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Related

time

m1: 60/5.5;

m2: 60/6.0;

m3: 60*0.75/6.6;

Calculate

time

? isolate_wrt_time;

Calculate

time

? isolate_wrt_time;

Calculate

time

? isolate_wrt_time;

Calculate

time

m1: 60/5.5;

m2: 60/6.0;

m3: 60*0.75/6.6;

Calculate

time

Run Example
(%i1)l:matrix([-2.59783648,-1.57661906,-2.85131233]);
(%o1)            [ - 2.59783648  - 1.57661906  - 2.85131233 ]
(%i2) m:matrix([0.18594505,-4.06072906,-0.91671590]);
(%o2)              [ 0.18594505  - 4.06072906  - 0.9167159 ]
(%i3) n:matrix([2.98558342,-1.52457786,-2.47516022]);
(%o3)             [ 2.98558342  - 1.52457786  - 2.47516022 ]
(%i4) o:matrix([1.52361432,-0.04724021,-3.87825114]);
(%o4)             [ 1.52361432  - 0.04724021  - 3.87825114 ]
(%i5) t1:88.497907;
(%o5)                              88.497907
(%i6) t2:77.424860;
(%o6)                              77.42486
(%i7) t3:83.298642;
(%o7)                              83.298642
(%i8) t4:89.640527;
(%o8)                          89.64052700000001
(%i9) c:299792458;
(%o9)                              299792458
(%i10) r:6378137;
(%o10)                              6378137
(%i11) v:c/(1000*r);
                                  149896229
(%o11)                            ----------
                                  3189068500
(%i12) e1:expand((x-l[1,1])^2+(y-l[1,2])^2+(z-l[1,3])^2=v^2*(t-t1)^2);
            2                       2                       2
(%o12) 1.0 z  + 5.70262466 z + 1.0 y  + 3.15323812 y + 1.0 x  + 5.19567296 x
                                          2
 + 17.3644640403841 = 0.0022092950467877 t  - 0.39103597517236 t
 + 17.30293268222889
(%i13) e2:expand((x-m[1,1])^2+(y-m[1,2])^2+(z-m[1,3])^2=v^2*(t-t2)^2);
            2                      2                       2
(%o13) 1.0 z  + 1.8334318 z + 1.0 y  + 8.12145812 y + 1.0 x  - 0.3718901 x
                                           2
 + 17.36446410166079 = 0.0022092950467877 t  - 0.34210871939246 t
 + 13.24385985187042
(%i14) e3:expand((x-n[1,1])^2+(y-n[1,2])^2+(z-n[1,3])^2=v^2*(t-t3)^2);
            2                       2                       2
(%o14) 1.0 z  + 4.95032044 z + 1.0 y  + 3.04915572 y + 1.0 x  - 5.97116684 x
                                           2
 + 17.36446412365153 = 0.0022092950467877 t  - 0.36806255434949 t
 + 15.3295554741817
(%i15) e4:expand((x-o[1,1])^2+(y-o[1,2])^2+(z-o[1,3])^2=v^2*(t-t4)^2);
            2                       2                       2
(%o15) 1.0 z  + 7.75650228 z + 1.0 y  + 0.09448042 y + 1.0 x  - 3.04722864 x
                                           2
 + 17.36446413846121 = 0.0022092950467877 t  - 0.39608474458508 t
 + 17.75262262063352
(%i16) l1:e2-e1;
(%o16) - 3.86919286 z + 4.96822 y - 5.56756306 x + 6.1276693941181293E-8 = 
                                        0.048927255779895 t - 4.059072830358472
(%i17) l2:e3-e1;
(%o17) - 0.75230422 z - 0.1040824 y - 11.1668398 x + 8.3267426731481464E-8 = 
                                        0.022973420822873 t - 1.973377208047197
(%i18) l3:e4-e1;
(%o18) 2.053877620000001 z - 3.0587577 y - 8.2429016 x
              + 9.8077109100813686E-8 = 0.44968993840462 - 0.0050487694127212 t
(%i19) sol:float(linsolve([l1,l2,l3],[z,y,x,t]));

