distance" = 0, "centerX" = earthCenterX, "centerY" = earthCenterY, "color" = "blue"]), "moon" = table(["radius" = 1737., "distance" = 384400., "centerX" = moonCenterX, "centerY" = moonCenterY, "color" = "gray"])]):
if trueToScale = false then: bodies["sun"]["radius"] := bodies["sun"]["radius"] / 25: bodies["sun"]["distance"] := bodies["sun"]["distance"] / 625: bodies["moon"]["radius"] := bodies["moon"]["radius"]: bodies["moon"]["distance"] := bodies["moon"]["distance"] / 25: fi:

GetBody := proc(body, t):
  return [body["centerX"](t) + body["radius"]*cos(l), body["centerY"](t) + body["radius"]*sin(l), l=0..2*Pi], axes=none, filled=true, color=body["color"], scaling=constrained:
end:

GetEarthOrbit := proc():
  return [bodies["sun"]["distance"]*cos(l), bodies["sun"]["distance"]*sin(l), l=0..2*Pi], axes=none, filled=false, color="blue", scaling=constrained:
end:

GetMoonOrbit := proc(t):
  return [earthCenterX(t) + bodies["moon"]["distance"]*cos(l), earthCenterY(t) + bodies["moon"]["distance"]*sin(l), l=0..2*Pi], axes=none, filled=false, color="gray", scaling=constrained:
end:

PlotBodies := proc(t) local container:
  container := plot(GetBody(bodies["sun"], t)):
  container := container, plot(GetBody(bodies["earth"], t)):
  container := container, plot(GetBody(bodies["moon"], t)):
  container := container, plot(GetEarthOrbit()):
  container := container, plot(GetMoonOrbit(t)):
  container := container, textplot([0, 0, "S"]):
  container := container, textplot([earthCenterX(t), earthCenterY(t), "E"]):
  container := container, textplot([moonCenterX(t), moonCenterY(t), "M"]):
  return container:
end:

GetBodies := proc():
  return [animate(plot, [GetBody(bodies["sun"], t)], t=0..2*Pi, frames=180),
  animate(plot, [GetBody(bodies["earth"], t)], t=0..2*Pi, frames=180),
  animate(plot, [GetBody(bodies["moon"], t)], t=0..2*Pi, frames=180),
  animate(plot, [GetEarthOrbit()], t=0..2*Pi, frames=180),
  animate(plot, [GetMoonOrbit(t)], t=0..2*Pi, frames=180),
  animate(textplot, [[0, 0, "S"]], t=0..2*Pi, frames=180),
  animate(textplot, [[earthCenterX(t), earthCenterY(t), "E"]], t=0..2*Pi, frames=180),
  animate(textplot, [[moonCenterX(t), moonCenterY(t), "M"]], t=0..2*Pi, frames=180)]:
end: