Iiiai ouny/aeaoee iacaae ethaee iaaa?iyea caia/aee, /oi aieueoay /anoue
i?aaeiaoia iaaeaao ana auno?aa e auno?aa, a iaeioi?ua iaaeatho
?aaiiia?ii. Ii eae eiaiii iaaeatho yoe i?aaeiaou – yoio aii?in ieeiai ia
caieiae. Ioeoaea o ia?aiauoiuo ethaeae aeieaeii auei iiyaeoueny
no?aieaiea auynieoue, eae eee ii/aio? Anee iie aiiaua ?aciuoeyee iaae
i?e/eiaie eee iauyniaieyie, oi noaaa?iue o?aiao n?aco aea canoaaeye eo
aeoiaoue i aeia?uo e ceuo aeooao. Iu eaaei i?aaenoaaeyai, /oi yoe ethaee
n eo iieiie iianiinoe aeeciueth n/eoaee aieueooth /anoue iau/iuo yaeaiee
«oi?ioeie», a iaiau/iua – «ieioeie».
Ana ethaee a naiai ?acaeoee i?ioiaeyo iiiai nooiaiae iiciaiey: io
aanniuneeoeu noaaa?ee aei iao/iiai iuoeaiey. Nia/aea ethaee i?iaeaeuaaee
iiuou n aeaoiy i?aaeiaoaie. Iai?eia? a?aee aeaa eaiiy, e aeaaaee
aiciiaeiinoue ei naiaiaeii iaaeaoue, auionoea eo ec ?oe iaeiia?aiaiii.
Caoai niiaa a?inaee aeaa eaiiy, ii oaea a noi?iiu ii ai?eciioaee. Iioii
a?inaee iaeei eaiaiue a noi?iio, e a oio aea iiiaio auioneaee ec ?oe
aoi?ie, ii oae, /oiau ii i?inoi iaaeae ii aa?oeeaee. Ethaee ecaeaeee ec
oaeeo iiuoia iiiai naaaeaiee i i?e?iaea.
?en.1
Ii ia?a naiaai ?acaeoey /aeiaa/anoai i?eia?aoaei ia oieueei ciaiey, ii e
i?aae?annoaeee. I?ioanneiiaeueiua nae?aou e o?aaeeoeee ?aianeaiieeia
onooieee ianoi i?aaieciaaiiiio iiciaieth i?e?iaeu, eioi?ia oei io
aaoi?eoaoia e nio?aieeinue a i?eciaiiuo ia/aoiuo o?oaeao.
Yoi auei ia/aeii ianoiyuae iaoee. Ethaee yenia?eiaioe?iaaee
iianaaeiaaii, eco/ay ?aianea eee nicaeaaay iiaua iaoeiu. Ec iiuoia n
iaaeathueie oaeaie ethaee onoaiiaeee, /oi iaeaiueeee e aieueoie eaiie,
auiouaiiua ec ?oe iaeiia?aiaiii, iaaeatho n iaeeiaeiaie nei?inoueth. Oi
aea naiia iiaeii neacaoue i eoneao naeioea, cieioa, aeaeaca, noaeea, e
o.ae. naiuo ?aciuo ?acia?ia. Ec iiaeiaiuo iiuoia auaiaeeoueny i?inoia
iauaa i?aaeei: naiaiaeiia iaaeaiea anao oae i?ienoiaeeo iaeeiaeiai
iacaaeneii io ?acia?a e iaoa?eaea, ec eioi?iai oaea naeaeaiu.
Iaaeaeo iaaethaeaieai ca i?e/eiiie naycueth yaeaiee e ouaoaeueii
auiieiaiiuie yenia?eiaioaie, aa?iyoii, aeieai nouanoaiaae ?ac?ua.
Eioa?an e aeaeaeaieth naiaiaeii iaaeathueo e a?ioaiiuo oae aic?anoae
aianoa n oniaa?oainoaiaaieai i?oaeey. I?eiaiaiea eiiee, no?ae,
eaoaioeueou e aua aieaa caiuneiaaouo «i?oaeee aieiu» iicaieeei iieo/eoue
i?eieoeaiua e ooiaiiua naaaeaiey ec iaeanoe aaeeenoeee, ii iie i?eieiaee
oi?io nei?aa ?aai/eo i?aaee ?aianeaiieeia, iaaeaee iao/iuo iiciaiee, –
yoi auee ia noi?ioee?iaaiiua i?aaenoaaeaiey.
Aeaa ouny/e eao iacaae a?aee oi?ioee?iaaee i?aaeea naiaiaeiiai iaaeaiey
oae e aeaee ei iauyniaiey, ii yoe i?aaeea e iauyniaiey auee
iaeiiainiiaaiiu. Iaeioi?ua ae?aaiea o/aiua, ii-aeaeeiiio, i?iaiaeeee
aiieia ?acoiiua iiuou n iaaeathueie oaeaie, ii eniieueciaaiea a n?aaeiea
aaea aioe/iuo i?aaenoaaeaiee, i?aaeeiaeaiiuo A?enoioaeai (i?eia?ii 340
a. aei i.y.), nei?aa caiooaei aii?in. E yoa iooaiieoea aeeeeanue aua
iiiai noieaoee. I?eiaiaiea ii?ioa cia/eoaeueii iiauneei eioa?an e
aeaeaeaieth oae. Ii eeoue Aaeeeae (i?eia?ii a 1600 a.) caiiai eceiaeee
iniiau aaeeenoeee a aeaea /aoeeo i?aaee, niaeanothueony n i?aeoeeie.
Aaeeeee a?a/aneee oeeinio e o/aiue A?enoioaeue, ii-aeaeeiiio
i?eaea?aeeaaeny ?ani?ino?aiaiiiai i?aaenoaaeaiey i oii, /oi oyaeaeua
oaea iaaeatho auno?aa, /ai eaaeea. A?enoioaeue e aai iineaaeiaaoaee
no?aieeenue iauynieoue, ii/aio i?ienoiaeyo oa eee eiua yaeaiey, ii ia
anaaaea caaioeeenue i oii, /oiau i?iiaaethaeaoue, /oi i?ienoiaeeo e eae
i?ienoiaeeo. A?enoioaeue aanueia i?inoi iauyniee i?e/eiu iaaeaiey oae:
ii aiai?ee, /oi oaea no?aiyony iaeoe naia anoanoaaiiia ianoi ia
iiaa?oiinoe Caiee. Iienuaay, eae iaaeatho oaea, ii auneacae
ooaa?aeaeaiey a?iaea neaaeothueo: «…oi/ii oaeaea, eae iai?aaeaiiia
aiec aeaeaeaiea eonea naeioea eee cieioa eee ethaiai ae?oaiai oaea,
iaaeaeaiiiai aanii, i?ienoiaeeo oai auno?aa, /ai aieueoa aai ?acia?…»,
«…iaeii oaei oyaeaeaa ae?oaiai, eiathuaai oio aea iauai, ii
aeaeaeouaainy aiec auno?aa…». A?enoioaeue ciae, /oi eaiie iaaeatho
auno?aa, /ai ioe/uee ia?uey, a eonee aea?aaa – auno?aa, /ai iieeee.
A XIV noieaoee a?oiia oeeinioia ec Ia?eaea ainnoaea i?ioea oai?ee
A?enoioaey e i?aaeeiaeeea cia/eoaeueii aieaa ?acoiioth noaio, eioi?ay
ia?aaeaaaeanue ec iieieaiey a iieieaiea e ?ani?ino?aieeanue aei Eoaeee,
ieacaa aeaoiy noieaoeyie iicaeiaa aeeyiea ia Aaeeeay. Ia?eaeneea
oeeiniou aiai?eee ia onei?aiiii aeaeaeaiee e aeaaea i iinoiyiiii
onei?aiee, iauyniyy yoe iiiyoey a?oae/iui ycueii.
Aaeeeee eoaeueyineee o/aiue Aaeeeai Aaeeeae iaiauee eiathueany naaaeaiey
e i?aaenoaaeaiey e e?eoe/anee eo i?iaiaeece?iaae, a caoai iienae e ia/ae
?ani?ino?aiyoue oi, /oi n/eoae aa?iui. Aaeeeae iiieiae, /oi
iineaaeiaaoaeae A?enoioaey naeaaei n oieeo nii?ioeaeaiea aicaeooa. Ii
oeacae, /oi ieioiua i?aaeiaou, aeey eioi?uo nii?ioeaeaiea aicaeooa
ianouanoaaiii, iaaeatho ii/oe n iaeeiaeiaie nei?inoueth. Aaeeeae ienae:
«…?acee/ea a nei?inoe aeaeaeaiey a aicaeooa oa?ia ec cieioa, naeioea,
iaaee, ii?oe?a e ae?oaeo oyaeaeuo iaoa?eaeia ianoieueei iacia/eoaeueii,
/oi oa? ec cieioa i?e naiaiaeiii iaaeaiee ia ?annoiyiee a iaeio nioith
eieoae iaaa?iyea iia?aaeee au oa? ec iaaee ia aieaa /ai ia /aou?a
iaeueoea. Naeaeaa yoi iaaethaeaiea, y i?eoae e caeeth/aieth, /oi a
n?aaea, iieiinoueth eeoaiiie anyeiai nii?ioeaeaiey, ana oaea iaaeaee au
n iaeeiaeiaie nei?inoueth». I?aaeiieiaeea, /oi i?iecioei au a neo/aa
naiaiaeiiai iaaeaiey oae a aaeooia, Aaeeeae auaae neaaeothuea caeiiu
iaaeaiey oae aeey eaeaaeueiiai neo/ay:
Ana oaea i?e iaaeaiee aeaeaeoony iaeeiaeiai: ia/aa iaaeaoue
iaeiia?aiaiii, iie aeaeaeoony n iaeeiaeiaie nei?inoueth
Aeaeaeaiea i?ienoiaeeo n «iinoiyiiui onei?aieai»; oaii oaaee/aiey
nei?inoe oaea ia iaiyaony, o.a. ca eaaeaeoth iineaaeothuoth naeoiaeo
nei?inoue oaea aic?anoaao ia iaeio e oo aea aaee/eio.
Nouanoaoao eaaaiaea, aoaeoi Aaeeeae i?iaeaeae aieueoie
aeaiiino?aoeeiiiue iiuo, a?inay eaaeea e oyaeaeua i?aaeiaou n aa?oeiu
Iecaineie iaaeathuae aaoie (iaeie aiai?yo, /oi ii a?inae noaeueiua e
aea?aayiiua oa?u, a ae?oaea ooaa?aeaeatho, aoaeoi yoi auee aeaeaciua
oa?u aanii 0,5 e 50 ea). Iienaiee oaeiai ioaee/iiai iiuoa iao, e
Aaeeeae, ianiiiaiii, ia noae oaeei niiniaii aeaiiino?e?iaaoue naia
i?aaeei. Aaeeeae ciae, /oi aea?aayiiue oa? iaiiiai ionoae au i?e
iaaeaiee io aeaeaciiai, ii n/eoae, /oi aeey aeaiiino?aoeee ?acee/iie
nei?inoe iaaeaiey aeaoo iaiaeeiaeiauo aeaeaciuo oa?ia iio?aaiaaeanue au
aieaa aunieay aaoiy.
Eoae, iaeeea eaiie neaaea ionoatho a iaaeaiee io e?oiiuo, e ?acieoea
noaiiaeony oai aieaa caiaoiie, /ai aieueoaa ?anoiyiea i?ieaoatho eaiie.
E aeaei ooo ia i?inoi a ?acia?a oae: aea?aayiiue e noaeueiie oa?u
iaeeiaeiaiai ?acia?a iaaeatho ia no?iai iaeeiaeiai. Aaeeeae ciae, /oi
i?inoiio iienaieth iaaeaiey oae iaoaao nii?ioeaeaiea aicaeooa.