rat: replaced 4.059072891635166 by 14361/3538 = 4.059072922555116

rat: replaced -0.0489272557799 by -1553/31741 = -0.04892725496991

rat: replaced -5.56756306 by -33333/5987 = -5.56756305328211

rat: replaced 4.96822 by 30172/6073 = 4.968219990120204

rat: replaced -3.86919286 by -14908/3853 = -3.86919283675058

rat: replaced 1.973377291314623 by 7783/3944 = 1.973377281947262

rat: replaced -0.02297342082287 by -1733/75435 = -0.02297342082588

rat: replaced -11.1668398 by -21485/1924 = -11.1668399168399

rat: replaced -0.1040824 by -2213/21262 = -0.1040824005268

rat: replaced -0.75230422 by -11672/15515 = -0.7523042217209

rat: replaced -0.4496898403275 by -4277/9511 = -0.4496898328251

rat: replaced 0.0050487694127212 by 999/197870 = 0.0050487693940466

rat: replaced -8.2429016 by -42385/5142 = -8.24290159471023

rat: replaced -3.0587577 by -5466/1787 = -3.05875769445999

rat: replaced 2.053877620000001 by 23597/11489 = 2.053877622073288
(%o19) [z = 6.5146569086060767E-51 (7.2510967492032188E+46 %r1
 + 2.2924362116603168E+49), y = 2.4842910726530269E-52
 (3.1370701323484879E+49 %r1 - 2.0473694525177474E+51), 
x = - 1.5857177059487408E-53 (1.3632648845479128E+50 %r1
 - 1.0808802520386623E+52), t = %r1]
(%i20) temp1:rhs(sol[1]);
(%o20) 6.5146569086060767E-51 (7.2510967492032188E+46 %r1
                                                      + 2.2924362116603168E+49)
(%i21) x(%r1):=''temp1;
(%o21) x(%r1) := 6.5146569086060767E-51
                          (7.2510967492032188E+46 %r1 + 2.2924362116603168E+49)
(%i22) temp2:rhs(sol[2]);
(%o22) 2.4842910726530269E-52 (3.1370701323484879E+49 %r1
                                                      - 2.0473694525177474E+51)
(%i23) y(%r1):=''temp2;
(%o23) y(%r1) := 2.4842910726530269E-52
                          (3.1370701323484879E+49 %r1 - 2.0473694525177474E+51)
(%i24) temp3:rhs(sol[3]);
(%o24) - 1.5857177059487408E-53 (1.3632648845479128E+50 %r1
                                                      - 1.0808802520386623E+52)
(%i25) z(%r1):=''temp3;
(%o25) z(%r1) := - 1.5857177059487408E-53
                          (1.3632648845479128E+50 %r1 - 1.0808802520386623E+52)
(%i26) time:float(solve((1.0*(z(t))^2+5.70262466*z(t)+1.0*(y(t))^2+3.15323812*y(t)+1.0*(x(t))^2+5.19567296*x(t)-0.0022092950467877*t^2+0.39103597517236*t+ 0.061531358155205)));

rat: replaced 0.061531358155205 by 933/15163 = 0.061531359229704

rat: replaced 0.39103597517236 by 8489/21709 = 0.39103597586255

rat: replaced 3.3848026743721779E-50 by 1/29543819720169729999342100189543533972874273488896 = 3.3848026743721784E-50

rat: replaced 2.2924362116603168E+49 by 22924362116603167617613524315571965618364709076992/1 = 2.2924362116603168E+49

rat: replaced 7.2510967492032188E+46 by 72510967492032188060371436946690487747054927872/1 = 7.2510967492032188E+46

rat: replaced 7.8335613114652143E-52 by 1/1276558592241306999771897818587361252033462857105408 = 7.8335613114652143E-52

