Date       : June 7, 2020
		Writer      : B.Engr.  Koji Makino
		Review    : June 10, 2023
		Calculations for Velocities and Sound Velocities of
		Tukuba Meteorite and  Calculations for Temperatures of
		the Meteorite by Aerodynamic Heating
		(When horizontal movement velocity is 1097.4m/s, 747.9m/s was added to vertical direction
		velocity to fall to height 13000m above the ground in lapse of 90 seconds as starting to fall
		from height of 120km.  It rushed to atmosphrere at angle of 15°of east side from the north.
		The direction shifted to 20°east side by the power of the earth rotation.  The meteorite falling
		down route crossed at angle of  35°to the north-south line.  "g" is gravity acceleration
		9.8m/s2.)  The meteorite entered atmosphere, and then changed the direction by the earth
		rotation. The meteorite started to fall from altitude of 120km after that.
		It is a calculating formula which asks for the temperature of the flight body by which
		aerodynamic heating is done by sound velocity.
		Tah = Rac × r × Tab × Vs2 - 273
		Tah : Aerodynamic Heating Temperature  Rac : Air Concentration Ratio  r : Form Coefficient
		Tab : Absolute Temperature  Vs : Velocity of Sound
		Absolute Temperature（Ｔａｂ）was 273 degree as celsius 0 degree.
		Aerodynamic heating temperature was calculated on absolute temperature.
		For it converted to celsius, -273 degree was added to upper formula.
		The meteorite was warmed by the solar heat, so it was not -273℃ really.
		Sound velocity in high altitude is slower than aboveground, since it changes in each altitudes.
		All sound velocity are calculated with 330m/s as average velocity.
	Table 1. calculated proceeding direction sound velocities and aerodynamic
		heating temperatures at elapse time every 5 seconds
	Elapse	Vertical	Horizontal	Proceeding	Proceeding	Height a-	Ratio of air	Coeffi-	Aerodyna-		Visual ob-
	time	direction	direction	direction	direction	bove ground	concent-	cient	mic heating		servation
		velocity	velocity	velocity	sound	start to fall	ration to	of form	tempe-		flying
		V=g×t	1097.4		velocity	from height	that on	r = 1	rature		object
		+747.9				120km	the ground				color ・
	(s)	(m/s)	(m/s)	(m/s)	(Mach)	(m)	(％)		(℃)		state
	0	747.9	1097.4	1328.0	4.02	120000.0	0.00	1	-273.0		G., W.C.
	5	796.9	1097.4	1356.2	4.11	116138.0	0.00	1	-273.0		G., W.C.
	10	845.9	1097.4	1385.6	4.20	112031.0	0.00	1	-273.0		G., W.C.
	15	894.9	1097.4	1416.0	4.29	107679.0	0.00	1	-273.0		G., W.C.
	20	943.9	1097.4	1447.5	4.39	103082.0	0.00	1	-273.0		G., W.C.
	25	992.9	1097.4	1479.9	4.48	98240.0	0.00	1	-273.0		G., W.C.
	30	1041.9	1097.4	1513.2	4.59	93153.0	0.00	1	-273.0		G., W.C.
	35	1090.9	1097.4	1547.4	4.69	87821.0	0.00	1	-273.0		G., W.C.
	40	1139.9	1097.4	1582.3	4.79	82244.0	0.00	1	-273.0		G., W.C.
	45	1188.9	1097.4	1618.0	4.90	76422.0	0.00	1	-273.0		G., W.C.
	50	1237.9	1097.4	1654.3	5.01	70355.0	0.00	1	-273.0		G., W.C.
	55	1286.9	1097.4	1691.3	5.13	64043.0	0.01	1	-272.3		G., W.C.
	60	1335.9	1097.4	1728.8	5.24	57486.0	0.03	1	-270.8		G., W.C.
	65	1384.9	1097.4	1767.0	5.35	50684.0	0.07	1	-267.5		G., W.C.
	70	1433.9	1097.4	1805.6	5.47	43637.0	0.17	1	-259.1		G., W.C.
	75	1482.9	1097.4	1844.8	5.59	36345.0	0.46	1	-233.8		G., W.C.
	80	1531.9	1097.4	1884.4	5.71	28808.0	1.37	1	-151.0		G., W.C.
	85	1580.9	1097.4	1924.5	5.83	21026.0	4.54	1	148.5		G., W.C.