Iaia?oaeea, /oi ii ia?a oaaee/aiey ?acia?ia oae eee ieioiinoe iaoa?eaea,
ec eioi?iai iie naeaeaiu, aeaeaeaiea oae ieacuaaaony aieaa iaeeiaeiaui,
iiaeii ia iniiaa iaeioi?iai i?aaeiieiaeaiey noi?ioee?iaaoue i?aaeei e
aeey eaeaaeueiiai neo/ay. Iiaeii auei au iiiuoaoueny oiaiueoeoue
nii?ioeaeaiea aicaeooa, eniieuecoy iaoaeaiea oaeiai i?aaeiaoa, eae eeno
aoiaae, iai?eia?.
Ii Aaeeeae iia eeoue oiaiueoeoue aai e ia iia ono?aieoue aai
iieiinoueth. Iiyoiio aio i?eoeinue aanoe aeieacaoaeuenoai, ia?aoiaey io
?aaeueiuo iaaethaeaiee e iinoiyiii oiaiueoathueiny nii?ioeaeaieai
aicaeooa e eaeaaeueiiio neo/ath, eiaaea nii?ioeaeaiea aicaeooa
ionoonoaoao. Iicaea, iaeyaeuaaynue iacaae, ii niia iauynieoue ?acee/ey a
?aaeueiuo yenia?eiaioao, i?eienaa eo nii?ioeaeaieth aicaeooa.
Anei?a iinea Aaeeeay auee nicaeaiu aicaeooiua ianinu, eioi?ua iicaieeee
i?iecaanoe yenia?eiaiou ni naiaiaeiui iaaeaieai a aaeooia. N yoie
oeaeueth Iuethoii auea/ae aicaeoo ec aeeeiiie noaeeyiiie o?oaee e a?inee
naa?oo iaeiia?aiaiii ioe/uea ia?i e cieiooth iiiaoo. Aeaaea noieue
neeueii ?acee/athueany ii naiae ieioiinoe oaea iaaeaee n iaeeiaeiaie
nei?inoueth. Eiaiii yoio iiuo aeae ?aoathuoth i?iaa?eo i?aaeiieiaeaiey
Aaeeeay. Iiuou e ?annoaeaeaiey Aaeeeay i?eaaee e i?inoiio i?aaeeo, oi/ii
ni?aaaaeeeaiio a neo/aa naiaiaeiiai iaaeaiey oae a aaeooia. Yoi i?aaeei
a neo/aa naiaiaeiiai iaaeaiey oae a aicaeooa auiieiyaony n ia?aie/aiiie
oi/iinoueth. Iiyoiio aa?eoue a iaai, eae a eaeaaeueiue neo/ae iaeuecy.
Aeey iieiiai eco/aiey naiaiaeiiai iaaeaiey oae iaiaoiaeeii ciaoue, eaeea
i?e iaaeaiee i?ienoiaeyo eciaiaiey oaiia?aoo?u, aeaaeaiey, e ae?., oi
anoue enneaaeiaaoue e ae?oaea noi?iiu yoiai yaeaiey. Ii oaeea
enneaaeiaaiey auee au caiooaiiuie e neiaeiuie, caiaoeoue eo acaeiinaycue
auei au o?oaeii, iiyoiio oae /anoi a oeceea i?eoiaeeony
aeiaieuenoaiaaoueny eeoue oai, /oi i?aaeei i?aaenoaaeyao niaie iaeia
oi?iuaiea aaeeiiai caeiia.
Eoae, aua o/aiua N?aaeiaaaeiauey e Aic?iaeaeaiey ciaee i oii, /oi aac
nii?ioeaeaiey aicaeooa oaei ethaie iannu iaaeaao n iaeeiaeiaie auniou ca
iaeii e oiaea a?aiy, Aaeeeae ia oieueei i?iaa?ee iiuoii e ionoaeaae yoi
ooaa?aeaeaiea, ii e onoaiiaee aeae aeaeaeaiey oaea, iaaeathuaai ii
aa?oeeaee: «…aiai?yo, /oi anoanoaaiiia aeaeaeaiea iaaeathuaai oaea
iai?a?uaii onei?yaony. Iaeiaei, a eaeii ioiioaiee i?ienoiaeeo, aei neo
ii? ia auei oeacaii; ianeieueei y ciath, ieeoi aua ia aeieacae, /oi
i?ino?ainoaa, i?ioiaeeiua iaaeathuei oaeii a iaeeiaeiaua i?iiaaeooee
a?aiaie, ioiinyony iaaeaeo niaith, eae iineaaeiaaoaeueiua ia/aoiua
/enea». Oae Aaeeeeae onoaiiaee i?eciae ?aaiionei?aiiiai aeaeaeaiey:
S1:S2:S3: … = 1:2:3: … (i?e V0 = 0)
, oi anee acyoue o?e iaeioi?ua oi/ee 1,2,3 /a?ac eioi?ua i?ioiaeeo oaei
i?e iaaeaiee e caienaoue:
(onei?aiea i?e naiaiaeiii iaaeaiee aeey anao oae iaeeiaeiai),
iieo/eony, /oi ioiioaiea ia?aiauaiee i?e ?aaiionei?aiiii aeaeaeaiee
?aaii:
S1:S2:S3 = t12:t22:t32
Yoi aua iaeei aaaeiue i?eciae ?aaiionei?aiiiai aeaeaeaiey, a cia/eo e
naiaiaeiiai iaaeaiey oae.
. Ionthaea a=2S/t2. Iinoiyiiia onei?aiea naiaiaeiiai iaaeaiey
iaicia/atho neiaieii g. Onei?aiea naiaiaeiiai iaaeaiey ciaiaieoi oai,
/oi iii ia caaeneo io iannu iaaeathuaai oaea. Aeaenoaeoaeueii, anee
aniiiieoue iiuo ciaiaieoiai aiaeeeneiai o/aiiai Iuethoiia n ioe/ueei
ia?ii e cieioie iiiaoie, oi iiaeii neacaoue, /oi iie iaaeatho n
iaeeiaeiaui onei?aieai, oioy o ieo ?aciua iannu.
Ecia?aiey aeatho cia/aiea g, ?aaiia 9,8156 i/n2.
Aaeoi? onei?aiey naiaiaeiiai iaaeaiey anaaaea iai?aaeai ii aa?oeeaee
aiec, aaeieue ioaaniie eeiee a aeaiiii ianoa Caiee.
E ana aea: ii/aio oaea iaaeatho? Iiaeii neacaoue, aneaaenoaea
a?aaeoaoeee eee caiiiai i?eoyaeaiey. Aaaeue neiai «a?aaeoaoeey»
eaoeineiai i?ienoiaeaeaiey e icia/aao «oyaeaeue» eee «aaniiue». Iiaeii
neacaoue, /oi oaea iaaeatho iioiio, /oi iie aanyo. Ii oiaaea ii/aio oaea
aanyo? E ioaaoeoue iiaeii oae: iioiio, /oi Caiey i?eoyaeaaao eo. E,
aeaenoaeoaeueii, ana ciatho, /oi Caiey i?eoyaeaaao oaea, iioiio, /oi iie
iaaeatho. Aea, oeceea ia aeaao iauyniaiey oyaioaieth, Caiey i?eoyaeaaao
oaea iioiio, /oi oae ono?iaia i?e?iaea. Iaeiaei, oeceea iiaeao niiaueoue
iiiai eioa?aniiai e iieaciiai i caiiii oyaioaiee. Enaae Iuethoii
(1643-1727) eco/ee aeaeaeaiea iaaaniuo oae – ieaiao e Eoiu. Aai ia ?ac
eioa?aniaaea i?e?iaea neeu, eioi?ay aeieaeia aeaenoaiaaoue ia Eoio,
/oiau i?e aeaeaeaiee aie?oa caiee iia oaea?aeeaaeanue ia ii/oe e?oaiaie
i?aeoa. Iuethoii oaeaea caaeoiuaaeny iaae ianaycaiiie, eacaeinue au, n
yoei i?iaeaiie a?aaeoaoeee. Iineieueeo iaaeathuea oaea onei?ythony,
Iuethoii caeeth/ee, /oi ia ieo aeaenoaoao neea, eioi?oth iiaeii iacaaoue
neeie oyaioaiey eee a?aaeoaoeee. Ii /oi aucuaaao yoo neeo oyaioaiey?
Aaaeue anee ia oaei aeaenoaoao neea, cia/eo iia aucuaaaony ni noi?iiu
eaeiai-eeai ae?oaiai oaea. Ethaia oaei ia iiaa?oiinoe Caiee eniuouaaao
aeaenoaea yoie neeu oyaioaiey, e aaea au oaei ie iaoiaeeeinue, neea,
aeaenoaothuay ia iaai iai?aaeaia e oeaio?o Caiee. Iuethoii caeeth/ee,
/oi naia Caiey nicaeaao neeo oyaioaiey, aeaenoaothuoth ia oaea,
iaoiaeyueany ia aa iiaa?oiinoe.
Enoi?ey ioe?uoey Iuethoiiii caeiia anaie?iiai oyaioaiey aeinoaoi/ii
ecaanoia. Ii eaaaiaea, Iuethoii neaeae a naiai naaeo e ia?aoee aieiaiea
ia iaaeathuaa n aea?aaa yaeiei. O iaai iaiaeeaeaiii aicieeea aeiaaaeea i
oii, /oi anee neea oyaioaiey aeaenoaoao ia aa?oeia aea?aaa e aeaaea ia
aa?oeia ai?, oi, aiciiaeii, iia aeaenoaoao e ia ethaii ?annoiyiee. Oae
iuneue i oii, /oi eiaiii i?eoyaeaiea Caiee oaea?aeeaaao Eoio ia aa
i?aeoa, iineoaeeea Iuethoiio iniiaie, n eioi?ie ii ia/ae iino?iaiea
naiae aaeeeie oai?ee a?aaeoaoeee.
Aia?aua iuneue i oii, /oi i?e?iaea nee, canoaaeythueo iaaeaoue eaiaiue e
ii?aaeaeythueo aeaeaeaiea iaaaniuo oae, – iaeia e oa aea, aicieeea aua o
Iuethoiia-nooaeaioa. Ii ia?aua au/eneaiey ia aeaee i?aaeeueiuo
?acoeueoaoia iioiio, /oi eiaaoeany a oi a?aiy aeaiiua i ?annoiyiee io
Caiee aei Eoiu auee iaoi/iuie. 16 eao nionoy iiyaeeenue iiaua,
eni?aaeaiiua naaaeaiey ia yoii ?annoiyiee. Iinea oiai, eae auee
i?iaaaeaiu iiaua ?an/aou, ioaaoeaoea aeaeaeaiea Eoiu, anao ioe?uouo e
oiio a?aiaie ieaiao nieia/iie nenoaiu, eiiao, i?eeeau e ioeeau, oai?ey
auea iioaeeeiaaia.
Iiiaea enoi?eee iaoee a ianoiyuaa a?aiy n/eoatho, /oi Iuethoii auaeoiae
yoo enoi?eth aeey oiai, /oiau ioiaeaeiooue aeaoo ioe?uoey e 60-i aiaeai
17 aaea, oiaaea eae aai ia?aienea e aeiaaieee oeacuaatho ia oi, /oi
ii-ianoiyuaio ii i?eoae e caeiio anaie?iiai oyaioaiey eeoue ieiei 1685
a.