rat: replaced -2.047369452517747E+51 by -2047369452517747376346696215767806000026274509094912/1 = -2.047369452517747E+51

rat: replaced 3.1370701323484879E+49 by 31370701323484879423026425755851519257995821187072/1 = 3.1370701323484879E+49

rat: replaced -9.042752893741917E-53 by -1/11058579303787622635203504214625043577215301948801024 = -9.042752893741917E-53

rat: replaced -1.080880252038662E+52 by -10808802520386622731436425358317709323391235138781184/1 = -1.080880252038662E+52

rat: replaced 1.3632648845479128E+50 by 136326488454791279754401580924698271417655332175872/1 = 1.3632648845479128E+50

rat: replaced -0.002209295046788 by -248/112253 = -0.002209295074519

rat: replaced 4.2440754636848885E-101 by 1/23562257753347229622376500296170620528522706926668915888290726004341534784516795029987485107454214144 = 4.2440754636848885E-101

rat: replaced 2.2924362116603168E+49 by 22924362116603167617613524315571965618364709076992/1 = 2.2924362116603168E+49

rat: replaced 7.2510967492032188E+46 by 72510967492032188060371436946690487747054927872/1 = 7.2510967492032188E+46

rat: replaced 6.1717021336635272E-104 by 1/16202985470499354928075779114019474646803738313180849249646998292919592999520995252654517349097913974784 = 6.1717021336635272E-104

rat: replaced -2.047369452517747E+51 by -2047369452517747376346696215767806000026274509094912/1 = -2.047369452517747E+51

rat: replaced 3.1370701323484879E+49 by 31370701323484879423026425755851519257995821187072/1 = 3.1370701323484879E+49

rat: replaced 2.514500642959337E-106 by 1/3976932767148118764804035022332075860933364873483229141069635729363713418057950710104947976121596652814336 = 2.514500642959337E-106

rat: replaced -1.080880252038662E+52 by -10808802520386622731436425358317709323391235138781184/1 = -1.080880252038662E+52

