Orbital Calculator – HTML Tool for Satellite Periods and Velocities for the Solar System. UKF

A lightweight HTML/JavaScript tool that computes orbital periods and mean velocities of satellites and Solar System objects using the Universal Kochenov Framework (UKF). The calculation uses only geometric addresses and kinematic invariants: a=araw/Reqa=araw/Req — dimensionless address, T=T0⋅a1.5T=T0⋅a1.5 — geometric scaling of the address, v=v0/av=v0/a — kinematic velocity profile. Optional corrections: J2 oblateness filter for close orbits, barycentric corrections for binary systems, S-E-M operator for the Moon. No masses, no G. Only geometry. Only addresses. !DOCTYPE html html lang=en head meta charset=UTF-8 meta name=viewport content=width=device-width, initial-scale=1.0 titleUKF Orbital Calculator v4.8.6title style {box-sizingborder-box;margin0;padding0} body{font-family'Segoe UI',Roboto,system-ui,sans-serif;background#0b0f1a;color#e8edf5;displayflex;justify-contentcenter;align-itemsflex-start;min-height100vh;padding20px} .card{max-width960px;width100%;background#141a26;padding36px 28px;border-radius28px;border1px solid #2a3344;box-shadow0 20px 40px rgba(0,0,0,.7)} h1{font-size26px;font-weight500;letter-spacing-.5px} .sub{color#8b9bb5;font-size14px;margin6px 0 22px;border-left3px solid #3b82f6;padding-left14px} .tabs{displayflex;gap8px;margin-bottom18px;flex-wrapwrap} .tab{padding10px 18px;border-radius30px;border1px solid #2e3a4e;background#1e2636;color#c5d0e0;cursorpointer;font-size14px} .tab.active{background#3b82f6;border-color#3b82f6;color#fff;font-weight600} .panel{displaynone} .panel.active{displayblock} .input-group{displayflex;gap10px;flex-wrapwrap;margin-bottom16px;align-itemscenter} .input-group select,.input-group input{ padding12px 16px;border-radius40px;border1px solid #2e3a4e;background#1e2636;color#f0f4fc;font-size15px;outlinenone } .input-group select{flex1;min-width140px} .input-group input{width140px} .input-group inputfocus,.input-group selectfocus{border-color#3b82f6} .input-group button{ padding12px 22px;bordernone;border-radius40px;background#3b82f6;color#fff;font-weight600;font-size15px;cursorpointer } .input-group buttonhover{background#2563eb} .input-group buttondisabled{opacity.4;cursornot-allowed} .grid{displaygrid;grid-template-columnsrepeat(auto-fill,minmax(160px,1fr));gap10px;margin-bottom14px} .grid label{displayflex;flex-directioncolumn;gap4px;font-size12px;color#8b9bb5} .grid input{padding10px 12px;border-radius12px;border1px solid #2e3a4e;background#1e2636;color#f0f4fc;font-size14px} .hint{font-size12px;color#5a6a82;margin-bottom12px;line-height1.5} .result-box{ background#0e131f;border-radius18px;padding18px 20px;border1px solid #26303f; font-size14px;line-height1.65;white-spacepre-wrap;font-family'Courier New',monospace;min-height140px } .highlight{color#facc15} .deviation-pos{color#4ade80} .deviation-neg{color#f87171} .note{color#8b9bb5;font-size12px} .footer{margin-top22px;font-size12px;color#4d5e78;text-aligncenter;border-top1px solid #1f2a3a;padding-top16px} .badge{displayinline-block;background#1f2a3a;padding3px 10px;border-radius20px;font-size11px;color#a5b9d4;margin-right6px} style head body div class=card h1⏱ UKF Orbital Calculatorh1 div class=subAligned to Mass-Free Kinematic Topology PDF · No G · No M · Address geometry only · a href=httpszenodo.orgrecords21970572 target=_blank rel=noopener style=color#7b9cd6;text-decorationnoneZenodo recordadiv div class=tabs button class=tab active data-tab=catalogCatalogbutton button class=tab data-tab=customCustom objectbutton div div class=panel active id=panel-catalog div class=input-group select id=planetSelect option value=EarthEarthoption option value=MarsMarsoption option value=Jupiter selectedJupiteroption option value=SaturnSaturnoption option value=UranusUranusoption option value=NeptuneNeptuneoption option value=PlutoPlutooption select select id=satelliteSelectselect button id=calcBtnComputebutton div div div class=panel id=panel-custom div class=hint Algorithm (PDF) a = a_rawReq · T_base = T0·a^1.5 · μ binarycascade · J2 if a<5 · η_spin if retrograde.br T0 empty → 2π·Req(86400·v0). S-E-M Moon uses T0_SEM = 0.058913 d. div div class=grid labelParent nameinput id=cParentName value=CustomParentlabel labelReq (km)input id=cReq type=number step=any value=71492label labelv0 (kms)input id=cV0 type=number step=any value=42.1label labelT0 (days, optional)input id=cT0 type=number step=any placeholder=autolabel labelJ2 (optional)input id=cJ2 type=number step=any value=0.014736label labelρ parent (gcm³)input id=cRhoP type=number step=any