Lorentz contraction analysis - Transformations under relative velocity

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Bronnen o.a.: H.A. Lorentz, 1904: Electromagnetic phenomena in a system moving with any velocity smaller than that of light, Proc. Acad. Science Amsterdam, vol 6, 1904: p.809-831.
A. Einstein, 1905: Zur Elektrodynamik bewegter Körper, In: 'Annalen der Physik', 30 juni 1905, Folge IV, Band 17, resp. Vol. 322 (no. 10): p.891-921.
A. Einstein, 1916: Die Grundlage der allgemeinen Relativitätstheorie, In: 'Annalen der Physik', 20 maart 1916, Folge IV, Band 49, resp. Vol.354 (no.7): p.769-822.

Lorentz-transformations - under relative velocity:

Speed of light

c

=  299 792 458 ________ (m /s);
Speed of light

c

= 1 079 252 848.8________ (km/h).
Body Speed v (km/h) Speed /

c

(%)		 Length l in rest (m) Length l in motion (m) Contraction (%) Mass m in rest (kg) Total energy E (J) Kinetic energy (%) Speed v needed (km/h)
__1 ______________5__________ __0.000000004632834 __0.5_ __0.5______________ __0________________ ____100___ _______________________0________________ ______0________________ ______________0__________
__2 _____________15__________ __0.000000013898503 __2___ __1.999999999999999 __0.000000000000011 _____50___ _____________________997.8186929347128__ ______0.000000000000022 _____________22.743553161
__3 _____________50__________ __0.000000046328346 __2___ __1.999999999999997 __0.000000000000111 ____100___ ____________________9978.186929347128___ ______0.000000000000113 _____________50.856130919
__4 ____________100__________ __0.000000092656693 __5___ __4.999999999999979 __0.000000000000426 ___1000___ __________________399127.4771738851_____ ______0.000000000000437 _____________99.136849848
__5 ____________200__________ __0.000000185313386 100___ _99.99999999999828_ __0.000000000001719 __10000___ ________________15565971.609781519______ ______0.000000000001735 ____________199.573869036
__6 ___________1000__________ __0.000000926566931 _44___ _43.99999999998111_ __0.000000000042939 __86184___ ______________3326325521.049323_________ ______0.000000000042940 ___________1000.199306612
__7 ___________1200__________ __0.000001111880317 _20___ _19.999999999987637 __0.000000000061817 __50000___ ______________2777927241.1302404________ ______0.000000000061811 ___________1200.032283649
__8 ___________3528__________ __0.000003268928132 _20___ _19.99999999989314_ __0.000000000534292 __50000___ _____________24010511208.087997_________ ______0.000000000534301 ___________3527.964248835
__9 __________10000__________ __0.000009265669311 _50___ _49.999999997853685 __0.000000004292630 _100000___ ____________385802606348.435____________ ______0.000000004292632 __________10000.001778275
_10 __________10000__________ __0.000009265669311 100___ _99.99999999570737_ __0.000000004292630 ____100___ _______________385802606.3484349________ ______0.000000004292628 __________10000.001778275
_11 __________50000__________ __0.000046328346555 100___ _99.99999989268422_ __0.000000107315784 ____100___ ______________9645063163.073488_________ ______0.000000107315800 __________49999.998545994
_12 _________100000__________ __0.000092656693110 100___ _99.99999957073686_ __0.000000429263138 ____100___ _____________38580246665.3818___________ ______0.000000429263134 __________99999.999678334
_13 __________25780.8________ __0.000023887636737 _50___ _49.99999998573452_ __0.000000028530962 ____100___ ______________2564236385.488728_________ ______0.000000028530976 __________25780.798161606
_14 __________27000__________ __0.000025017307139 _50___ _49.99999998435335_ __0.000000031293296 ____100___ ______________2812501658.8404284________ ______0.000000031293305 __________27000.007962432
_15 _________500000__________ __0.000463283465552 100___ _99.99998926842095_ __0.000010731579052 ____100___ ____________964506328281.1731___________ ______0.000010731580199 _________500000.053739476
_16 ________1000000__________ __0.000926566931105 100___ _99.9999570736769__ __0.000042926323104 ____100___ ___________3858027175054.3735___________ ______0.000042926341524 ________1000000.429220315
_17 ________5000000__________ __0.004632834655529 100___ _99.99892683639432_ __0.001073163605681 ____100___ __________96452169913931.56_____________ ______0.001073175122617 ________5000053.658792609
_18 _______10000000__________ __0.009265669311059 100___ _99.99570727647352_ __0.004292723526475 ____100___ _________385827312530853.2______________ ______0.004292907809140 _______10000429.29079629_