rat: replaced 1.3632648845479128E+50 by 136326488454791279754401580924698271417655332175872/1 = 1.3632648845479128E+50
(%o26)         [t = - 1.303614944028307, t = 186.5983819022283]
(%i27) time1:rhs(time[1]);
(%o27)                        - 1.303614944028307
(%i28) time2:rhs(time[2]);
(%o28)                         186.5983819022283
(%i29) F:x(time1)^2+y(time1)^2+z(time1)^2;
(%o29)                         0.32160976929642
(%i30) G:x(time2)^2+y(time2)^2+z(time2)^2;
(%o30)                         1.004393615514375
(%i31) coord1:x(time2);
(%o31)                         0.23749045812972
(%i32) coord2:y(time2);
(%o32)                         0.94560879166645
(%i33) coord3:z(time2);
(%o33)                        - 0.23198256601485
(%i34) g1:coord1*r;
(%o34)                         1514746.678144129
(%i35) g2:coord2*r;
(%o35)                         6031222.421653055
(%i36) g3:coord3*r;
(%o36)                        - 1479616.587654235
(%i37) D:float(sqrt(g1^2+g2^2+g3^2));
(%o37)                         6392133.184224244
(%i38) lat:float(asin(g3/D));
(%o38)                        - 0.23359319559899
(%i39) lon:float(atan(g2/g1));
(%o39)                         1.324734798073671
(%i40) lat1:float((lat*360)/(2*%pi));
(%o40)                        - 13.38390423079593
(%i41) lon2:float((lon*360)/(2*%pi));
(%o41)                         75.90171290373667
(%i42) 
Run Example
c:299792458;
(%o1)                              299792458
(%i2) rt:6378137;
(%o2)                               6378137
(%i3) vc:(c/(1000*rt));
                                  149896229
(%o3)                             ----------
                                  3189068500
(%i4) E1:expand(((x-3.54112999)^2+(y-1.20767489)^2+(z-1.83477078)^2)=((vc^2)*(t-67.975651)^2));
           2                       2                       2
(%o4) 1.0 z  - 3.66954156 z + 1.0 y  - 2.41534978 y + 1.0 x  - 7.08225998 x
                                           2
 + 17.36446406115572 = 0.0022092950467877 t  - 0.30035653811294 t
 + 10.20846560516673
(%i5) E2:expand(((x+0.36937107)^2+(y-2.61106894)^2+(z+3.22650710)^2)=((vc^2)*(t-42.307987)^2));
           2                      2                       2
(%o5) 1.0 z  + 6.4530142 z + 1.0 y  - 5.22213788 y + 1.0 x  + 0.73874214 x
                                           2
 + 17.36446406313608 = 0.0022092950467877 t  - 0.18694165223732 t
 + 3.954562496307486
(%i6) E3:expand(((x-1.88394827)^2+(y+1.98448333)^2+(z+3.14277408)^2)=((vc^2)*(t-39.119433)^2));
           2                       2                       2
(%o6) 1.0 z  + 6.28554816 z + 1.0 y  + 3.96896666 y + 1.0 x  - 3.76789654 x
                                           2
 + 17.36446408900373 = 0.0022092950467877 t  - 0.17285273912009 t
 + 3.380950573437375
(%i7) E4:expand(((x+0.86766850)^2+(y-1.09882894)^2+(z-3.92481725)^2)=((vc^2)*(t-55.255462)^2));
           2                      2                       2
(%o7) 1.0 z  - 7.8496345 z + 1.0 y  - 2.19765788 y + 1.0 x  + 1.735337 x
                                           2
 + 17.36446411117133 = 0.0022092950467877 t  - 0.24415123700913 t
 + 6.745344699405586
(%i8) L1:expand(E2-E1);
(%o8) 10.12255576 z - 2.8067881 y + 7.82100212 x + 1.9803607642643328E-9 = 
                                         0.11341488587562 t - 6.253903108859241
(%i9) L2:expand(E3-E1);
(%o9) 9.95508972 z + 6.38431644 y + 3.31436344 x + 2.7848013672837624E-8 = 
                                         0.12750379899285 t - 6.827515031729351
(%i10) L3:expand(E4-E1);
(%o10) - 4.18009294 z + 0.2176919 y + 8.817596979999999 x
               + 5.0015614760923199E-8 = 0.056205301103807 t - 3.46312090576114
(%i11) k:float(linsolve([L1,L2,L3],[z,y,x,t]));