Iuethoii ia/ae n ii?aaeaeaiey aaee/eiu a?aaeoaoeeiiiiai acaeiiaeaenoaey,
n eioi?ui Caiey aeaenoaoao ia Eoio iooai n?aaiaiey aa n aaee/eiie neeu,
aeaenoaothuae ia oaea ia iiaa?oiinoe Caiee. Ia iiaa?oiinoe Caiee neea
oyaioaiey i?eaeaao oaeai onei?aiea g = 9,8i/n2. Ii /aio ?aaii
oeaio?ino?aieoaeueiia onei?aiea Eoiu? Oae eae Eoia aeaeaeaony ii
ie?oaeiinoe ii/oe ?aaiiia?ii, aa onei?aiea iiaeao auoue ?ann/eoaii ii
oi?ioea:
a = (2/r
Iooai ecia?aiee iiaeii iaeoe yoi onei?aiea. Iii ?aaii
2,73*10-3i/n2. Anee au?aceoue yoi onei?aiea /a?ac onei?aiea naiaiaeiiai
iaaeaiey g aaeece iiaa?oiinoe Caiee, oi iieo/ei:
Oaeei ia?acii, onei?aiea Eoiu, iai?aaeaiiia e Caiea, ninoaaeyao 1/3600
onei?aiey oae aaeece iiaa?oiinoe Caiee. Eoia oaeaeaia io Caiee ia 385000
ei, /oi i?aauoaao i?eaeeceoaeueii a 60 ?ac ?aaeeon Caiee, ?aaiue 6380
ei. Cia/eo Eoia a 60 ?ac aeaeueoa io oeaio?a Caiee, /ai oaea,
iaoiaeyueany ia iiaa?oiinoe Caiee. Ii 60*60 = 3600! Ec yoiai Iuethoii
naeaeae auaiae, /oi neea oyaioaiey, aeaenoaothuay ni noi?iiu Caiee ia
ethaua oaea oiaiueoaaony ia?aoii i?iii?oeeiiaeueii eaaae?aoo eo
?annoiyiey io oeaio?a Caiee:
Neea oyaioaiey ( 1/r2
Eoia, oaeaeaiiay ia 60 caiiuo ?aaeeonia, eniuouaaao neeo
a?aaeoaoeeiiiiai i?eoyaeaiey, ninoaaeythuoth anaai eeoue 1/602 = 1/3600
oie neeu, eioi?oth iia eniuouaaea au, anee au iaoiaeeeanue ia
iiaa?oiinoe Caiee. Ethaia oaei, iiiauaiiia ia ?annoiyiee 385000 ei io
Caiee, aeaaiaea?y i?eoyaeaieth Caiee i?eia?aoaao oi aea onei?aiea, /oi e
Eoia, a eiaiii 2,73*10-3 i/n2.
Iuethoii iiieiae, /oi neea oyaioaiey caaeneo ia oieueei io ?annoiyiey
aei i?eoyaeaaaiiai oaea, ii e io aai iannu. Aeaenoaeoaeueii, neea
oyaioaiey i?yii i?iii?oeeiiaeueia ianna i?eoyaeaaaiiai oaea, niaeanii
aoi?iio caeiio Iuethoiia. Ec o?aoueaai caeiia Iuethoiia aeaeii, /oi
eiaaea Caiey aeaenoaoao neeie oyaioaiey ia ae?oaia oaei (iai?eia?,
Eoio), yoi oaei, a naith i/a?aaeue, aeaenoaoao ia Caieth n ?aaiie ii
aaee/eia e i?ioeaiiieiaeii iai?aaeaiiie neeie:
?en. 2
Aeaaiaea?y yoiio Iuethoii i?aaeiieiaeee, /oi aaee/eia neeu oyaioaiey
i?iii?oeeiiaeueia iaaei iannai. Oaeei ia?acii:
aaea m3 – ianna Caiee, mT – ianna ae?oaiai oaea, r – ?annoiyiea io
oeaio?a Caiee aei oeaio?a oaea.
I?iaeieaeay eco/aiea a?aaeoaoeee, Iuethoii i?iaeaeioeny aua ia oaa
aia?aae. Ii ii?aaeaeee, /oi neea, iaiaoiaeeiay aeey oaea?aeaiey
?acee/iuo ieaiao ia eo i?aeoao aie?oa Nieioea, oauaaao ia?aoii
i?iii?oeeiiaeueii eaaae?aoo eo ?annoiyiee io Nieioea. Yoi i?eaaei aai e
iunee i oii, /oi neea, aeaenoaothuay iaaeaeo Nieioeai e eaaeaeie ec
ieaiao e oaea?aeeaathuay eo ia i?aeoao, oaeaea yaeyaony neeie
a?aaeoaoeeiiiiai acaeiiaeaenoaey. Oaeaea ii i?aaeiieiaeee, /oi i?e?iaea
neeu, oaea?aeeaathuae ieaiaou ia eo i?aeoao, oiaeaeanoaaiia i?e?iaea
neeu oyaeanoe, aeaenoaothuae ia ana oaea o caiiie iiaa?oiinoe (i neea
oyaeanoe iu iiaiai?ei iicaea). I?iaa?ea iiaeoaa?aeeea i?aaeiieiaeaiea i
aaeeiie i?e?iaea yoeo nee. Oiaaea anee a?aaeoaoeeiiiia aicaeaenoaea
nouanoaoao iaaeaeo yoeie oaeaie, oi ii/aio au aio ia nouanoaiaaoue
iaaeaeo anaie oaeaie? Oaeei ia?acii Iuethoii i?eoae e naiaio ciaiaieoiio
Caeiio anaie?iiai oyaioaiey, eioi?ue iiaeii noi?ioee?iaaoue oae:
Eaaeaeay /anoeoea ai Anaeaiiie i?eoyaeaaao ethaoth ae?oaoth /anoeoeo n
neeie, i?yii i?iii?oeeiiaeueiie i?iecaaaeaieth eo iann e ia?aoii
i?iii?oeeiiaeueiie eaaae?aoo ?annoiyiey iaaeaeo ieie. Yoa neea
aeaenoaoao aaeieue eeiee, niaaeeiythuae yoe aeaa /anoeoeu.
Aaee/eia yoie neeu iiaeao auoue caienaia a aeaea:
aaea e – iannu aeaoo /anoeoe, –
?annoiyiea iaaeaeo ieie, a – a?aaeoaoeeiiiay iinoiyiiay,
eioi?ay iiaeao auoue ecia?aia yenia?eiaioaeueii e aeey anao oae eiaao
iaeii e oi aea /eneaiiia cia/aiea.
Yoi au?aaeaiea ii?aaeaeyao aaee/eio neeu oyaioaiey, n eioi?ie iaeia
/anoeoea aeaenoaoao ia ae?oaoth, iaoiaeyuothny io iaa ia ?annoiyiee
. Aeey aeaoo ia oi/a/iuo, ii iaeii?iaeiuo oae yoi au?aaeaiea
i?aaeeueii iienuaaao acaeiiaeaenoaea, anee – ?annoiyiea iaaeaeo
oeaio?aie oae. E?iia oiai, anee i?ioyaeaiiua oaea iaeu ii n?aaiaieth n
?annoiyieyie iaaeaeo ieie, oi iu ia iaiiiai ioeaainy, anee aoaeai
?anniao?eaaoue oaea eae oi/a/iua /anoeoeu (eae yoi eiaao ianoi aeey
nenoaiu Caiey – Nieioea).
Anee ioaeii ?anniio?aoue neeo a?aaeoaoeeiiiiai i?eoyaeaiey,
aeaenoaothuoth ia aeaiioth /anoeoeo ni noi?iiu aeaoo eee ianeieueeeo
ae?oaeo /anoeoe, iai?eia? neeo, aeaenoaothuoth ia Eoio ni noi?iiu Caiee
e Nieioea, oi iaiaoiaeeii aeey eaaeaeie ia?u acaeiiaeaenoaothueo /anoeoe
ainiieueciaaoueny oi?ioeie caeiia anaie?iiai oyaioaiey, iinea /aai
aaeoi?ii neiaeeoue neeu, aeaenoaothuea ia /anoeoeo.
Aaee/eia iinoiyiiie aeieaeia auoue i/aiue iaea, oae eae iu
ia caia/aai ieeaeie neeu, aeaenoaothuae iaaeaeo oaeaie iau/iuo ?acia?ia.
Neea, aeaenoaothuay iaaeaeo aeaoiy oaeaie iau/iuo ?acia?ia, aia?aua auea
ecia?aia a 1798a. Aai?e Eaaaiaeeoai – /a?ac 100 eao iinea oiai, eae
Iuethoii iioaeeeiaae naie caeii. Aeey iaia?oaeaiey e ecia?aiey noieue
iaaa?iyoii iaeie neeu ii eniieueciaae onoaiiaeo, iieacaiioth ia ?en. 3.
Aeaa oa?eea cae?aieaiu ia eiioeao eaaeiai ai?eciioaeueiiai noa?aeiy,
iiaeaaoaiiiai ca na?aaeeio e oiieie ieoe. Eiaaea oa?, iaicia/aiiue
aoeaie A, iiaeiinyo aeecei e iaeiiio ec iiaeaaoaiiuo oa?ia, neea
a?aaeoaoeeiiiiai i?eoyaeaiey canoaaeyao cae?aieaiiue ia noa?aeia oa?
naeaeiooueny, /oi i?eaiaeeo e iaaieueoiio cae?o/eaaieth ieoe. Yoi
iacia/eoaeueiia niauaiea ecia?yaony n iiiiuueth oceiai io/ea naaoa,
iai?aaeaiiiai ia ca?eaei, oe?aieaiiia ia ieoe oae, /oi io?aaeaiiue io/ie
naaoa iaaeaao ia oeaeo. I?iaeaeaiiua ?aiaa ecia?aiey cae?o/eaaiey ieoe
iiae aeaenoaeai ecaanoiuo nee iicaieytho ii?aaeaeeoue aaee/eio neeu
a?aaeoaoeeiiiiai acaeiiaeaenoaey, aeaenoaothuae iaaeaeo aeaoiy oaeaie.
I?eai? oaeiai oeia i?eiaiaiea a eiino?oeoeee ecia?eoaey neeu oyaeanoe, n
iiiiuueth eioi?iai iiaeii ecia?eoue aanueia iaaieueoea eciaiaiey neeu
oyaeanoe aaeece ai?iie ii?iaeu, ioee/athuaeny ii ieioiinoe io ninaaeieo
ii?iae. Yoio i?eai? eniieuecoaony aaieiaaie aeey enneaaeiaaiee caiiie
ei?u e ?acaaaeee aaieiae/aneeo iniaaiiinoae, oeacuaathueo ia
ianoi?iaeaeaiea iaooe. A iaeiii ec aa?eaioia i?eai?a Eaaaiaeeoa aeaa
oa?eea iiaeaaoeaathony ia ?aciie aunioa. Oiaaea iie aoaeoo ii ?aciiio
i?eoyaeaaoueny aeeceei e iiaa?oiinoe ianoi?iaeaeaieai ieioiie ai?iie
ii?iaeu; iiyoiio ieaiea i?e iaaeeaaeauae i?eaioaoeee ioiineoaeueii
ianoi?iaeaeaiey aoaeao neaaea iiai?a/eaaoueny. ?acaaae/eee iaooe
caiaiytho oaia?ue yoe ecia?eoaee neeu oyaeanoe eino?oiaioaie,
iaiin?aaenoaaiii ecia?ythueie iaaieueoea eciaiaiey aaee/eiu onei?aiey
neeu oyaeanoe g i eioi?uo aoaeao neacaii iicaea.
Eaaaiaeeo ia oieueei iiaeoaa?aeee aeiioaco Iuethoiia i oii, /oi oaea
i?eoyaeaatho ae?oa ae?oaa e oi?ioea i?aaeeueii
iienuaaao yoo neeo. Iineieueeo Eaaaiaeeo iia n oi?ioae oi/iinoueth
ecia?eoue aaee/eiu , aio oaeaeinue
oaeaea ?ann/eoaoue aaee/eio iinoiyiiie . A ianoiyuaa a?aiy
i?eiyoi n/eoaoue, /oi yoa iinoiyiiay ?aaia
Noaia iaeiiai ec iiuoia ii ecia?aieth iieacaia ia ?en.4.
E eiioeai ei?iiunea aania iiaeaaoaiu aeaa oa?eea iaeeiaeiaie iannu.
Iaeei ec ieo iaoiaeeony iaae naeioeiaie ieeoie, ae?oaie – iiae iae.
