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--- ss20:himmelskoerper.comments [2020/09/13 13:52]
icks [Code-Kommentierung]
+++ ss20:himmelskoerper.comments [2020/09/18 21:38] (aktuell)
icks
@@ Zeile 1: / Zeile 1: @@
 [[Himmelsmechanik|← Zurück zur Projektseite]]
-===== Code-Kommentierung =====
+===== Code =====
+====Kepler-Methode====
+<file python keplermethode.py>
+import vpython as vpy
+import math
+vpy.scene.width = 1920
+vpy.scene.height = 1080
+class Body:     #planet/trabant
+	def __init__(self, name, radius, position, winkelgeschwindigkeit, exzentrizitaet, grossehalbachse, objekt): #(mass)
+		self.name = name
+		#self.mass = masse
+		self.rad = radius
+		#self.geschwindigkeit = geschwindigkeit, verworfen fuer Winkelgeschwindigkeit
+		self.pos = position
+		self.angularv = winkelgeschwindigkeit #mean angular velocity
+		self.ecc = exzentrizitaet
+		self.axis = grossehalbachse
+		self.ob = objekt
+        # a: Große Halbachse
+        # ε: Exzentrizität
+        # ω: Winkelgeschwindigkeit
+        # name, masse[kg], radius[m], position/anfangs der Abstand zur Sonne[m]
+def InverseKepler(f, f1, x0, d=5):	#general Newton-Method for non-linear equations, used specifically to solve the Kepler-Equation with f1 = f' = df/dx ∀x
+	for i in range(d):
+		x0 = x0-(f(x0)/f1(x0))
+	return x0
+class Viewer:
+	def __init__(self, himmelskoerper_liste):
+		self.himmelskoerper_liste = himmelskoerper_liste
+	def visualize(self, scale = 50):	#scaling changes distance between objects, but maintains object size
+		global tags
+		tags = []
+		for i in range(len(self.himmelskoerper_liste)):
+			var = self.himmelskoerper_liste[i].pos/self.himmelskoerper_liste[1].pos
+			print(var, type(var))
+			self.himmelskoerper_liste[i].ob = vpy.sphere(pos=vpy.vector(self.himmelskoerper_liste[i].pos,0,0), radius = scale* self.himmelskoerper_liste[i].rad, make_trail=True, retain = var*125+1, trail_color=Colours[i], texture=Skins[i]) #colour, retain/value, texture add seperately for specific object
+			tags.append(vpy.label(pos = self.himmelskoerper_liste[i].ob.pos, text = self.himmelskoerper_liste[i].name, yoffset = 5, line = False, box = False, opacity = 0))
+	def update(self, Tges, scale = 50): #Tges in Seconds
+		for i in range(len(self.himmelskoerper_liste)):
+			e, v, a = self.himmelskoerper_liste[i].ecc, self.himmelskoerper_liste[i].angularv, self.himmelskoerper_liste[i].axis
+			M = v * Tges # M = mean anomaly
+			def f(x):
+				return x-e*math.sin(x)-M #Kepler Equation
+			def f1(x):
+				return 1-e*math.cos(x) #derivative of Kepler Equation
+			E = InverseKepler(f, f1, 1) # E = eccentric anomaly
+			θ = 2*math.atan(math.sqrt((1+e)/(1-e))*math.tan(E/2)) # θ = real anomaly
+			r = (a*(1-e**2))/(1+e*math.cos(θ)) # r = euclidean distance to center object