rat: replaced 6.253903110839602 by 7611/1217 = 6.253903040262942

rat: replaced -0.1134148858756 by -547/4823 = -0.1134148869998

rat: replaced 7.82100212 by 66807/8542 = 7.82100210723484

rat: replaced -2.8067881 by -16953/6040 = -2.8067880794702

rat: replaced 10.12255576 by 36755/3631 = 10.1225557697604

rat: replaced 6.827515059577364 by 39702/5815 = 6.827515047291487

rat: replaced -0.1275037989929 by -923/7239 = -0.1275037988672

rat: replaced 3.31436344 by 29236/8821 = 3.314363450855912

rat: replaced 6.38431644 by 18074/2831 = 6.384316495937831

rat: replaced 9.95508972 by 3325/334 = 9.955089820359282

rat: replaced 3.463120955776755 by 6902/1993 = 3.46312092323131

rat: replaced -0.05620530110381 by -668/11885 = -0.05620530079933

rat: replaced 8.817596979999999 by 42492/4819 = 8.81759701182818

rat: replaced 0.2176919 by 1228/5641 = 0.21769189859954

rat: replaced -4.18009294 by -10793/2582 = -4.18009295120062
(%o11) [z = 1.3236241772626055E-53 (4.4663908627867916E+50 %r1
 - 2.2733183491830905E+52), y = 3.3090604431565134E-53
 (1.8333853279667287E+50 %r1 - 9.8656247717750592E+51), 
x = 3.8605705170159322E-54 (2.3382593277347015E+51 %r1
 - 1.3659579455439278E+53), t = %r1]
(%i12) temp1:rhs(k[1]);
(%o12) 1.3236241772626055E-53 (4.4663908627867916E+50 %r1
                                                      - 2.2733183491830905E+52)
(%i13) z(%r1):=''temp1;
(%o13) z(%r1) := 1.3236241772626055E-53
                          (4.4663908627867916E+50 %r1 - 2.2733183491830905E+52)
(%i14) temp2:rhs(k[2]);
(%o14) 3.3090604431565134E-53 (1.8333853279667287E+50 %r1
                                                      - 9.8656247717750592E+51)
(%i15) y(%r1):=''temp2;
(%o15) y(%r1) := 3.3090604431565134E-53
                          (1.8333853279667287E+50 %r1 - 9.8656247717750592E+51)
(%i16) temp3:rhs(k[3]);
(%o16) 3.8605705170159322E-54 (2.3382593277347015E+51 %r1
                                                      - 1.3659579455439278E+53)
(%i17) x(%r1):=''temp3;
(%o17) x(%r1) := 3.8605705170159322E-54
                          (2.3382593277347015E+51 %r1 - 1.3659579455439278E+53)
(%i18) time:float(expand(solve([(x(t)-3.54112999)^2+(y(t)-1.20767489)^2+(z(t)-1.83477078)^2=(vc^2)*(t-67.975651)^2],[t])));

rat: replaced -67.975651 by -39086/575 = -67.975652173913

rat: replaced -1.20767489 by -50668/41955 = -1.20767488976284

rat: replaced 3.3090604431565134E-53 by 1/30220058447953273614767215692104399676901946386546688 = 3.3090604431565134E-53

rat: replaced -9.865624771775059E+51 by -9865624771775059194765548155136118949622956620251136/1 = -9.865624771775059E+51

rat: replaced 1.8333853279667287E+50 by 183338532796672871531223770810300137691499001282560/1 = 1.8333853279667287E+50

rat: replaced -1.83477078 by -4042/2203 = -1.83477076713572

rat: replaced 1.3236241772626055E-53 by 1/75550146119883186695374030800092744999868986527055872 = 1.3236241772626055E-53

rat: replaced -2.273318349183091E+52 by -22733183491830904757905765353234610976984470520856576/1 = -2.273318349183091E+52

rat: replaced 4.4663908627867916E+50 by 446639086278679164882818365248586572715535672279040/1 = 4.4663908627867916E+50

rat: replaced -3.54112999 by -20620/5823 = -3.54113000171733

rat: replaced 3.8605705170159322E-54 by 1/259029072411028074746324657759933401845525943660052480 = 3.8605705170159322E-54

rat: replaced -1.365957945543928E+53 by -136595794554392783339927448628635413422323975449477120/1 = -1.365957945543928E+53