Naeiaoe (aeey iiuoa acyoi 100 ea naeioea) oaaee/eaaao naiei i?eoyaeaieai
aan i?aaiai oa?eea e oiaiueoaao aan eaaiai. I?aaue oa?ee ia?aaaoeaaao
eaaue. Ii aaee/eia ioeeiiaiey ei?iiunea aania au/eneyaony cia/aiea
.
Ioe?uoea caeiia anaie?iiai oyaioaiey ii i?aao n/eoaaony iaeiei ec
aaee/aeoeo o?eoioia iaoee. E, naycuaay yoio o?eoio n eiaiai Iuethoiia,
iaaieueii oi/aony ni?ineoue, ii/aio eiaiii yoiio aaieaeueiiio
anoanoaieniuoaoaeth, a ia Aaeeeath, iai?eia?, ioe?uaoaio caeiiu
naiaiaeiiai iaaeaiey oae, ia ?iaa?oo Aoeo eee eiio-eeai ec ae?oaeo
caia/aoaeueiuo i?aaeoanoaaiieeia eee nia?aiaiieeia Iuethoiia oaeaeinue
naeaeaoue yoi ioe?uoea?
Aeaei caeanue ia a i?inoie neo/aeiinoe e ia a iaaeathueo yaeieao.
Aeaaiui ii?aaeaeythuei auei oi, /oi a ?oeao Iuethoiia auee ioe?uoua ei
caeiiu, i?eiaieiua e iienaieth ethauo aeaeaeaiee. Eiaiii yoe caeiiu,
caeiiu iaoaieee Iuethoiia, iicaieeee n iieiie i/aaeaeiinoueth iiiyoue,
/oi iniiaie, ii?aaeaeythuae iniaaiiinoe aeaeaeaiey, yaeythony neeu.
Iuethoii aue ia?aui, eoi aaniethoii ynii iiieiae, /oi eiaiii ioaeii
eneaoue aeey iauyniaiey aeaeaeaiey ieaiao, – eneaoue ioaeii auei neeu e
oieueei neeu. Iaeii ec naiuo caia/aoaeueiuo naienoa nee anaie?iiai
oyaioaiey, eee, eae eo /anoi iacuaatho, a?aaeoaoeeiiiuo nee, io?aaeaii
oaea a naiii iacaaiee, aeaiiii Iuethoiiii: anaie?iua. Ana, /oi eiaao
ianno – a ianna i?enoua ethaie oi?ia, ethaiio aeaeo iaoa?ee, – aeieaeii
eniuouaaoue a?aaeoaoeeiiiua acaeiiaeaenoaey. I?e yoii caai?iaeeoueny io
a?aaeoaoeeiiiuo nee iaaiciiaeii. Aeey anaie?iiai oyaioaiey iao i?aa?aae.
Anaaaea iiaeii iinoaaeoue iai?aiaeieeiue aa?uea? aeey yeaeo?e/aneiai,
iaaieoiiai iiey. Ii a?aaeoaoeeiiiia acaeiiaeaenoaea naiaiaeii
ia?aaeaaony /a?ac ethaua oaea. Ye?aiu ec iniauo aauanoa, iai?iieoeaaiuo
aeey a?aaeoaoeee, iiaoo nouanoaiaaoue oieueei a aiia?aaeaiee aaoi?ia
iao/ii-oaioanoe/aneeo eiea.
Eoae, a?aaeoaoeeiiiua neeu aacaeanoue e anai?iieeathue. Ii/aio aea iu
ia iuouaai i?eoyaeaiey aieueoeinoaa oae? Anee iiaen/eoaoue, eaeoth
aeieth io i?eoyaeaiey Caiee ninoaaeyao, iai?eia?, i?eoyaeaiea Yaa?anoa,
oi ieaaeaony, /oi eeoue ouny/iua aeiee i?ioeaioa. Neea aea acaeiiiai
i?eoyaeaiey aeaoo ethaeae n?aaeiaai aana i?e ?annoiyiee iaaeaeo ieie a
iaeei iao? ia i?aauoaao o?ao niouo ieeeea?aiia. Oae neaau
a?aaeoaoeeiiiua neeu. Oio oaeo, /oi a?aaeoaoeeiiiua neeu, aiiaua aiai?y
ai?acaei neaaaa yeaeo?e/aneeo, aucuaaao naiaia?aciia ?acaeaeaiea noa?
aeeyiey yoeo nee. Iai?eia?, iiaen/eoaa, /oi a aoiiao a?aaeoaoeeiiiia
i?eoyaeaiea yeaeo?iiia e yae?o neaaaa, /ai yeaeo?e/aneia a
?ac, eaaei iiiyoue, /oi i?ioeannu aioo?e aoiia ii?aaeaeythony
i?aeoe/anee iaeieie eeoue yeaeo?e/aneeie neeaie. A?aaeoaoeeiiiua neeu
noaiiayony iuooeiuie, a ii?ie e a?aiaeeiciuie, eiaaea ai acaeiiaeaenoaee
oeao?e?otho oaeea ia?iiiua iannu, eae iannu einie/aneeo oae: ieaiao,
caacae e o.ae. Oae, Caiey e Eoia i?eoyaeaathony n neeie i?eia?ii a 20
000 000 000 000 000 oiii. Aeaaea oaeea aeaeaeea io ian caacaeu, naao
eioi?uo aiaeu eaeao io Caiee, i?eoyaeaathony n iaoae ieaiaoie n neeie,
au?aaeathuaeny aiooeoaeueiie oeeo?ie, – yoi nioie ieeeeiiia oiii.
Acaeiiia i?eoyaeaiea aeaoo oae oauaaao ii ia?a eo oaeaeaiey ae?oa io
ae?oaa. Iuneaiii i?iaeaeaai oaeie iiuo: aoaeai ecia?youe neeo, n eioi?ie
Caiey i?eoyaeaaao eaeia-eeai oaei, iai?eia?, aeaaaeoeaoeeeeia?aiiiaoth
ae?th. Ia?aue iiuo ionoue niioaaonoaoao oaeei oneiaeyi, eiaaea ae?y
iiiauaia ia i/aiue aieueoii ?annoiyiee io Caiee. A yoeo oneiaeyo neea
i?eoyaeaiey (eioi?oth iiaeii ecia?youe n iiiiuueth naiuo iaueiiaaiiuo
i?oaeeiiuo aania) i?aeoe/anee aoaeao ?aaia ioeth. Ii ia?a i?eaeeaeaiey e
Caiea iiyaeony e aoaeao iinoaiaiii aic?anoaoue acaeiiia i?eoyaeaiea, e,
iaeiiaoe, eiaaea ae?y ieaaeaony ia iiaa?oiinoe Caiee no?aeea i?oaeeiiuo
aania inoaiiaeony ia aeaeaiee «20 eeeia?aiiia», iineieueeo oi, /oi iu
iacuaaai aanii, ioaeaeaynue io a?auaiey caiee, anoue ie /oi eiia, eae
neea, n eioi?ie Caiey i?eoyaeaaao oaea, ?aniieiaeaiiua ia aa
iiaa?oiinoe(ni. ieaea). Anee aea i?iaeieaeeoue yenia?eiaio e iionoeoue
ae?th a aeoaieoth oaooo, yoi oiaiueoeo aeaenoaothuoth ia ae?th neeo. Yoi
aeaeii oioy au ec oiai, /oi anee ae?th iiianoeoue a oeaio? caiee,
i?eoyaeaiea ni anao noi?ii acaeiii o?aaiiaaneony e no?aeea i?oaeeiiuo
aania inoaiiaeony oi/ii ia ioea.
Eoae, iaeuecy i?inoi neacaoue, /oi a?aaeoaoeeiiiua neeu oauaatho n
oaaee/aieai ?annoiyiey – ioaeii anaaaea iaiaa?eaaoue, /oi naie yoe
?annoiyiey i?e oaeie oi?ioee?iaea i?eieiathony iiiai aieueoeie, /ai
?acia?u oae. Eiaiii a yoii neo/aa i?aa noi?ioee?iaaiiue Iuethoiiii caeii
i oii, /oi neeu anaie?iiai oyaioaiey oauaatho ia?aoii i?iii?oeeiiaeueii
eaaae?aoo ?annoiyiey iaaeaeo i?eoyaeaathueieny oaeaie. Iaeiaei inoaaony
iayniui, /oi yoi – auno?ia eee ia i/aiue auno?ia eciaiaiea n
?annoiyieai? Icia/aao ee oaeie caeii, /oi acaeiiaeaenoaea i?aeoe/anee
iuouaaony eeoue iaaeaeo aeeaeaeoeie ninaaeyie, eee aea iii caiaoii e ia
aeinoaoi/ii aieueoeo ?annoiyieyo?
N?aaiei caeii oauaaiey n ?annoiyieai a?aaeoaoeeiiiuo nee n caeiiii, ii
eioi?iio oiaiueoaaony inaauaiiinoue ii ia?a oaeaeaiey io enoi/ieea. Eae
a iaeiii, oae e a ae?oaii neo/aa aeaenoaoao iaeei e oio aea caeii –
ia?aoiay i?iii?oeeiiaeueiinoue eaaae?aoo ?annoiyiey. Ii aaaeue iu aeaeei
caacaeu, iaoiaeyueany io ian ia oaeeo ia?iiiuo ?annoiyieyo, i?ieoe
eioi?ua aeaaea naaoiaie eo/, ia eiathuee niia?ieeia a nei?inoe, iiaeao
eeoue ca ieeeea?aeu eao. A aaaeue anee aei ian aeioiaeeo naao io yoeo
caacae, cia/eo aeieaeii, oioy au i/aiue neaai, /oanoaiaaoueny eo
i?eoyaeaiea. Neaaeiaaoaeueii, aeaenoaea nee anaie?iiai oyaioaiey
i?inoe?aaony, iai?aiaiii oauaay, i?aeoe/anee ia iaia?aie/aiiua
?annoiyiey. ?aaeeon eo aeaenoaey ?aaai aaneiia/iinoe. A?aaeoaoeeiiiua
neeu – yoi aeaeueiiaeaenoaothuea neeu. Aneaaenoaea aeaeueiiaeaenoaey
a?aaeoaoeey naycuaaao ana oaea ai anaeaiiie.
Ioiineoaeueiay iaaeeaiiinoue oauaaiey nee n ?annoiyieai ia eaaeaeii
oaao i?iyaeythony a iaoeo caiiuo oneiaeyo: aaaeue ana oaea, aoaeo/e
ia?aiauaiiuie n iaeiie auniou ia ae?oaoth, iaiytho naie aan e?aeia
iacia/eoaeueii. Eiaiii iioiio, /oi i?e ioiineoaeueii iaeii eciaiaiee
?annoiyiey – a aeaiiii neo/aa aei oeaio?a Caiee – a?aaeoaoeeiiiua neeu
i?aeoe/anee ia eciaiythony.
Auniou, ia eioi?uo aeaeaeoony eneonnoaaiiua niooieee, oaea n?aaieiu n
?aaeeonii Caiee, oae /oi aeey ?an/aoa eo o?aaeoi?ee o/ao eciaiaiey neeu
caiiiai i?eoyaeaiey n oaaee/aieai ?annoiyiey niaa?oaiii iaiaoiaeei.
Eoae, Aaeeeae ooaa?aeaeae, /oi ana oaea, ioiouaiiua n iaeioi?ie auniou
aaeece iiaa?oiinoe Caiee aoaeoo iaaeaoue n iaeeiaeiaui onei?aieai g
(anee i?aiaa?a/ue nii?ioeaeaieai aicaeooa). Neea, aucuaathuay yoi
onei?aiea iacuaaaony neeie oyaeanoe. I?eiaiei e neea oyaeanoe aoi?ie
caeii Iuethoiia, ?anniao?eaay a ea/anoaa onei?aiey a onei?aiea
naiaiaeiiai iaaeaiey g. Oaeei ia?acii, aeaenoaothuoth ia oaei neeo
oyaeanoe iiaeii caienaoue eae:
Fg=mg
Yoa neea iai?aaeaia aiec, e oeaio?o Caiee.