+			self.himmelskoerper_liste[i].ob.pos = r*vpy.vector(math.cos(θ), math.sin(θ), 0)
+			tags[i].pos = self.himmelskoerper_liste[i].ob.pos
+#List excerpt not part of main()
+Sonne = Body ("Sun", 696342E3, 0, 0, 0, 0, "")													#mass = 1.9884E30 kg
+Merkur = Body ("Mercury", 2440E3, 46E9, 8.266757558468652e-07, 0.20563069, 57909E6, "")			#mass = 0.33E24 kg
+Venus = Body ("Venus", 6052E3, 107.5E9, 3.2363949047127294e-07, 0.00677323, 108209E6, "")		#mass = 4.8685E24 kg
+Erde = Body ("Earth", 6378E3, 147.1E9, 1.991021277657232e-07, 0.01671022, 149598E6, "")			#mass = 5.9737E24 kg
+Mars = Body ("Mars", 3397E3, 206.7E9, 1.0585766107031914e-07, 0.09341233, 227937E6, "")			#mass = 0.64185E24 kg
+Jupiter = Body ("Jupiter", 71493E3,740.7E9, 1.678399979816619e-08, 0.04839266, 778412E6, "") 	#mass = 1898.7E24 kg
+Saturn = Body ("Saturn", 60267E3, 1349.8E9, 6.761257875481413e-09, 0.05415060, 1426725E6, "") 	#mass = 568.51E24 kg
+Uranus = Body ("Uranus", 25559E3, 2735E9, 2.369788170407197e-09, 0.04716771, 2870972E6, "")		#mass = 86.849E24 kg
+Neptun = Body ("Neptune", 24764E3,4459.8E9, 1.20820761533874e-09, 0.00858587, 4498253E6, "") 	#mass = 102.44E24 kg
+Colours = [vpy.color.black, vpy.color.white, vpy.color.magenta, vpy.color.green, vpy.color.red, vpy.color.orange, vpy.color.yellow, vpy.color.cyan, vpy.color.blue]
+Skins = ["https://i.imgur.com/XdRTvzj.jpg", "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/e0763947-6f42-4d09-944f-c2d6f41c415b/dcaig77-18800e1e-24aa-43e5-9dd0-3dff9bcf8d0c.jpg?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3sicGF0aCI6IlwvZlwvZTA3NjM5NDctNmY0Mi00ZDA5LTk0NGYtYzJkNmY0MWM0MTViXC9kY2FpZzc3LTE4ODAwZTFlLTI0YWEtNDNlNS05ZGQwLTNkZmY5YmNmOGQwYy5qcGcifV1dLCJhdWQiOlsidXJuOnNlcnZpY2U6ZmlsZS5kb3dubG9hZCJdfQ.vigtUwmhB5u_KrjxZcgE04UH7OoC16HyLTD5pulA4OA", "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/90ad8232-4e09-4675-b9e7-bc2898960870/dc0ss1u-9ce1cbd0-6f56-4bb1-ab24-e64089914504.png/v1/fill/w_1024,h_512,q_80,strp/venus_cloud_texture_map_by_jcpag2010_dc0ss1u-fullview.jpg?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3siaGVpZ2h0IjoiPD01MTIiLCJwYXRoIjoiXC9mXC85MGFkODIzMi00ZTA5LTQ2NzUtYjllNy1iYzI4OTg5NjA4NzBcL2RjMHNzMXUtOWNlMWNiZDAtNmY1Ni00YmIxLWFiMjQtZTY0MDg5OTE0NTA0LnBuZyIsIndpZHRoIjoiPD0xMDI0In1dXSwiYXVkIjpbInVybjpzZXJ2aWNlOmltYWdlLm9wZXJhdGlvbnMiXX0.5Q0wcthS2JaVk3qEWsKsh_6zmmCcL7j6uiaXAGJnoLY",vpy.textures.earth, "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/6e527eb9-99dc-4554-9ea2-dd0e84e79860/dckiu8c-727ad23f-7760-42f2-9669-aa2de0f3c832.png?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3sicGF0aCI6IlwvZlwvNmU1MjdlYjktOTlkYy00NTU0LTllYTItZGQwZTg0ZTc5ODYwXC9kY2tpdThjLTcyN2FkMjNmLTc3NjAtNDJmMi05NjY5LWFhMmRlMGYzYzgzMi5wbmcifV1dLCJhdWQiOlsidXJuOnNlcnZpY2U6ZmlsZS5kb3dubG9hZCJdfQ.4w-Xl7_hjAtdYK2z9zk0nhkWpa38FMStpsO177zrOJw", "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/58d3c051-62a0-4471-818b-b9b92759d6b6/db6is8m-065c1dbf-d125-4729-a015-f79553c16bf9.jpg?