rat: replaced 2.3382593277347015E+51 by 2338259327734701483284355314547938488555312148119552/1 = 2.3382593277347015E+51
(%o18)         [t = - 47.30246304765326, t = 136.3266216031066]
(%i19) time1:rhs(time[1]);
(%o19)                        - 47.30246304765326
(%i20) time2:rhs(time[2]);
(%o20)                         136.3266216031066
(%i21) Z:z(time1);
(%o21)                        - 0.58054569870147
(%i22) Y:y(time1);
(%o22)                        - 0.61343325912251
(%i23) X:x(time1);
(%o23)                        - 0.95433774170389
(%i24) z:z(time2);
(%o24)                         0.50503693475185
(%i25) y:y(time2);
(%o25)                         0.50060452530628
(%i26) x:x(time2);
(%o26)                         0.70328476387608
(%i27) verif1:(Z^2)+(Y^2)+(X^2);
(%o27)                         1.624094196918921
(%i28) verif2:(z^2)+(y^2)+(x^2);
(%o28)                         1.000276655320903
(%i29) r:sqrt((z^2)+(y^2)+(x^2));
(%o29)                         1.000138318094504
(%i30) dct:rt*r;
(%o30)                         6379019.211756325
(%i31) Altitude:dct-rt;
(%o31)                         882.2117563253269
(%i32) Latitude:(asin(z/r))*(360)/(float(2*%pi));
(%o32)                         30.3291676601964
(%i33) Longitude:(atan(y/x))*(360)/(float(2*%pi));
(%o33)                         35.44360882307072
(%i34) 
Run Example
l:matrix([-2.59783648,-1.57661906,-2.85131233]);
(%o1)            [ - 2.59783648  - 1.57661906  - 2.85131233 ]
(%i2) m:matrix([0.18594505,-4.06072906,-0.91671590]);
(%o2)              [ 0.18594505  - 4.06072906  - 0.9167159 ]
(%i3) n:matrix([2.98558342,-1.52457786,-2.47516022]);
(%o3)             [ 2.98558342  - 1.52457786  - 2.47516022 ]
(%i4) o:matrix([1.52361432,-0.04724021,-3.87825114]);
(%o4)             [ 1.52361432  - 0.04724021  - 3.87825114 ]
(%i5) t1:88.497907;
(%o5)                              88.497907
(%i6) t2:77.424860;
(%o6)                              77.42486
(%i7) t3:83.298642;
(%o7)                              83.298642
(%i8) t4:89.640527;
(%o8)                          89.64052700000001
(%i9) c:299792458;
(%o9)                              299792458
(%i10) r:6378137;
(%o10)                              6378137
(%i11) v:c/(1000*r);
                                  149896229
(%o11)                            ----------
                                  3189068500
(%i12) e1:expand((x-l[1,1])^2+(y-l[1,2])^2+(z-l[1,3])^2=v^2*(t-t1)^2);
            2                       2                       2
(%o12) 1.0 z  + 5.70262466 z + 1.0 y  + 3.15323812 y + 1.0 x  + 5.19567296 x
                                          2
 + 17.3644640403841 = 0.0022092950467877 t  - 0.39103597517236 t
 + 17.30293268222889
(%i13) e2:expand((x-m[1,1])^2+(y-m[1,2])^2+(z-m[1,3])^2=v^2*(t-t2)^2);
            2                      2                       2
(%o13) 1.0 z  + 1.8334318 z + 1.0 y  + 8.12145812 y + 1.0 x  - 0.3718901 x
                                           2
 + 17.36446410166079 = 0.0022092950467877 t  - 0.34210871939246 t
 + 13.24385985187042
(%i14) e3:expand((x-n[1,1])^2+(y-n[1,2])^2+(z-n[1,3])^2=v^2*(t-t3)^2);
            2                       2                       2
(%o14) 1.0 z  + 4.95032044 z + 1.0 y  + 3.04915572 y + 1.0 x  - 5.97116684 x
                                           2
 + 17.36446412365153 = 0.0022092950467877 t  - 0.36806255434949 t
 + 15.3295554741817
(%i15) e4:expand((x-o[1,1])^2+(y-o[1,2])^2+(z-o[1,3])^2=v^2*(t-t4)^2);
            2                       2                       2
(%o15) 1.0 z  + 7.75650228 z + 1.0 y  + 0.09448042 y + 1.0 x  - 3.04722864 x
                                           2
 + 17.36446413846121 = 0.0022092950467877 t  - 0.39608474458508 t
 + 17.75262262063352
(%i16) l1:e2-e1;
(%o16) - 3.86919286 z + 4.96822 y - 5.56756306 x + 6.1276693941181293E-8 = 
                                        0.048927255779895 t - 4.059072830358472
(%i17) l2:e3-e1;
(%o17) - 0.75230422 z - 0.1040824 y - 11.1668398 x + 8.3267426731481464E-8 = 
                                        0.022973420822873 t - 1.973377208047197
(%i18) l3:e4-e1;
(%o18) 2.053877620000001 z - 3.0587577 y - 8.2429016 x
              + 9.8077109100813686E-8 = 0.44968993840462 - 0.0050487694127212 t
(%i19) sol:float(linsolve([l1,l2,l3],[z,y,x,t]));