O.e. a nenoaia NE g = 9,8, oi neea oyaeanoe, aeaenoaothuay ia oaei
iannie 1ea, ninoaaeyao .
I?eiaiei oi?ioeo caeiia anaie?iiai oyaioaiey aeey iienaiey neeu oyaeanoe
– neeu oyaioaiey iaaeaeo caieae e oaeii, iaoiaeyueiny ia aa iiaa?oiinoe.
Oiaaea m1 caiaieony ia ianno Caiee m3 , a r – ia ?annoiyiea aei oeaio?a
Caiee, o.a. ia ?aaeeon Caiee r3. Oaeei ia?acii iieo/ei:
Aaea m – ianna oaea, iaoiaeyuaainy ia iiaa?oiinoe Caiee. Ec yoiai
?aaainoaa neaaeoao, /oi:
Eiuie neiaaie onei?aiea naiaiaeiiai iaaeaiey ia iiaa?oiinoe caiee g
ii?aaeaeyaony aaee/eiaie m3 e r3.
Ia Eoia, ia ae?oaeo ieaiaoao, eee a einie/aneii i?ino?ainoaa neea
oyaeanoe, aeaenoaothuay ia oaei iaeeiaeiaie iannu, aoaeao ?acee/ia.
Iai?eia?, ia Eoia aaee/eia g i?aaenoaaeyao anaai eeoue iaeio oanooth g
ia Caiea, e ia oaei iannie 1 ea aeaenoaoao neea oyaeanoe, ?aaiay anaai
eeoue 1,7 I.
Aei oao ii?, iiea ia auea ecia?aia a?aaeoaoeeiiiay iinoiyiiay G, ianna
Caiee inoaaaeanue iaecaanoiie. E oieueei iinea oiai, eae G auea
ecia?aia, n iiiiuueth niioiioaiey oaeaeinue au/eneeoue ianno caiee. Yoi
aia?aua i?iaeaeae nai Aai?e Eaaaiaeeo. Iiaenoaaeyy a oi?ioeo onei?aiea
naiaiaeiiai iaaeaiey cia/aiea g=9,8i/n e ?aaeeona caiee rc=6,38(106
iieo/aai neaaeothuaa cia/aiea iannu Caiee:
Aeey neeu oyaioaiey, aeaenoaothuae ia oaea, iaoiaeyueany aaeece
iiaa?oiinoe Caiee, iiaeii i?inoi iieueciaaoueny au?aaeaieai mg. Anee aea
iaiaoiaeeii ?ann/eoaoue neeo i?eoyaeaiey, aeaenoaothuoth ia oaei,
?aniieiaeaiiia ia iaeioi?ii ioaeaeaiee io Caiee, eee neeo, aucuaaaioth
ae?oaei iaaaniui oaeii(iai?eia? Eoiie eee ae?oaie ieaiaoie), oi neaaeoao
eniieueciaaoue cia/aiea aaee/eiu g, au/eneaiiia n iiiiuueth ecaanoiie
oi?ioeu, a eioi?ie r3 e m3aeieaeiu auoue caiaiaiu ia niioaaonoaothuaa
?annoiyiea e ianno, iiaeii oaeaea iaiin?aaenoaaiii ainiieueciaaoueny
oi?ioeie caeiia anaie?iiai oyaioaiey. Nouanoaoao ianeieueei iaoiaeia
i/aiue oi/iiai ii?aaeaeaiey onei?aiey neeu oyaeanoe. Iiaeii iaeoe g
i?inoi acaaoeaaieai noaiaea?oiiai a?oca ia i?oaeeiiuo aanao.
Aaieiae/aneea aanu aeieaeiu auoue oaeeaeoaeueiu – eo i?oaeeia eciaiyao
?anoyaeaiea i?e aeiaaaeaiee iaa?ocee iaiueoa /ai a ieeeeiiioth aeieth
a?aiia. I?aainoiaeiua ?acoeueoaou aeatho e?ooeeueiua eaa?oeaaua aanu.
Ono?ienoai eo a i?eioeeia ianeiaeii. E ai?eciioaeueii iaoyiooie
eaa?oeaaie ieoe i?eaa?ai ?u/aa, aanii eioi?iai ieoue neaaea
cae?o/eaaaony:
iiaeii iaeoe cia/aiea g aeinoaoi/ii oi/ii. Ecia?yy ia iaeiii i?eai?a
cia/aiea g a ?aciuo ianoao, iiaeii noaeeoue ia ioiineoaeueiuo eciaiaieyo
neeu oyaeanoe n oi/iinoueth aei ieeeeiiiuo aeieae.
Cia/aiey onei?aiey naiaiaeiiai iaaeaiey g a ?aciuo oi/eao Caiee
ianeieueei ?acee/athony. Ec oi?ioeu g = Gm3 iiaeii oaeaeaoue, /oi
aaee/eia g aeieaeia auoue iaiueoa, iai?eia?, ia aa?oeiao ai?, /ai ia
o?iaia ii?y, iineieueeo ?annoiyiea io oeaio?a Caiee aei aa?oeiu ai?u
ianeieueei aieueoa. Aeaenoaeoaeueii, yoio oaeo onoaiiaeee
yenia?eiaioaeueii. Iaeiaei oi?ioea g=Gm3/r32 ia aeaao oi/iiai cia/aiey g
ai anao oi/eao, oae eae iiaa?oiinoue caiee ia yaeyaony a oi/iinoe
noa?e/aneie: ia aa iiaa?oiinoe ia oieueei nouanoaotho ai?u e ii?y, ii
oaeaea eiaao ianoi eciaiaiea ?aaeeona Caiee ia yeaaoi?a; e?iia oiai,
ianna caiee ?ani?aaeaeaia iaiaeii?iaeii; a?auaiea Caiee oaeaea aeeyao ia
eciaiaiea g.
Iaeiaei naienoaa onei?aiey naiaiaeiiai iaaeaiey ieacaeenue neiaeiaa, /ai
i?aaeiieaaae Aaeeeae. Auynieoue, /oi aaee/eia onei?aiey caaeneo io
oe?iou, ia eioi?ie aai ecia?ytho:
Aaee/eia onei?aiey naiaiaeiiai iaaeaiey iaiyaony oaeaea n aunioie iaae
iiaa?oiinoueth Caiee:
Aaeoi? onei?aiey naiaiaeiiai iaaeaiey anaaaea iai?aaeai ii aa?oeeaee
aiec, a aaeieue ioaaniie eeiee a aeaiiii ianoa Caiee.
Oaeei ia?acii, ia iaeiie e oie aea oe?ioa e ia iaeiie e oie aea aunioa
iaae o?iaiai ii?y onei?aiea neeu oyaeanoe aeieaeii auoue iaeeiaeiaui.
Oi/iua ecia?aiey iieacuaatho, /oi aanueia /anoi ano?a/athony ioeeiiaiey
io yoie ii?iu – aiiiaeee oyaioaiey. I?e/eia aiiiaeee ninoieo a
iaiaeii?iaeiii ?ani?aaeaeaiee iannu aaeece ianoa ecia?aiey.
Eae oaea auei neacaii, neea oyaioaiey ni noi?iiu aieueoiai oaea iiaeao
auoue, i?aaenoaaeaia eae noiia nee, aeaenoaothueo ni noi?iiu ioaeaeueiuo
/anoeoe aieueoiai oaea. I?eoyaeaiea iayoieea Caieae anoue ?acoeueoao
aeaenoaey ia iaai anao /anoeoe Caiee. Ii ynii, /oi aeeceea /anoeoeu
aiinyo iaeaieueoee aeeaae a noiia?ioth neeo – aaaeue i?eoyaeaiea ia?aoii
i?iii?oeeiiaeueii eaaae?aoo ?annoiyiey.
Anee aaeece ianoa ecia?aiey nin?aaeioi/aiu oyaeaeua iannu, g aoaeao
aieueoa ii?iu, a ia?aoiii neo/aa g iaiueoa ii?iu.
Anee, iai?eia?, ecia?eoue g ia ai?a eee ia naiieaoa, eaoyuai iaae ii?ai
ia aunioa ai?u, oi a ia?aii neo/aa iieo/eony aieueoay oeeo?a. Oaeaea
auoa ii?iu aaee/eia g ia oaaeeiaiiuo ieaaineeo ino?iaao. ssnii, /oi a
iaieo neo/ayo aic?anoaiea g iauyniyaony nin?aaeioi/aieai
aeiiieieoaeueiuo iann a ianoa ecia?aiey.
Ia oieueei aaee/eia g, ii e iai?aaeaiea neeu oyaeanoe iiaeao
ioeeiiyoueny io ii?iu. Anee iiaeaaneoue a?oc ia ieoea, oi auoyiooay
ieoue iieaaeao aa?oeeaeue aeey yoiai ianoa. Yoa aa?oeeaeue iiaeao
ioeeiieoueny io ii?iu. «Ii?iaeueiia» iai?aaeaiea aa?oeeaee ecaanoii
aaieiaai ec niaoeeaeueiuo ea?o, ia eioi?uo ii aeaiiui i cia/aieyo g
iino?iaia «eaeaaeueiay» oeao?a Caiee.
I?iecaaaeai iiuo n ioaanii o iiaeiiaeey aieueoie ai?u. A?ocee ioaana
i?eoyaeaaaony Caieae e aa oeaio?o e ai?ie – a noi?iio. Ioaan aeieaeai
ioeeiieoueny i?e oaeeo oneiaeyo io iai?aaeaiey ii?iaeueiie aa?oeeaee.
Oae eae ianna Caiee iiiai aieueoa iannu ai?u, oi oaeea ioeeiiaiey ia
i?aauoatho ianeieueeeo oaeiauo naeoiae.
«Ii?iaeueiay» aa?oeeaeue ii?aaeaeyaony ii caacaeai, oae eae aeey ethaie
aaia?aoe/aneie oi/ee au/eneaii, a eaeia ianoi iaaa a aeaiiue iiiaio
nooie e aiaea «oie?aaony» aa?oeeaeue «eaeaaeueiie» oeao?u Caiee.
Ioeeiiaiey ioaana i?eaiaeyo eiiaaea e no?aiiui ?acoeueoaoai. Iai?eia?,
ai Oei?aioeee aeeyiea Aiaiiei i?eaiaeeo ia e i?eoyaeaieth, a e
iooaeeeaaieth ioaana. Iauyniaiea iiaeao auoue iaeii: a ai?ao anoue
ia?iiiua ionoiou.
Caia/aoaeueiue ?acoeueoao aeatho ecia?aiey onei?aiey neeu oyaeanoe a
ianooaaa iaoa?eeia e ieaaiia. Iaoa?eee cia/eoaeueii oyaeaeaa ieaaiia,
iiyoiio, eacaeinue au, cia/aiey g iaae iaoa?eeaie aeieaeiu auoue
aieueoa. *ai iaae ieaaiaie. A aeaenoaeoaeueiinoe aea cia/aiey g, aaeieue
iaeiie oe?iou iaae ieaaiaie e iaoa?eeaie, a n?aaeiai iaeeiaeiau.
Iauyniaiea iiyoue -oaee eeoue iaeii: iaoa?eee iieiyony ia aieaa eaaeeo
ii?iaeao, a ieaaiu – ia aieaa oyaeaeuo. E aeaenoaeoaeueii, oai, aaea
aiciiaeiu iaiin?aaenoaaiiua ecuneaiey, aaieiae onoaiaaeeaatho, /oi
ieaaiu iieiyony ia oyaeaeuo aacaeueoiauo ii?iaeao, a iaoa?eee- ia eaaeeo
a?aieoao.
Ii n?aco aea aicieeaao neaaeothuee aii?in: ii/aio oyaeaeua e eaaeea
ii?iaeu oi/ii eiiiaine?otho ?acee/ea aania iaoa?eeia e ieaaiia? Oaeay
eiiiainaoeey ia iiaeao auoue aeaeii neo/ay, i?e/eiu aa aeieaeiu
ei?aieony a ono?ienoaa iaiei/ee Caiee.