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3sicGF0aCI6IlwvZlwvNThkM2MwNTEtNjJhMC00NDcxLTgxOGItYjliOTI3NTlkNmI2XC9kYjZpczhtLTA2NWMxZGJmLWQxMjUtNDcyOS1hMDE1LWY3OTU1M2MxNmJmOS5qcGcifV1dLCJhdWQiOlsidXJuOnNlcnZpY2U6ZmlsZS5kb3dubG9hZCJdfQ.lYxq2GPyUQyWVogIVdRYiJvPzlVsYkDaRHXUwYjRxF4", "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/e0763947-6f42-4d09-944f-c2d6f41c415b/dcaift0-422ad564-f7b0-4291-914f-425b9ac29a35.jpg?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3sicGF0aCI6IlwvZlwvZTA3NjM5NDctNmY0Mi00ZDA5LTk0NGYtYzJkNmY0MWM0MTViXC9kY2FpZnQwLTQyMmFkNTY0LWY3YjAtNDI5MS05MTRmLTQyNWI5YWMyOWEzNS5qcGcifV1dLCJhdWQiOlsidXJuOnNlcnZpY2U6ZmlsZS5kb3dubG9hZCJdfQ.REEY4eftTjq2duJpeXgsJ5QaAU7dFnCUwojV9Ez2XS0", "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/90ad8232-4e09-4675-b9e7-bc2898960870/dc0ss0c-aa6fd748-5785-41ec-9b6e-00356bf444c7.png/v1/fill/w_1024,h_512,q_80,strp/uranus_texture_map_by_jcpag2010_dc0ss0c-fullview.jpg?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3siaGVpZ2h0IjoiPD01MTIiLCJwYXRoIjoiXC9mXC85MGFkODIzMi00ZTA5LTQ2NzUtYjllNy1iYzI4OTg5NjA4NzBcL2RjMHNzMGMtYWE2ZmQ3NDgtNTc4NS00MWVjLTliNmUtMDAzNTZiZjQ0NGM3LnBuZyIsIndpZHRoIjoiPD0xMDI0In1dXSwiYXVkIjpbInVybjpzZXJ2aWNlOmltYWdlLm9wZXJhdGlvbnMiXX0.cz2NsO66AT-KlAIOvDYkXXpZ7SgFiuSg1bRgPjaTiCo", "https://images-wixmp-ed30a86b8c4ca887773594c2.wixmp.com/f/e0763947-6f42-4d09-944f-c2d6f41c415b/dcaifld-8408b286-dfb4-4b94-9d36-029c36cc636f.jpg?token=eyJ0eXAiOiJKV1QiLCJhbGciOiJIUzI1NiJ9.eyJzdWIiOiJ1cm46YXBwOiIsImlzcyI6InVybjphcHA6Iiwib2JqIjpbW3sicGF0aCI6IlwvZlwvZTA3NjM5NDctNmY0Mi00ZDA5LTk0NGYtYzJkNmY0MWM0MTViXC9kY2FpZmxkLTg0MDhiMjg2LWRmYjQtNGI5NC05ZDM2LTAyOWMzNmNjNjM2Zi5qcGcifV1dLCJhdWQiOlsidXJuOnNlcnZpY2U6ZmlsZS5kb3dubG9hZCJdfQ.K_9vTX6VPK01nodrwD3YztdaOG9VpBXA8_qlkHQ9Tk0"]
+SolarSys = [Sonne, Merkur, Venus, Erde, Mars, Jupiter, Saturn, Uranus, Neptun]
+#main()
+Tges = 60 #minute intervals
+ViewSol = Viewer(SolarSys)
+ViewSol.visualize()
+while True:
+	ViewSol.update(Tges)
+	Tges += 60
+</file>
+====Newton-Methode====
 <file python projektnewton.py>
 import vpython as vpy
 import math
+vpy.scene.width = 1920
+vpy.scene.height = 1080
 class Body:     #planet/trabant
@@ Zeile 62: / Zeile 157: @@
 				a += G * M[i2]*(X[i2]-X[i])*1/(((X[i2]-X[i]).mag**3))
-			print(X[i], self.himmelskoerper_liste[i].v)
+			#print(X[i], self.himmelskoerper_liste[i].v)
-			print(leapfrog(X[i], self.himmelskoerper_liste[i].v, a))
+			#print(leapfrog(X[i], self.himmelskoerper_liste[i].v, a))
 			self.himmelskoerper_liste[i].ob.pos = leapfrog(X[i], self.himmelskoerper_liste[i].v, a)[0]
 			self.himmelskoerper_liste[i].v = leapfrog(X[i], self.himmelskoerper_liste[i].v, a)[1]

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