rat: replaced 4.059072891635166 by 14361/3538 = 4.059072922555116

rat: replaced -0.0489272557799 by -1553/31741 = -0.04892725496991

rat: replaced -5.56756306 by -33333/5987 = -5.56756305328211

rat: replaced 4.96822 by 30172/6073 = 4.968219990120204

rat: replaced -3.86919286 by -14908/3853 = -3.86919283675058

rat: replaced 1.973377291314623 by 7783/3944 = 1.973377281947262

rat: replaced -0.02297342082287 by -1733/75435 = -0.02297342082588

rat: replaced -11.1668398 by -21485/1924 = -11.1668399168399

rat: replaced -0.1040824 by -2213/21262 = -0.1040824005268

rat: replaced -0.75230422 by -11672/15515 = -0.7523042217209

rat: replaced -0.4496898403275 by -4277/9511 = -0.4496898328251

rat: replaced 0.0050487694127212 by 999/197870 = 0.0050487693940466

rat: replaced -8.2429016 by -42385/5142 = -8.24290159471023

rat: replaced -3.0587577 by -5466/1787 = -3.05875769445999

rat: replaced 2.053877620000001 by 23597/11489 = 2.053877622073288
(%o19) [z = 6.5146569086060767E-51 (7.2510967492032188E+46 %r1
 + 2.2924362116603168E+49), y = 2.4842910726530269E-52
 (3.1370701323484879E+49 %r1 - 2.0473694525177474E+51), 
x = - 1.5857177059487408E-53 (1.3632648845479128E+50 %r1
 - 1.0808802520386623E+52), t = %r1]
(%i20) temp1:rhs(sol[1]);
(%o20) 6.5146569086060767E-51 (7.2510967492032188E+46 %r1
                                                      + 2.2924362116603168E+49)
(%i21) x(%r1):=''temp1;
(%o21) x(%r1) := 6.5146569086060767E-51
                          (7.2510967492032188E+46 %r1 + 2.2924362116603168E+49)
(%i22) temp2:rhs(sol[2]);
(%o22) 2.4842910726530269E-52 (3.1370701323484879E+49 %r1
                                                      - 2.0473694525177474E+51)
(%i23) y(%r1):=''temp2;
(%o23) y(%r1) := 2.4842910726530269E-52
                          (3.1370701323484879E+49 %r1 - 2.0473694525177474E+51)
(%i24) temp3:rhs(sol[3]);
(%o24) - 1.5857177059487408E-53 (1.3632648845479128E+50 %r1
                                                      - 1.0808802520386623E+52)
(%i25) z(%r1):=''temp3;
(%o25) z(%r1) := - 1.5857177059487408E-53
                          (1.3632648845479128E+50 %r1 - 1.0808802520386623E+52)
(%i26) time:float(solve((1.0*(z(t))^2+5.70262466*z(t)+1.0*(y(t))^2+3.15323812*y(t)+1.0*(x(t))^2+5.19567296*x(t)-0.0022092950467877*t^2+0.39103597517236*t+ 0.061531358155205)));

rat: replaced 0.061531358155205 by 933/15163 = 0.061531359229704

rat: replaced 0.39103597517236 by 8489/21709 = 0.39103597586255

rat: replaced 3.3848026743721779E-50 by 1/29543819720169729999342100189543533972874273488896 = 3.3848026743721784E-50