Aaieiae iieaaatho, /oi aa?oiea /anoe caiiie ei?u eae au ieaaatho ia
iiaenoeeathuae ieanoe/iie, oi anoue eaaei aeaoi?ie?oaiie ianna.
Aeaaeaiea ia aeoaeiao ieiei 100 ei aeieaeii auoue anthaeo iaeeiaeiaui,
oae aea eae iaeeiaeiai aeaaeaiea ia aeia ninoaea n aiaeie, a eioi?ii
ieaaatho eonee aea?aaa ?aciiai aana. Iiyoiio noiea aauanoaa ieiuaaeueth
1 i2 io iiaa?oiinoe aei aeoaeiu 100 ei aeieaeai eiaoue e iiae ieaaiii e
iiae iaoa?eeaie iaeeiaeiaue aan.
Yoi au?aaieaaiea aeaaeaiee (aai iacuaatho ecinoaceae) e i?eaiaeeo e
oiio, /oi iaae ieaaiaie e iaoa?eeaie aaeieue iaeiie oe?ioiie eeiee
cia/aiea onei?aiey neeu oyaeanoe g ia ioee/aaony nouanoaaiii. Ianoiua
aiiiaeee neeu oyaeanoe neoaeao aaieiae/aneie ?acaaaeea, oeaeue eioi?ie-
iaeoe caeaaee iieaciuo eneiiaaiuo iiae caieae, ia ?iy yi, ia eiiay oaoo.
Oyaeaeoth ?oaeo ioaeii eneaoue a oao ianoao, aaea g iaeaieueoaa.
Iai?ioea, caeaaee eaaeie niee iaia?oaeeaatho ii ianoiui caieaeaiiui
cia/aieyi aaee/eiu g. Ecia?eoue g iiaeii n oi/iinoueth aei ieeeeiiiuo
aeieae io 1 i/nae2.
Iaoiaeu ?acaaaeee i?e iiiiue iayoieeia e naa?ooi/iuo aania iacuaatho
a?aaeoaoeeiiiuie. Iie eiatho aieueoia i?aeoe/aneia cia/aiea, a /anoiinoe
aeey iieneia iaooe. Aeaei a oii, /oi i?e a?aaeoaoeeiiiuo iaoiaeao
?acaaaeee eaaei iaia?oaeeoue iiaecaiiua nieyiua eoiiea, a i/aiue /anoi
ieacuaaaony, /oi aaea anoue nieue, oai e iaooue. I?e/ai iaooue eaaeeo a
aeoaeia, a nieue aeeaea e caiiie iiaa?oiinoe. Iaoiaeii a?aaeoaoeeiiiie
?acaaaeee auea ioe?uoa iaooue a Eacaonoaia e a ae?oaeo ianoao.
***
Aianoi oiai, /oiau oyiooue oaeaaeeo n iiiiuueth i?oaeeiu, ae iiaeii
i?eaeaoue onei?aiea, i?ee?aiea ia?aeeiooue /a?ac aeie oio?, e
i?ioeaiiieiaeiiio eiioeo eioi?iai iiaeaaoeaaaony a?oc. Oiaaea neea,
niiauathuay onei?aiea, aoaeao iaoneiaeaia aanii yoiai a?oca. Onei?aiea
naiaiaeiiai iaaeaiey iiyoue oaee niiauaaony oaeo aai aanii.
A oeceea aan – yoi ioeoeeaeueiia iaeiaiiaaiea neeu, eioi?ay iaoneiaeaia
i?eoyaeaieai i?aaeiaoia e caiiie iiaa?oiinoe – «i?eoyaeaieai neeu
oyaeanoe». Oi ianoiyoaeuenoai, /oi oaea i?eoyaeaathony ii iai?aaeaieth e
oeaio?o Caiee, aeaeaao oaeia iauyniaiea ?acoiiui.
Eae au aai ia ii?aaeaeeee, aan – yoi neea. Ii ie/ai ia ioee/aaony io
ethaie ae?oaie neeu, anee ia n/eoaoue aeaoo iniaaiiinoae: aan iai?aaeai
aa?oeeaeueii e aeaenoaoao iinoiyiii, aai iaaiciiaeii ono?aieoue.
*oiau iaiin?aaenoaaiii ecia?eoue aan oaea, iu aeieaeiu ainiieueciaaoueny
i?oaeeiiuie aanaie, i?ia?aaeoe?iaaiiuie a aaeeieoeao neeu. Iineieueeo
yoi ca/anooth naeaeaoue iaoaeiaii, iu n?aaieaaai iaeei aan n ae?oaei i?e
iiiiue ?u/aaeiuo aania, o.a. iaoiaeei ioiioaiea:
CAIIIA I?EOssAEAIEA, AeAENOAOTHUAA IA OAEI O CAIIIA I?EOssAE-A,
AeAENOAOTHUAA IA YOAEII IANNU
I?aaeiieiaeei, /oi oaei O i?eoyaeaaaony a 3 ?aca neeueiaa, /ai yoaeii
iannu. A yoii neo/aa iu aiai?ei, /oi caiiia i?eoyaeaiea, aeaenoaothuaa
ia oaei O ?aaii 30 iuethoiiai neeu, /oi icia/aao, /oi iii a 3 ?aca
aieueoa caiiiai i?eoyaeaiey, eioi?ia aeaenoaoao ia eeeia?aii iannu.
Ia?aaeei iooatho iiiyoea iannu e aana, iaaeaeo eioi?uie eiaaony
nouanoaaiiia ?acee/ea. Ianna – yoi naienoai naiiai oaea (iia yaeyaony
ia?ie eia?oiinoe eee aai «eiee/anoaa aauanoaa»). Aan aea – yoi neea, n
eioi?ie oaei aeaenoaoao ia iii?o eee ?anoyaeaaao iiaeaan (aan /eneaiii
?aaai neea oyaeanoe, anee iii?a eee iiaeaan ia eiatho onei?aiey).
Anee iu i?e iiiiue i?oaeeiiuo aania ecia?ei aan eaeiai-ieaoaeue
i?aaeiaoa n i/aiue aieueoie oi/iinoueth, a iioii ia?aianai aanu a
ae?oaia ianoi, oi iaia?oaeei, /oi aan i?aaeiaoa ia iiaa?oiinoe Caiee
ianeieueei iaiyaony io ianoa e ianoo. Iu ciaai, /oi aaeaee io
iiaa?oiinoe Caiee, eee a aeoaeia caiiiai oa?a, aan aeieaeai auoue
cia/eoaeueii iaiueoa.
Iaiyaony ee ianna? O/aiua, ?aciuoeyy iaae yoei aii?inii, aeaaii i?eoee e
auaiaeo, /oi ianna aeieaeia inoaaaoueny iaeciaiiie. Aeaaea a oeaio?a
Caiee, aaea oyaioaiea, aeaenoaoy ai anao iai?aaeaieyo, aeieaeii aeaaaoue
ioeaaoth ?acoeueoe?othuoth neeo, oaei ii-i?aaeiaio eiaei au oo aea
naioth ianno.
Oaeei ia?acii, ianna, ioeaieaaaiay ii o?oaeiinoe, eioi?oth iu ano?a/aai
i?e iiiuoea onei?eoue aeaeaeaiea iaeaiueeie oaeaaeee, iaeia e oa aea
anthaeo: ia iiaa?oiinoe Caiee, a oeaio?a Caiee, ia Eoia. Aan,
ioeaieaaaiue ii oaeeeiaieth i?oaeeiiuo aania(e iuouaieth
a ioneoeao ?oee /aeiaaea, aea?aeauaai aanu), aoaeao cia/eoaeueii iaiueoa
ia Eoia e i?aeoe/anee ?aaai ioeth a oeaio?a Caiee. (?en.7)
Eae aaeeei caiiia i?eoyaeaiea, aeaenoaothuaa ia ?aciua iannu? Eae
n?aaieoue aana aeaoo i?aaeiaoia? Aicueiai aeaa iaeeiaeiauo eonea
naeioea, neaaeai, ii 1 ea eaaeaeue. Caiey i?eoyaeaaao eaaeaeue ec ieo n
iaeeiaeiaie neeie, ?aaiie aano 10 I. Anee niaaeeieoue iaa eonea a 2 ea,
oi aa?oeeaeueiua neeu i?inoi neeaaeuaathony: Caiey i?eoyaeaaao 2 ea
aaeaia neeueiaa, /ai 1 ea. Iu iieo/ei oi/ii oaeia aea oaeaiaiiia
i?eoyaeaiea, anee nieaaei iaa eonea a iaeei eee iiianoei eo iaeei ia
ae?oaie. A?aaeoaoeeiiiua i?eoyaeaiey ethaiai iaeii?iaeiiai iaoa?eaea
i?inoi neeaaeuaathony, e iao ie iiaeiuaiey, ie ye?aie?iaaiey iaeiiai
eonea aauanoaa ae?oaei.
Aeey ethaiai iaeii?iaeiiai iaoa?eaea aan i?iii?oeeiiaeai ianna. Iiyoiio
iu n/eoaai, /oi Caiey yaeyaony enoi/ieeii «iiey neeu oyaeanoe»,
enoiaeyuaai ec aa oeaio?a ii aa?oeeaee e niiniaiiai i?eoyaeaaoue ethaie
eonie aauanoaa. Iiea neeu oyaeanoe aicaeaenoaoao iaeeiaeiai, neaaeai, ia
eaaeaeue eeeia?aii naeioea. A eae ianoieo aeaei n neeaie i?eoyaeaiey,
aeaenoaothueie ia iaeeiaeiaua iannu ?aciuo iaoa?eaeia, iai?eia? 1 ea
naeioea e 1 ea aethieiey? Niune yoiai aii?ina caaeneo io oiai, /oi
ioaeii iiieiaoue iiae iaeeiaeiauie iannaie. Iaeaieaa i?inoie niinia
n?aaiaiey iann, eioi?ui iieuecothony a iao/iuo enneaaeiaaieyo e a
oi?aiaie i?aeoeea – yoi i?eiaiaiea ?u/aaeiuo aania. A ieo n?aaieaathony
neeu, eioi?ua oyioo iaa a?oca. Ii iieo/ea oaeei iooai iaeeiaeiaua iannu,
neaaeai naeioea e aethieiey, iiaeii i?aaeiieiaeeoue, /oi ?aaiua aana
eiatho ?aaiua iannu. Ii oaeoe/anee caeanue ?acaiai? eaeao i aeaoo
niaa?oaiii ?aciuo aeaeao iannu – ia eia?oiie e i a?aaeoaoeeiiiie ianna.
Aaee/eia a oi?ioea I?aaenoaaeyao niaie
eia?oioth ianno. A iiuoao n oaeaaeeaie, eioi?ui i?eaeatho onei?aiea
i?oaeeiu, aaee/eia aunooiaao eae oa?aeoa?enoeea
«oyaeaeiaaniinoe aauanoaa» iieacuaathuay, ianeieueei o?oaeii niiaueoue
onei?aiea ?anniao?eaaaiiio oaeo. Eiee/anoaaiiie oa?aeoa?enoeeie neoaeeo
ioiioaiea . Yoa ianna i?aaenoaaeyao niaie ia?o
eia?oiinoe, oaiaeaioeee iaoaie/aneeo nenoai nii?ioeaeyoueny eciaiaieth
ninoiyiey. Ianna – yoi naienoai, eioi?ia aeieaeii auoue iaeiei e oai aea
e aaeece iiaa?oiinoe Caiee, e ia Eoia, e a aeaeaeii einiina, e a oeaio?a
Caiee. Eaeiaa aa naycue n oyaioaieai e /oi ia naiii aeaea i?ienoiaeeo
i?e acaaoeaaiee?
Niaa?oaiii iacaaeneii io eia?oiie iannu iiaeii aaanoe iiiyoea
a?aaeoaoeeiiiie iannu eae eiee/anoaa aauanoaa, i?eoyaeaaaiiai Caieae.
