1 of 7 Enigmas In Modeling By Ian Beardsley © 2016
2 of 7 Presented are the equations for modeling average annual temperature for a planet given the orbital distance of the planet from the star, the star’s luminosity and the albedo of the planet. The source code is written on an HP 35s Scientific Calculator and values for it run with an enigmatic result. Similarly, the source code is presented for modeling the mass of a planet with three layers of varying density and an idealized scenario is run for the that which presents, also, enigmatic results. 
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The Equations For The Modeling of Average Annual Temperature of A Planet With a Single Atmospheric Layer
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H001 LBL H H002 INPUT U (Solar Luminosities) H003 STO U H004 3.9E26 H005 X (MULTIPLY) H006 STO W H007 VIEW W (Joules/Sec) H008 INPUT R (AU) H009 STO R H010 1.5E11 H011 X (MULTIPLY) H012 STO M H013 VIEW M (Meters) H014 RCL M H015 x^2 H016 pi H017 X (MULTIPLY) H018 4 H019 X (MULTIPLY) H020 STO V H021 RCL W H022 RCL V H023 / (DIVIDE) H024 STO S H025 VIEW S (Stellar Constant) H026 RCL U H027 sqrt H028 STO H H029 VIEW H (Habitable Zone) H030 INPUT A (Albedo) H031 STO A H032 1 H033 RCL A H034 - (SUBTRACT) H035 STO B H036 RCL S H037 X (MULTIPLY) H038 4 H039 / (DIVIDE) H040 STO C H041 VIEW C H042 5.67E-8 H043 / (Divide) H044 4 H045 x root of y H046 1.189 H047 X (MULTIPLY)
H048 STO K H049 VIEW K (Plantet Temperature Kelvin) H050 273 H051 - (SUBTRACT) H052 STO T H053 VIEW T (Planet Temperature Centigrade) H054 —> F H055 STO F H056 VIEW F (Planet Temperature Fahrenheit) H057 RTN
XEQ H000 U? 1.618 W=6.31E26 R? 1.618 M=242,… S=852 H=1.272 A? 0.618 C=81 K=231 T=-41.5 F=-43
R/S R/S R/S R/S R/S R/S R/S R/S R/S R/S R/S
We have run the program, here, for: 1.618 solar luminosities = PHI 0.618 albedo = phi 1.618 orbital distance = PHI And we got near Fahrenheit-Celcius equivalence:
F=(9/5)C+32 F=C C=(9/5)C+32 (5/5)C - (9/5)C = 32 -(4/5)C = 32 -4C = 160 C=-40 -40C = -40F
5 of 7 density.c (determines mass of planet for three layers) #include <stdio.h> #include <math.h> int main(void) { float r1=0.00, r2=0.00, r3=0.00, p1=0.00, p2=0.00, p3=0.00; printf("what is r1, the radius of the core in km? "); scanf("%f", &r1); printf("what is p1, its density in g/cm^3? "); scanf("%f", &p1); printf("what is r2, outer edge of layer two in km? "); scanf("%f", &r2); printf("what is p2, density of layer two in g/cm^3? "); scanf("%f", &p2); printf("what is r3, the radius of layer 3 in km? "); scanf("%f", &r3); printf("what is p3, density of layer three in g/cm^3? "); scanf("%f", &p3); printf("\n"); printf("\n"); printf("r1=%.2f, r2=%.2f, r3=%.2f, p1=%.2f, p2=%.2f, p3=%.2f \n", r1,r2,r3,p1,p2,p3); printf("\n"); float R1, v1, m1, M1; { R1=(r1)*(1000.00)*(100.00); v1=(3.141)*(R1)*(R1)*(R1)*(4.00)/(3.00); m1=(p1)*(v1); M1=m1/1000.00; printf("the core has a mass of %.2f E23 Kg\n", M1/1E23); printf("thickness of core is %.2f \n", r1); } float R2, v2, m2, M2; { R2=(r2)*(1000.00)*(100.00); v2=(3.141)*(R2*R2*R2-R1*R1*R1)*(4.00)/(3.00); m2=(p2)*(v2); M2=m2/1000.00; printf("layer two has a mass of %.2f E23 Kg\n", M2/1E23); printf("layer two thickness is %.2f \n", r2-r1); } float R3, v3, m3, M3; { R3=(r3)*(1000.00)*(100.00); v3=(3.141)*(R3*R3*R3-R2*R2*R2)*(4.00)/(3.00); m3=(p3)*(v3); M3=m3/1000.00;
6 of 7 printf("layer three has a mass of %.2f E23 Kg\n", M3/1E23); printf("layer three thickness is %.2f \n", r3-r2); } printf("\n"); printf("\n"); printf("the mass of the planet is %.2f E24 Kg\n", (M1+M2+M3)/1E24); }
jharvard@appliance (~): cd Dropbox jharvard@appliance (~/Dropbox): make density clang -ggdb3 -O0 -std=c99 -Wall -Werror density.c -lcs50 -lm -o density jharvard@appliance (~/Dropbox): ./density what is r1, the radius of the core in km? 500 what is p1, its density in g/cm^3? 7.87 what is r2, outer edge of layer two in km? 5000 what is p2, density of layer two in g/cm^3? 8.91 what is r3, the radius of layer 3 in km? 6371 what is p3, density of layer three in g/cm^3? 2.33
r1=500.00, r2=5000.00, r3=6371.00, p1=7.87, p2=8.91, p3=2.33 the core has a mass of 0.04 E23 Kg thickness of core is 500.00 layer two has a mass of 46.60 E23 Kg layer two thickness is 4500.00 layer three has a mass of 13.04 E23 Kg layer three thickness is 1371.00
the mass of the planet is 5.97 E24 Kg jharvard@appliance (~/Dropbox): The actual mass of the Earth is 5.972E24 The Modeled Value is 100% accurate We used Iron core, Nickel middle region, Silicon outer region While there are more than three layers to the Earth Iron, Nickel, Silicon are only predominant to the regions And, are not the only elements or compounds found in them We used the actual densities of Iron, Nickel, and Siliconâ&#x20AC;Š
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