Distance from the Sun & Orbital Speed
06-27-2015, 04:00 PM
Post: #1 Eddie W. Shore Senior Member Posts: 1,150 Joined: Dec 2013
Distance from the Sun & Orbital Speed
Link to the full blog entry: http://edspi31415.blogspot.com/2015/06/h...ocity.html

Equations

Angle used:

θ = 360° * d/N
d = number of days from perihelion
N = number of days in a planet’s “year”, or number of days it takes for a planet to make one orbit around the Sun

Distance from Sun (in meters):

r = (a*(1 - ϵ)/(1 + ϵ cos θ ))
a = length of semi-major axis of a planet’s orbit
ϵ = the eccentricity of an orbit (ellipse)

Orbital Speed (in meters/second):

v = √( G * (M_Sun + M_planet) * (2/r – 1/a))
G = Gravitational Constant = 6.63784 * 10^-11 m^3/(s^2 *kg)
M_Sun = Mass of the Sun ≈ 1.9884 * 10^30 kg
M_planet = Mass of the planet

Code:
EXPORT ORBSD() BEGIN // Orbital distance and // speed around the Sun // EWS 2015-06-25 // Initialization LOCAL lm,pm,la,pa,le,pe; LOCAL ld,pd; LOCAL p,sp,θ,d,v,r; // Planets sp:={"Mercury","Venus","Earth", "Mars","Jupiter","Saturn", "Uranus","Neptune", "Pluto (Dwarf)"}; // Mass (kg) lm:={3.29438ᴇ23,4.85749ᴇ24, 5.9722ᴇ24,6.40397ᴇ23,1.89469ᴇ27, 5.67312ᴇ26,8.66437ᴇ25,1.02224ᴇ26, 1.31ᴇ22}; // Semi-Major Axis (m) la:={57909829824,108209876544, 149594962176,227921734656, 778412012083,1.42673ᴇ12, 2.87097ᴇ12,4.49825ᴇ12, 5.90637ᴇ12}; // Eccentricity (ε) le:={.206,.007,.017,.093,.048, .056,.046,.009,.249}; // Days in a year ld:={87.96899,224.701,365.256, 686.98,4332.58899,10759.22, 30685.4,60189,90465}; // Input INPUT({{p,sp},d},"Data", {"Planet:","# Days:"}, {"Planet","# Days after  Perihelion"}); pm:=lm[p]; pa:=la[p]; pe:=le[p]; pd:=ld[p]; θ:=360*d/pd; HAngle:=1; // degree // distance r:=(pa*(1-pe^2))/(1+pe*COS(θ)); // orbit distance v:=√((1.9884ᴇ30+pm)*6.63784ᴇ−11* (2/r-1/pa));  // output PRINT(); PRINT("Distance from the Sun:"); PRINT(STRING(r)+" m"); PRINT("Orbital Speed:"); PRINT(STRING(v)+" m/s"); RETURN {r,v}; END;
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