Iu n/eoaai, /oi iiea oyaioaiey Caiee iaeeiaeiai aeey anao iaoiaeyueony
a iai i?aaeiaoia, ii i?eienuaaai ?acee/iui i?aae
iaoai ?aciua iannu, eioi?ua i?iii?oeeiiaeueiu i?eoyaeaieth yoeo
i?aaeiaoia iieai. Yoi a?aaeoaoeeiiiay ianna. Iu aiai?ei, /oi ?aciua
i?aaeiaou eiatho ?aciue aan, iineieueeo iie iaeaaeatho ?acee/iuie
a?aaeoaoeeiiiuie iannaie, eioi?ua i?eoyaeaathony iieai oyaioaiey. Oaeei
ia?acii, a?aaeoaoeeiiiua iannu ii ii?aaeaeaieth i?iii?oeeiiaeueiu aanai,
a oaeaea neea oyaeanoe. A?aaeoaoeeiiiay ianna ii?aaeaeyao, n eaeie neeie
oaei i?eoyaeaaaony Caieae. I?e yoii oyaioaiea acaeiii: anee Caiey
i?eoyaeaaao eaiaiue, oi eaiaiue oi/ii oaeaea i?eoyaeaaao Caieth. Cia/eo,
a?aaeoaoeeiiiay ianna oaea ii?aaeaeyao oaeaea, ianeieueei neeueii iii
i?eoyaeaaao ae?oaia oaei, Caieth. Oaeei ia?acii, a?aaeoaoeeiiiay ianna
ecia?yao eiee/anoai aauanoaa, ia eioi?ia aeaenoaoao caiiia i?eoyaeaiea,
eee eiee/anoai aauanoaa, iaoneaaeeaathuaa a?aaeoaoeeiiiua i?eoyaeaiey
iaaeaeo oaeaie.
A?aaeoaoeeiiiia i?eoyaeaiea aeaenoaoao ia aeaa iaeeiaeiauo eonea naeioea
aaeaia neeueiaa, /ai ia iaeei. A?aaeoaoeeiiiua iannu eoneia naeioea
aeieaeiu auoue i?iii?oeeiiaeueiu eia?oiui iannai, iineieueeo iannu oiai
e ae?oaiai aeaea, i/aaeaeii, i?iii?oeeiiaeueiu /eneo aoiiia naeioea. Oi
aea naiia ioiineony e eoneai ethaiai ae?oaiai iaoa?eaea, neaaeai, ainea,
ii eae n?aaieoue eonie naeioea n eoneii ainea? Ioaao ia yoio aii?in
aeaao neiaiee/aneee yenia?eiaio ii eco/aieth iaaeaiey oae anaaiciiaeiuo
?acia?ia n aa?oeiu iaeeiiiie Iecaineie aaoie, oio, eioi?ue ii eaaaiaea
i?iecaiaeee Aaeeeae. Na?inei aeaa eonea ethaiai iaoa?eaea ethauo
?acia?ia. Iie iaaeatho n iaeeiaeiaui onei?aieai g. Neea, aeaenoaothuay
ia oaei e niiauathuay aio onei?aiea6 – yoi i?eoyaeaiea Caiee,
i?eeiaeaiiia e yoiio oaeo. Neea i?eoyaeaiey oae Caieae i?iii?oeeiiaeueia
a?aaeoaoeeiiiie ianna. Ii neeu oyaeanoe niiauatho anai oaeai iaeeiaeiaia
onei?aiea g. Iiyoiio neea oyaeanoe, eae e aan, aeieaeia auoue
i?iii?oeeiiaeueia eia?oiie ianna. Neaaeiaaoaeueii, oaea ethaie oi?iu
niaea?aeao iaeeiaeiaua i?iii?oeee iaaeo iann.
Anee i?eiyoue 1 ea a ea/anoaa aaeeieoeu iaaeo iann, oi a?aaeoaoeeiiiay e
eia?oiay iannu aoaeoo iaeeiaeiau o anao oae ethauo ?acia?ia ec ethaiai
iaoa?eaea e a ethaii ianoa.
Aio eae yoi aeieacuaaaony. N?aaiei yoaeii eeeia?aiia, naeaeaiiue ec
ieaoeiu6 n eaiiai iaecaanoiie iannu. N?aaiei eo eia?oiua iannu,
ia?aiauay iii/a?aaeii eaaeaeia ec oae a ai?eciioaeueiii iai?aaeaiee iiae
aeaenoaeai iaeioi?ie neeu e ecia?yy onei?aiea. I?aaeiieiaeei, /oi ianna
eaiiy ?aaia 5,31 ea. Caiiia oyaioaiea a yoii n?aaiaiee ia o/anoaoao.
Caoai n?aaiei a?aaeoaoeeiiiua iannu iaieo oae, ecia?ea a?aaeoaoeeiiiia
i?eoyaeaiea iaaeaeo eaaeaeui ec ieo e eaeei-ieaoaeue o?aoueei oaeii,
i?iua anaai Caieae. Yoi iiaeii i?iaeaeaoue iooai acaaoeaaiey iaieo oae.
Iu oaeaeei, /oi a?aaeoaoeeiiiay ianna eaiiy oiaea ?aaia 5,31 ea.
Aieaa /ai ca iienoieaoey aei oiai eae Iuethoii i?aaeeiaeee naie caeii
anaie?iiai oyaioaiey, Eiaaii Eaiea? (1571-1630) iaia?oaeee, /oi
“caiooaiiia aeaeaeaiea ieaiao Nieia/iie nenoaiu iiaeii auei au iienaoue
n iiiiuueth o?ao i?inouo caeiiia. Caeiiu Eaiea?a oe?aieee aa?o a
aeiioaco Eiia?ieea i oii, /oi ieaiaou a?auathony aie?oa Nieioea, a.
Ooaa?aeaeaoue a ia/aea XVII aaea, /oi ieaiaou aie?oa Nieioea, a ia
aie?oa Caiee, auei aaee/aeoae a?anueth. Aeaei?aeaii A?oii ioe?uoi
caueuaaoee nenoaio Eiia?ieea, eae a?aoee aue inoaeaeai nayoie
eieaeceoeeae e niaeaeai ia eino?a. Aeaaea aaeeeee Aaeeeeae, ianiio?y ia
oanioth ae?oaeao n iaiie ?eineei, aue caoi/ai a oth?ueio, inoaeaeai
eieaeceoeeae e auioaeaeai aue ioaee/ii io?a/ueny io naieo acaeyaeia.
A oa a?aiaia nayuaiiuie e iai?eeiniiaaiiuie n/eoaeenue o/aiey A?enoioaey
e Ioieaiay, aeaneaoea, /oi i?aeou ieaiao aicieeatho a ?acoeueoaoa
neiaeiuo aeaeaeaiee ii nenoaia ie?oaeiinoae. Oae aeey iienaiey i?aeou
Ia?na o?aaiaaeanue aethaeeia, eee ieiei oiai, ie?oaeiinoae ?acee/iiai
aeeaiao?a. Eiaaii Eaiea? iinoaaee caaea/o “aeieacaoue”, /oi Ia?n e Caiey
aeieaeiu ia?auaoueny aie?oa Nieioea. Ii iuoaeny iaeoe i?aeoo i?inoaeoae
aaiiao?e/aneie oi?iu, eioi?ay oi/ii au niioaaonoaiaaea iiiai/eneaiiui
ecia?aieyi iieiaeaiey ieaiaou. I?ioee aiaeu ooiieoaeueiuo au/eneaiee,
i?aaeaea /ai Eaiea? niia noi?ioee?iaaoue o?e i?inouo caeiia, i/aiue
oi/ii iienuaathueo aeaeaeaiea anao ieaiao:
Ia?aue caeii: Eaaeaeay ieaiaoa aeaeaeaony ii yeeeino, a
iaeiii ec oieonia eioi?iai iaoiaeeony
Nieioea.
Aoi?ie caeii: ?aaeeon-aaeoi? (eeiey, niaaeeiythuay Nieioea
e ieaiaoo) iienuaaao ca ?aaiua i?iiaaeooee
a?aiaie ?aaiua ieiuaaee
O?aoee caeii: Eaaae?aou ia?eiaeia ia?auaiey ieaiao
i?iii?oeeiiaeueiu eoaai eo n?aaeieo
?annoiyiee io Nieioea:
R13/T12 = R23/T22
Cia/aiea o?oaeia Eaiea?a ia?iiii. Ii ioe?ue caeiiu, eioi?ua caoai
Iuethoii naycae n caeiiii anaie?iiai oyaioaiey Eiia/ii, nai Eaiea? ia
ioaeaaae naaa io/aoa a oii, e /aio i?eaaaeoo aai ioe?uoey. “Ii caieiaeny
ooiieoaeueiuie iaiaeaie yiie?e/aneeo i?aaee, eioi?ua a aoaeouai aeieaeai
aue i?eaanoe e ?aoeeiiaeueiiio aeaeo Iuethoii”. Eaiea? ia iia
iauynieoue, /ai iaoneiaeaii nouanoaiaaiea yeeeioe/aneeo i?aeo, ii
ainoeuaeny oai, /oi iie nouanoaotho.
Ia iniiaa o?aoueaai caeiia Eaiea?a Iuethoii naeaeae auaiae, /oi neeu
i?eoyaeaiey aeieaeiu oauaaoue n oaaee/aieai ?annoiyiey e /oi i?eoyaeaiea
aeieaeii eciaiyoueny eae (?annoiyiea)-2. Ioe?ua caeii anaie?iiai
oyaioaiey, Iuethoii ia?aian i?inoia i?aaenoaaeaiea i aeaeaeaiee Eoiu ia
anth ieaiaoioth nenoaio. Ii iieacae, /oi i?eoyaeaiea ii auaaaeaiiui ei
caeiiai iaoneiaeeaaao aeaeaeaiea ieaiao ii yeeeioe/aneei i?aeoai, i?e/ai
a iaeiii ec oieonia yeeeina aeieaeii iaoiaeeony Nieioea. Aio oaeaeinue
eaaei auaanoe aeaa ae?oaeo caeiia Eaiea?a, eioi?ua oaeaea auoaeatho ec
aai aeiioacu anaie?iiai oyaioaiey. Yoe caeiiu ni?aaaaeeeau, anee
o/eouaaaony oieueei i?eoyaeaiea Nieioeai. Ii ioaeii o/eouaaoue e
aeaenoaea ia aeaeaeouothny ieaiaoo ae?oaeo ieaiao, oioy a Nieia/iie
nenoaia yoe i?eoyaeaiey iaeu ii n?aaiaieth n i?eoyaeaieai Nieioea.
Aoi?ie caeii Eaiea?a neaaeoao ec i?iecaieueiie caaeneiinoe neeu
i?eoyaeaiey io ?annoiyiey, anee yoa neea aeaenoaoao ii i?yiie,
niaaeeiythuae oeaio?u ieaiaou e Nieioea. Ii ia?aiio e o?aoueaio caeiiai
Eaiea?a oaeiaeaoai?yao oieueei caeii ia?aoiie i?iii?oeeiiaeueiinoe nee
i?eoyaeaiey eaaae?aoo ?annoiyiey.