rat: replaced 2.2924362116603168E+49 by 22924362116603167617613524315571965618364709076992/1 = 2.2924362116603168E+49

rat: replaced 7.2510967492032188E+46 by 72510967492032188060371436946690487747054927872/1 = 7.2510967492032188E+46

rat: replaced 7.8335613114652143E-52 by 1/1276558592241306999771897818587361252033462857105408 = 7.8335613114652143E-52

rat: replaced -2.047369452517747E+51 by -2047369452517747376346696215767806000026274509094912/1 = -2.047369452517747E+51

rat: replaced 3.1370701323484879E+49 by 31370701323484879423026425755851519257995821187072/1 = 3.1370701323484879E+49

rat: replaced -9.042752893741917E-53 by -1/11058579303787622635203504214625043577215301948801024 = -9.042752893741917E-53

rat: replaced -1.080880252038662E+52 by -10808802520386622731436425358317709323391235138781184/1 = -1.080880252038662E+52

rat: replaced 1.3632648845479128E+50 by 136326488454791279754401580924698271417655332175872/1 = 1.3632648845479128E+50

rat: replaced -0.002209295046788 by -248/112253 = -0.002209295074519

rat: replaced 4.2440754636848885E-101 by 1/23562257753347229622376500296170620528522706926668915888290726004341534784516795029987485107454214144 = 4.2440754636848885E-101

rat: replaced 2.2924362116603168E+49 by 22924362116603167617613524315571965618364709076992/1 = 2.2924362116603168E+49

rat: replaced 7.2510967492032188E+46 by 72510967492032188060371436946690487747054927872/1 = 7.2510967492032188E+46

rat: replaced 6.1717021336635272E-104 by 1/16202985470499354928075779114019474646803738313180849249646998292919592999520995252654517349097913974784 = 6.1717021336635272E-104

rat: replaced -2.047369452517747E+51 by -2047369452517747376346696215767806000026274509094912/1 = -2.047369452517747E+51

rat: replaced 3.1370701323484879E+49 by 31370701323484879423026425755851519257995821187072/1 = 3.1370701323484879E+49

rat: replaced 2.514500642959337E-106 by 1/3976932767148118764804035022332075860933364873483229141069635729363713418057950710104947976121596652814336 = 2.514500642959337E-106

rat: replaced -1.080880252038662E+52 by -10808802520386622731436425358317709323391235138781184/1 = -1.080880252038662E+52

rat: replaced 1.3632648845479128E+50 by 136326488454791279754401580924698271417655332175872/1 = 1.3632648845479128E+50
(%o26)         [t = - 1.303614944028307, t = 186.5983819022283]
(%i27) time1:rhs(time[1]);
(%o27)                        - 1.303614944028307
(%i28) time2:rhs(time[2]);
(%o28)                         186.5983819022283
(%i29) F:x(time1)^2+y(time1)^2+z(time1)^2;
(%o29)                         0.32160976929642
(%i30) G:x(time2)^2+y(time2)^2+z(time2)^2;
(%o30)                         1.004393615514375
(%i31) coord1:x(time2);
(%o31)                         0.23749045812972
(%i32) coord2:y(time2);
(%o32)                         0.94560879166645
(%i33) coord3:z(time2);
(%o33)                        - 0.23198256601485
(%i34) g1:coord1*r;
(%o34)                         1514746.678144129
(%i35) g2:coord2*r;
(%o35)                         6031222.421653055
(%i36) g3:coord3*r;
(%o36)                        - 1479616.587654235
(%i37) D:float(sqrt(g1^2+g2^2+g3^2));
(%o37)                         6392133.184224244
(%i38) pi:%pi;
(%o38)                                %pi
(%i39) lat:float(asin(g3/D));
(%o39)                        - 0.23359319559899
(%i40) lon:float(atan(g2/g1));
(%o40)                         1.324734798073671
(%i41) 

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