value=1.326label labelObject nameinput id=cSatName value=MyMoonlabel labela_raw (km)input id=cAraw type=number step=any value=421800label labele (optional)input id=cE type=number step=any value=0label labelR_patient km (binary)input id=cRp type=number step=any placeholder=—label labelρ_patient (binary)input id=cRhoS type=number step=any placeholder=—label labelNASA period (d)input id=cNasa type=number step=any placeholder=optionallabel div div class=input-group label style=flex-directionrow;align-itemscenter;gap8px;color#c5d0e0;font-size14px input type=checkbox id=cUseJ2 checked J2 if a<5 (PDF) label label style=flex-directionrow;align-itemscenter;gap8px;color#c5d0e0;font-size14px input type=checkbox id=cBinary binary μ label label style=flex-directionrow;align-itemscenter;gap8px;color#c5d0e0;font-size14px input type=checkbox id=cRetro retrograde η_spin label button id=customBtnCompute custombutton div div div class=result-box id=resultBox span class=highlight▶ Catalog pick planet + satellite · Custom enter object and Computespan div div class=footer span class=badgeUKF v4.8.6span PDF-aligned · Steps A–F · S-E-M Moon · binary · J2 (a<5) · retrograde η_spinbr a href=httpszenodo.orgrecords21970572 target=_blank rel=noopener style=color#7b9cd6;text-decorationnonehttpszenodo.orgrecords21970572a div div script Parent constants — Table 1 of the PDF const PARENT = { Earth { Req6378.137, v07.90537, T00.0586728, T0_SEM0.058913, J20.00108263, rho5.515 }, Mars { Req3396.200, v03.55115, T00.069549, J20.0019604, rho3.934 }, Jupiter { Req71492.000, v042.1000, T00.123500, J20.0147360, rho1.326 }, Saturn { Req60268.000, v025.1000, T00.174800, J20.0162980, rho0.687 }, Uranus { Req25559.000, v015.0600, T00.123420, J20.0033412, rho1.270 }, Neptune { Req24764.000, v016.6200, T00.108360, J20.0034000, rho1.638 }, Pluto { Req1188.300, v00.85600, T00.100950, J20.0000100, rho1.854 } }; const SATELLITES = { Moon { parent'Earth', a_raw384400, e0.0549, R_patient1737.4, rho_patient3.344, mode'SEM' }, ISS { parent'Earth', a_raw6796.137, e0.0006 }, GPS { parent'Earth', a_raw26578.137,e0.02 }, Phobos { parent'Mars', a_raw9376, e0.0151 }, Deimos { parent'Mars', a_raw23463.2, e0.00033 }, Io { parent'Jupiter', a_raw421800, e0.0041 }, Europa { parent'Jupiter', a_raw671100, e0.009 }, Ganymede { parent'Jupiter', a_raw1070400, e0.0013 }, Callisto { parent'Jupiter', a_raw1882700, e0.0074 }, Amalthea { parent'Jupiter', a_raw181365.8, e0.0032 }, Himalia { parent'Jupiter', a_raw11461000, e0.16 }, Elara { parent'Jupiter', a_raw11741000, e0.22 }, Pasiphae { parent'Jupiter', a_raw23624000, e0.41 }, Sinope { parent'Jupiter', a_raw23939000, e0.25 }, Lysithea { parent'Jupiter', a_raw11717000, e0.11 }, Titan { parent'Saturn', a_raw1221870, e0.0288 }, Rhea { parent'Saturn', a_raw527108, e0.001 }, Iapetus { parent'Saturn', a_raw3560820, e0.0283 }, Dione { parent'Saturn', a_raw377396, e0.0022 }, Tethys { parent'Saturn', a_raw294619, e0.0001 }, Enceladus{ parent'Saturn', a_raw237948, e0.0047 }, Mimas { parent'Saturn', a_raw185539, e0.0196 }, Hyperion { parent'Saturn', a_raw1481010, e0.123 }, Phoebe { parent'Saturn', a_raw12952000, e0.163 }, Janus { parent'Saturn', a_raw151460, e0.0068 }, Titania { parent'Uranus', a_raw435910, e0.0011 }, Oberon { parent'Uranus', a_raw583520, e0.0014 }, Ariel { parent'Uranus', a_raw190900, e0.0012 }, Umbriel { parent'Uranus', a_raw266000, e0.0039 }, Miranda { parent'Uranus', a_raw129858, e0.0013 }, Triton { parent'Neptune', a_raw354759, e0.000016, retrogradetrue }, Proteus { parent'Neptune', a_raw117647, e0.00053 }, Nereid { parent'Neptune', a_raw5513818, e0.751 }, Larissa { parent'Neptune', a_raw73548, e0.0012 }, Charon { parent'Pluto', a_raw19596, e0.0002, R_patient606, rho_patient1.702, mode'binary' } }; const NASA_PERIODS = { Moon27.321661, ISS0.064493, GPS0.49865, Phobos0.31891023, Deimos1.2624407, Io1.769137786, Europa3.551181, Ganymede7.15455296, Callisto16.6890184, Amalthea0.49817943, Himalia250.5662, Elara259.6528, Pasiphae743.63, Sinope758.9, Lysithea259.2, Titan15.945421, Rhea4.518212, Iapetus79.3215, Dione2.736915, Tethys1.887802, Enceladus1.370218, Mimas0.9424218, Hyperion21.27661, Phoebe550.564636, Janus0.6945, Titania8.705872, Oberon13.463234, Ariel2.520379, Umbriel4.144177, Miranda1.413479, Triton5.876854, Proteus1.12231477, Nereid360.13619, Larissa0.55465332, Charon6.387227 }; PDF algorithm Steps A–F A a = a_raw Req B T_base = T0 a^1.5 C μ binary or cascade; T_int = T_base sqrt(μ) D J2 if a 5 T_J2 = T_int sqrt(1 + 1.5J2a^2) E retrograde η_spin = 1 + J2a Φ (Φ=-1); T_final = T_J2 η_spin F v_mean = v0sqrt(a) (1 - e^24 - 3e^464) function r