*oiau iieo/eoue o?aoee caeii Eaiea?a, Iuethoii i?inoi iauaaeeiee caeiiu
aeaeaeaiey n caeiiii anaie?iiai oyaioaiey. Aeey neo/ay e?oaiauo i?aeo
iiaeii ?annoaeaeaoue neaaeothuei ia?acii: ionoue ieaiaoa, ianna eioi?ie
?aaia m, aeaeaeaony ni nei?inoueth v ii ie?oaeiinoe ?aaeeona R aie?oa
Nieioea, ianna eioi?iai ?aaia I. Yoi aeaeaeaiea iiaeao inouanoaeyoueny
oieueei a oii neo/aa, anee ia ieaiaoo aeaenoaoao aiaoiyy neea F = mv2/R,
nicaeathuay oeaio?ino?aieoaeueiia onei?aiea v2/R. I?aaeiieiaeei, /oi
i?eoyaeaiea iaaeaeo Nieioeai e ieaiaoie eae ?ac e nicaeaao iaiaoiaeeioth
neeo. Oiaaea:
GMm/r2 = mv2/R
e ?annoiyiea r iaaeaeo m e M ?aaii ?aaeeono i?aeou R. Ii nei?inoue
v = = 2
aaea O – a?aiy, ca eioi?ia ieaiaoa niaa?oaao iaeei iai?io. Oiaaea
*oiau iieo/eoue o?aoee caeii Eaiea?a, ioaeii ia?aianoe ana R e O a iaeio
noi?iio o?aaiaiey, a ana inoaeueiua aaee/eiu – a ae?oaoth:
R3/T2 = GM/4(2
Anee ia?aeoe oaia?ue e ae?oaie ieaiaoa n ae?oaei ?aaeeonii i?aeou e
ia?eiaeii ia?auaiey, oi iiaia ioiioaiea iiyoue aoaeao ?aaii GM/4(2; yoa
aaee/eia aoaeao iaeeiaeiaie aeey anao ieaiao, oae eae G -oieaa?naeueiay
iinoiyiiay, a ianna I – iaeia e oa aea aeey anao ieaiao, a?auathueony
aie?oa Nieioea. Oaeei ia?acii, aaee/eia R3/T2 aoaeao iaeiie e oie aea
aeey anao ieaiao a niaeanee n o?aoueei caeiiii Eaiea?a. Oaeia au/eneaiea
iicaieyao iieo/eoue o?aoee caeii e aeey yeeeioe/aneeo i?aeo, ii a yoii
neo/aa R – n?aaeiyy aaee/eia iaaeaeo iaeaieueoei e iaeiaiueoei
?annoiyieai ieaiaou io Nieioea.
Aii?oaeaiiue iiuiuie iaoaiaoe/aneeie iaoiaeaie e ?oeiaiaeeiue
aaeeeieaiiie eiooeoeeae, Iuethoii i?eiaiee naith oai?eth e aieueoiio
/eneo caaea/, aioaaeoeo a aai I?EIOeEIU, eanathueany iniaaiiinoae Eoiu,
Caiee ae?oaeo ieaiao e eo aeaeaeaiey, a oaeaea ae?oaeo iaaaniuo oae:
niooieeia, eiiao.
Eoia eniuouaaao iiiai/eneaiiua aiciouaiey, ioeeiiythuea aa io
?aaiiia?iiai e?oaiaiai aeaeaeaiey. I?aaeaea anaai, iia aeaeaeaony ii
eaiea?ianeiio yeeeino, a iaeiii ec oieonia eioi?iai iaoiaeeony Caiey,
eae e ethaie niooiee. Ii yoa i?aeoa eniuouaaao iaaieueoea aa?eaoeee ca
n/ao i?eoyaeaiey Nieioeai. I?e iiaieoiee Eoia iaoiaeeony aeeaea e
Nieioeo, /ai iieiay Eoia, iiyaeythuayny ia aeaa iaaeaee iicaeiaa; yoa
i?e/eia eciaiyao i?eoyaeaiea, /oi aaaeao e caiaaeeaieth e onei?aieth
aeaeaeaiey Eoiu a oa/aiea ianyoea. Yoio yooaeo oaaee/eaaaony, eiaaea
ceiie Nieioea aeeaea, oae, /oi iaaethaeathony e aiaeiaua aa?eaoeee
nei?inoe aeaeaeaiey Eoiu. E?iia oiai, eciaiaiey nieia/iiai i?eoyaeaiey
iaiytho yeeeioe/iinoue eoiiie i?aeou; eoiiay i?aeoa ioeeiiyaony aaa?o e
aiec, ieineinoue i?aeou iaaeeaiii a?auaaony. Oaeei ia?acii, Iuethoii
iieacae, /oi ioia/aiiua ia?aaoey?iinoe a aeaeaeaiee Eoiu aucaaiu
anaie?iui oyaioaieai. Ii ia ?ac?aaioae ai anao aeaoaeyo aii?in i
nieia/iii i?eoyaeaiee, aeaeaeaiea Eoiu inoaeinue neiaeiie i?iaeaiie,
eioi?ay ?ac?aaaouaaaony ni ana aic?anoathueie iiae?iaiinoyie e aei iaoeo
aeiae.
Ieaaineea i?eeeau e ioeeau aeieaia a?aiy inoaaaeenue caaaaeeie,
iauynieoue eioi?oth eacaeinue iiaeii auei au, onoaiiaea eo naycue n
aeaeaeaieai Eoiu. Iaeiaei ethaee n/eoaee, /oi oaeay naycue ?aaeueii
nouanoaiaaoue ia iiaeao, e aeaaea Aaeeeae iniaye yoo eaeath. Iuethoii
iieacae, /oi i?eeeau e ioeeau iaoneiaeaiu ia?aaiiia?iui i?eoyaeaieai
aiaeu a ieaaia ni noi?iiu Eoiu. Oeaio? eoiiie i?aeou ia niaiaaeaao n
oeaio?ii Caiee. Eoia e Caiey aianoa a?auathony aie?oa eo iauaai oeaio?a
iann. Yoio oeaio? iann iaoiaeeony ia ?annoiyiee i?eia?ii 4800 ei io
oeaio?a Caiee, anaai eeoue a 1600 ei io iiaa?oiinoe Caiee. Eiaaea Caiey
i?eoyaeaaao Eoio, eoia i?eoyaeaaao Caieth n ?aaiie e i?ioeaiiieiaeii
iai?aaeaiiie neeie, aeaaiaea?y /aio aicieeaao neea Mv2/r, aucuaathuay
aeaeaeaiea Caiee aie?oa iauaai oeaio?a iann n ia?eiaeii, ?aaiui iaeiiio
ianyoeo. Aeeaeaeoay e Eoia /anoue ieaaia i?eoyaeaaaony neeueiaa (iia
aeeaea), aiaea iiaeieiaaony – e aicieeaao i?eeea. Iaoiaeyuayny ia
aieueoai io Eoiu ?annoiyiee /anoue ieaaia i?eoyaeaaaony neaaaa, /ai
nooa, e a yoie /anoe ieaaia oaeaea iiaeieiaaony aiaeyiie ai?a. Iiyoiio,
ca 24 /ana iaaethaeaaony aeaa i?eeeaa. Nieioea oiaea aucuaaao i?eeeau,
oioy e ia noieue neeueiua, eai aieueoia ?annoiyiea io Nieioea
naeaaeeaaao iaiaeeiaeiainoue i?eoyaeaiey.
Iuethoii ?ane?ue i?e?iaeo eiiao – yoeo ainoae nieia/iie nenoaiu, eioi?ua
anaaaea aucuaaee eioa?an e aeaaea nayuaiiue oaean. Iuethoii iieacae, /oi
eiiaou aeaeaeoony ii i/aiue auoyiooui yeeeioe/aneei i?aeoai, aiaeiii ec
oieonia eioi?iai iaoiaeeony Nieioea. Eo aeaeaeaiea ii?aaeaeyaony, eae e
aeaeaeaiea ieaiao, a?aaeoaoeeae. Ii iie eiatho i/aiue iaeoth aaee/eio,
oae /oi eo iiaeii oaeaeaoue oieueei oiaaea, eiaaea e iie i?ioiaeyo
aaeece Nieioea. Yeeeioe/aneay i?aeoa eiiaou iiaeao auoue ecia?aia, e
a?aiy aa aica?auaiey a iaoo iaeanoue oi/ii i?aaeneacaii. Eo ?aaoey?iia
aica?auaiea a i?aaeneacaiiua n?iee iicaieyao i?iaa?eoue iaoe
iaaethaeaiey e aeaao aua iaeii iiaeoaa?aeaeaiea caeiia anaie?iiai
oyaioaiey.
A iaeioi?uo neo/ayo eiiaoa eniuouaaao neeueiia a?aaeoaoeeiiiia
aiciouaiea, i?ioiaey aaeece aieueoeo ieaiao, e ia?aoiaeeo ia iiaoth
i?aeoo n ae?oaei ia?eiaeii. Aio ii/aio iu ciaai, /oi o eiiao ianna
iaaaeeea: ieaiaou ieacuaatho aicaeaenoaea ia eo aeaeaeaiea, a eiiaou ia
aeeytho ia aeaeaeaiea ieaiao, oioy e aeaenoaotho ia ieo n oaeie aea
neeie.
Eiiaou aeaeaeoony oae auno?i e i?eoiaeyo oae ?aaeei, /oi aua aei neo ii?
o/aiua aeaeoo iiiaioa, eiaaea iiaeii i?eiaieoue nia?aiaiiua n?aaenoaa e
enneaaeiaaieth aieueoie eiiaou.
Anee aaeoiaoueny, eaeoth ?ieue ea?atho neeu oyaioaiey a aeecie iaoae
ieaiaou, oi ioe?uaathony oeaeua ieaaiu yaeaiee, e aeaaea ieaaiu a
aoeaaeueiii niunea yoiai neiaa: ieaaiu aiaeu, aicaeooiue ieaai. Aac
oyaioaiey iie au ia nouanoaiaaee.
Aieia a ii?a, ana oa/aiey, ana aao?u, iaeaea, aanue eeeiao ieaiaou
ii?aaeaeythony ea?ie aeaoo iniiaiuo oaeoi?ia: nieia/iie aeayoaeueiinoe e
caiiiai i?eoyaeaiey.
A?aaeoaoeey ia oieueei oaea?aeeaaao ia Caiea ethaeae, aeeaioiuo, aiaeo e
aicaeoo, ii e naeeiaao eo. Yoi naeaoea o iiaa?oiinoe Caiee ia oae oae
aaeeei, ii ?ieue aai iaiaeiaaaeia.
Ciaiaieoay auoaeeeaathuay neea A?oeiaaea iiyaeyaony oieueei iioiio, /oi
naeaoa oyaioaieai n neeie, oaaee/eaathuaeny n aeoaeiie.
Nai caiiie oa? naeao neeaie oyaioaiey aei eieinnaeueiuo aeaaeaiee. A
oeaio?a Caiee aeaaeaiea, ii-aeaeeiiio, i?aauoaao 3 ieeeeiia aoiinoa?.
Eae oai?aoe iaoee Iuethoii nicaeae iiaue noeeue, eioi?ue aei neo ii? aua
nio?aiyao naia cia/aiea. Eae iao/iue iuneeoaeue ii auaeathueiny
iniiaiiieiaeieeii eaeae. Iuethoii i?eoae e caia/aoaeueiie eaeaa
anaie?iiai oyaioaiey. Ii inoaaee iinea naay eieae, iinayuaiiua caeiiai
aeaeaeaiey, a?aaeoaoeee, ano?iiiiee e iaoaiaoeea. Iuethoii aicaunee
ano?iiiieth; ii aeae ae niaa?oaiii iiaia ianoi a iaoea e i?eaae aa a
ii?yaeie, eniieueciaaa iauyniaiey, a iniiaa eioi?uo eaaeaee nicaeaiiua e
i?iaa?aiiua ei caeiiu.
Iienee iooae, aaaeoueo ei ana aieaa iieiiio e aeoaieiio iiieiaieth
Anaie?iiai Oyaioaiey i?iaeieaeathony. ?aoaiea aaeeeeo i?iaeai o?aaoao
aaeeeeo o?oaeia.
Ii eae au ia iioei aeaeueiaeoaa ?acaeoea iaoaai iiieiaiey a?aaeoaoeee,
aaieaeueiia oai?aiea Iuethoiia aeaaaeoeaoiai aaea anaaaea aoaeao
iiei?youe naiae iaiiaoi?eiie aea?ciiaaiiinoueth, anaaaea inoaiaony
aaeeeei oaaii ia iooe iiciaiey i?e?iaeu.
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