	90	1629.9	1097.4	1964.9	5.95	12999.0	16.2	1	1295.0		Bright White
		G., W.C. :	Gray, White Cloud
		Date       : June 7, 2020
		Writer      : B.Engr.  Koji Makino
		Review    : June 10, 2023
		How to calculate about ratio of air concentration at the altitude to that on the ground
		Atmospheric pressure at the altitude were corrected atmospheric pressure at the alititude
		from data of JMA's Aerological observatory (at Tukuba) on the very day.
		Ratio of air concentraion were calculated from atmospheric pressure at the altitude with
		that on the ground.   Atmospheric pressure were data from the ground to altitude of 33.4km by
		the observatory. Atmospheric pressure were calculated by formula of U.S. standard atmosphere,
		1976. over that altitude.
		Date      : June 7, 2020
		Writer     : B.Engr.  Koji Makino
		Review   : June 10, 2023
		The following table was drawn to confirm illuminant state every second.
	Table 2. calculated proceeding direction sound velocities and aerodynamic
		heating temperatures at elapse time from 85 second to 99 second
	Elapse	Vertical	Horizontal	Proceeding	Proceeding	Height a-	Ratio of air	Coeffi-	Aerodyna-		Visual ob-
	time	direction	direction	direction	direction	bove ground	concent-	cient	mic heating		servation
		velocity	velocity	velocity	sound	start to fall	ration to	of form	tempe-		flying
		V=g×t	1097.4		velocity	from height	that on	r = 1	rature		object
		+747.9				120km	the ground				color ・
	(s)	(m/s)	(m/s)	(m/s)	(Mach)	(m)	(％)		(℃)		state
	85	1580.9	1097.4	1924.5	5.83	21026.0	4.54	1	148.5		G., W.C.
	86	1590.7	1097.4	1932.5	5.86	19440.2	5.81	1	270.9		G., W.C.
	87	1600.5	1097.4	1940.6	5.88	17844.6	7.48	1	433.2		G., W.C.
	88	1610.3	1097.4	1948.7	5.91	16239.2	9.68	1	648.5		Light Pink
	89	1620.1	1097.4	1956.8	5.93	14624.0	12.6	1	931.7		Orenge
	90	1629.9	1097.4	1964.9	5.95	12999.0	16.2	1	1295.0		Bright White
	91	1639.7	1097.4	1973.0	5.98	11364.2	20.9	1	1761.8		Big Flash
	92	1649.5	1097.4	1981.2	6.00	9719.6	26.9	1	2374.9		Huge Flash
	93	1659.3	17800.0	17877.2	54.17	8065.2	34.6	0.02	5269.6		Y.W.P.
	94	1669.1	17800.0	17878.1	54.18	6401.0	44.0	0.02	6776.5		Y.W.P.
	95	800.0	1200.0	1442.2	4.37	5601.0	49.3	−−	−−−		P.B.
	96	600.0	600.0	848.5	2.57	5001.0	53.4	−−	−−−		M.S.D.
	97	400.0	400.0	565.7	1.71	4601.0	56.3	−−	−−−		E.A.M.S.D.
	98	300.0	300.0	424.3	1.29	4301.0	58.6	−−	−−−		H.T.M.S.
	99	150.0	200.0	250.0	0.76	4151.0	59.8	−−	−−−		H.T.M.S.
			These velocitys are calculated			G., W.C.  :	Gray, White Cloud
			to divide moving distance in			Y.W.P.    :	Yellow White Photosphere
			2 seconds by time.			P.B.      :	Photosphere Burst
			Those velocitys are put to			M.S.D.   :	Molten Substance Diffussion
			suitable value.			E.A.M.S.D.:	Explosion After Molten Substance Diffusion
			Calculated height by observed			H.T.M.S. :	High Temperature Meteorites Shower
			elevation angle at sighting site.
			When it became a photosphere,
			since it became the sphere fully,
			that form factor becomes small.						June 10, 2023
		How to determine the coefficient of form
		The shape of flying object gives influence for aerodynamic heating.  It is determined
		aerodynamic heating coefficient of form  r = 1 through trial and error because meteorite is
		almost sphere.