_19 _______50000000__________ __0.046328346555298 100___ _99.89262657000526_ __0.107373429994737 ____100___ ________9660615560936506________________ ______0.107488844453883 _______50053744.42222577_
_20 ______100000000__________ __0.092656693110597 100___ _99.56981155058035_ __0.430188449419645 ____100___ _______38830453801979700________________ ______0.432047065993603 ______100432047.06599346_
_21 ______108000000__________ __0.100069228559445 100___ _99.49804769418932_ __0.501952305810675 ____100___ _______45340812687379530________________ ______0.504484577781293 ______108544843.34400499_
_22 ______150000000__________ __0.138985039665896 100___ _99.02944808232897_ __0.970551917671031 ____100___ _______88083754795300000________________ ______0.980063947104035 ______151470095.92065728_
_23 ______152247349.933238___ __0.141067359796658 100___ _99.00000000000001_ __0.999999999999985 ____100___ _______90783351387555920________________ ______1.010101010100993 ______153785201.95276523_
_24 ______152247349.93323812_ __0.141067359796658 100___ _99.00000000000001_ __0.999999999999985 ____100___ _______90783351387555920________________ ______1.010101010100993 ______153785201.95276523_
_25 ______152247349.9332385__ __0.141067359796658 100___ _99________________ __1________________ ____100___ _______90783351387557920________________ ______1.010101010101016 ______153785201.95276693_
_26 ______152247349.93323898_ __0.141067359796659 100___ _98.99999999999999_ __1.000000000000014 ____100___ _______90783351387557920________________ ______1.010101010101016 ______153785201.95276693_
_27 ______152247349.933239___ __0.141067359796659 100___ _98.99999999999999_ __1.000000000000014 ____100___ _______90783351387557920________________ ______1.010101010101016 ______153785201.95276693_
_28 ______175000000__________ __0.162149212943546 100___ _98.67662503054046_ __1.323374969459536 ____100___ ______120534129216956880________________ ______1.341123056296206 ______177346965.3485183__
_29 ______200000000__________ __0.185313386221195 100___ _98.26794741355057_ __1.732052586449427 ____100___ ______158412918239225820________________ ______1.762581423584919 ______203525162.84716883_
_30 ______300000000__________ __0.277970079331793 100___ _96.05897329225816_ __3.941026707741841 ____100___ ______368733710316322700________________ ______4.102715834523154 ______312308147.50356936_
_31 ______400000000__________ __0.370626772442391 100___ _92.87818880388097_ __7.121811196119027 ____100___ ______689156924454406000________________ ______7.667904906239344 ______430671619.6249574__
_32 ______500000000__________ __0.463283465552989 100___ _88.62101503284717_ _11.378984967152832 ____100___ _____1154006379209988600________________ _____12.840052625142267 ______564200263.1257117__
_33 ______750000000__________ __0.694925198329483 100___ _71.90820319871219_ _28.091796801287817 ____100___ _____3511094246842752000________________ _____39.06619210559127_ _____1042996440.7919346__
_34 _____1000000000__________ __0.926566931105978 100___ _37.6129927260315__ _62.3870072739685__ ____100___ ____14907254597309633000________________ ____165.86557663302128_ _____2658655766.330213___
_35 _____1050000000__________ __0.972895277661276 100___ _23.124614311245686 _76.8753856887543__ ____100___ ____29878185242448822000________________ ____332.4396448479108__ _____4540616270.903064___
_36 _____1070000000__________ __0.991426616283396 100___ _13.066470267388642 _86.93352973261136_ ____100___ ____59795766151213520000________________ ____665.317625599168___ _____8188898593.9110985__
_37 _____1075000000__________ __0.996059450938926 100___ __8.868804990101435 _91.13119500989856_ ____100___ ____92351374904551160000________________ ___1027.5476246417759__ ____12121136964.899088___
_38 _____1079000000__________ __0.999765718663350 100___ __2.164504066882207 _97.8354959331178__ ____100___ ___406236975848378800000________________ ___4519.995939487511___ ____49849756187.07024____
_39 _____1079200000__________ __0.999951032049571 100___ __0.989613576084258 _99.01038642391575_ ____100___ ___899200452557769400000________________ __10004.954339418413___ ___109052667231.00351____
_40 _____1079252848.8________ __1________________ 100___ __0________________ 100________________ ____100___ ________________Infinity________________ _ _______Infinity__________
_41 _____1079252848.8________ __1________________ 100___ __0________________ 100________________ ____100___ ________________Infinity________________ _ _______Infinity__________
_42 _____1079252848.9________ __1.000000000092656 100___ NaN________________ NaN________________ ____100___ _____________________NaN________________ ____NaN________________ ____________NaN__________