		The molten substance continued to spread after photosphere bursting.  So the yellow
		white photosphere became early for 1second. Ratios of air concentration to that on the
		ground were reviewed, those numerical values were revised.							August 2, 2021
		When lapse time were from 90 second to 92 second, it became the huge flash fireball
		and the velocity became 1.98km/s (Mach 6.0). The ice of the meteorite vapored in large
		amounts, it became a huge black cloud. When lapse time were from 93 second to 94 second,
		it became a photosphere and it flew with the velocity 17.9km/s (Mach 54.2).
									August 2, 2021
		Date      : June 7, 2020
		Writer     : B.Engr.  Koji Makino
		Review   : June 10, 2023
		The confirmation with the actual temperature has not been performed about
		calculative numerical values with aerodynamic heating temperatures from 93 second
		to 94 second at the lapse time. Till 92 second, it is confirmed from the relation
		between luminescent color and temperature above the ground.							August 2, 2021
		When the temperature inside a photosphere exceeds 2862 ℃, the ferrum of an
		interiority substance becomes gas and it will vapor. Since the interiority substance of
		the photosphere turned into a molten substance and the waterish viscosity was shown,
		it was surmised that the bulk temperature of a photosphere was probably 2200 ℃.
		Supposing the form factor was 1, since the temperature would be too high, it set the
		form factor to 0.02. Probably, the surface temperature of a photosphere will be
		from 5000℃ to 7000℃.							June 10, 2023
		Date       : June 7, 2020
		Writer      : B.Engr.  Koji Makino
		Review    : June 10, 2023
		the Verification about the Altitude of 120km where
						the Meteorite Start to Fall from.
		(It is verified by comparing calculated distances with measured distances
		on route map at each illuminant state whether it is suitable that the height of meteorite
		start to fall from 120km. )
		Table 1 : Table of doing decision that caluculated horizontal distances compare with
		measured distances on the route map at each illuminant state from point of
		meteorite starting to fall
		Calculation of the horizontal　distance from point of					Verification
		starting meteorite fall, the height and the illuminant state					(Measurement on the route map)
		Elapsed	Horizontal	Distance	Height	Calculat-	Route map	Route map	Deci-
		time from	direction	from		ed temp.	point name	measure.	sion
		starting p.	velocity	starting p.		illuminant		distance	(within 2%
		(s)	(m/s)	(m)	(m)	state		(mm)	of error)
		88	1097.4	96571	16239.2	Light Pink	Lumi. Start	96.5	Agree.
		89	1097.4	97669	14624.0	Orenge
		90	1097.4	98766	12999.0	Bright White	Bright White	98.5	Agree.
		91	1097.4	99863	11364.2	Big Flash	----	----	----
		92	1097.4	100961	9719.6	Huge Flash	Huge Flash	102	Agree.
		93	17800	118761	8065.2	Y.W.Photo.	----	----	----
		94	17800	136561	6401.0	Y.W.Photo.	----	----	----
		95	1200	137761	5601.0	P.B.	----	----	----
		96	600	138361	5001.0	M.S.D.	M.S.D.	138	Agree.
		97	400	138761	4601.0	E.A.M.S.D.	----	----	----
		98	300	139061	4301.0	H.T.M.S.	----	----	----
		99	200	139261	4151.0	H.T.M.S.	----	----	----
		The route map is scale 1/1000000.
		1mm on the route map correspond to 1km in real distance value.
		starting p. : starting point of meteorite fall				Lumi. Start : Luminous Start
		Y.W.Photo. : Yellow White Photosphere				P.B.          : Photosphere Burst
		M.S.D.      : Molten Substance Diffusion				Agree.       : Agreement
		E.A.M.S.D.   : Explosion After Molten Substance Diffusion
		H.T.M.S.   : High Temperature Meteorites Shower
		Agreement means that calculated distance is equal with measured distance on the route map.
			Comparation with calculated horizontal distance and measured distance from
			starting point of merteorite fall
			This numeric value match up with calculated height from witnessed elevation angle.
		The molten substance continued to spread after photosphere bursting.
		So the yellow white photosphere became early for 1second and the molten substance diffusion
		time was added on the table 1.						August 2, 2021
		※ In the case of falling from height of 120km,  the calculated value of the distance
		were suitable well with the measured distance on the route map at each illuminant
		state point from the starting point.
		It is judged that the meteorite starting to
						fall from height of 120km is suitable.
							Transl. date :	August 28, 2020
							Translator   :	B.Engr.  Koji Makino
							Transl. rev.  :	June 12, 2023