Ajụjụ na Mkparịta ụka gbasara Einstein's Relativity
Njiko Einstein bụ otu n'ime echiche kachasị mkpa na fiziki nke oge a, na-agbanwe ụzọ anyị si aghọta oghere na oge. O nwere akụkụ abụọ: njiko pụrụ iche (1905) na njiko izugbe (1915). N'isiokwu a, anyị ga-atụle ọtụtụ ihe atụ metụtara njiko Einstein ma kparịta ha iji nye nghọta miri emi.
Mmekọrịta Pụrụ Iche
Njirịta pụrụ iche na-akọwa ihe ndị na-agagharị n'ọsọ na-aga n'ihu na-eru nso ọsọ ìhè. Isi ihe abụọ sitere na ozizi a bụ mgbasa oge na mkpụmkpụ ogologo.
1. Mgbasa Oge
Ọ bụrụ na e nwere mmadụ abụọ na-ekiri ihe, otu na-aga n'ụwa, otu na-agakwa n'ọsọ dị elu, ha ga-atụ oge dị iche iche maka otu ihe ahụ.
Ihe atụ nke nsogbu:
Onye na-aga mbara igwe ji ọsọ ìhè dị okpukpu 0.8 (c) gawa kpakpando nke dị afọ iri site n'ụwa. Ogologo oge ole ka onye na-aga mbara igwe na-ewe iji ruo kpakpando ahụ?
Azịza:
Nke mbụ, anyị na-agbakọ oge onye na-ekiri ihe na-eme n'ụwa tụrụ:
\[ t_B = \frac{d}{v} = \frac{10 \text{ afọ ọkụ}}{0.8 \, c} = 12.5 \text{ afọ} \]
Iji gbakọọ oge nke onye na-aga mbara igwe tụrụ (mgbasawanye oge), anyị na-eji usoro a:
\[ t_A = t_B \sqrt{1 – \frac{v^2}{c^2}} \]
Dochie ụkpụrụ ndị a maara:
\[ t_A = 12.5 \sqrt{1 – (0.8)^2} \]
\[ t_A = 12.5 \sqrt{1 – 0.64} \]
\[ t_A = 12.5 \sqrt{0.36} \]
\[ t_A = 12.5 \ugboro 0.6 \]
\[ t_A = 7.5 \ederede{ afọ} \]
Ya mere, oge ndị na-aga mbara igwe tụrụ bụ afọ 7.5.
2. Mkpụkọ ogologo
Mgbe ihe na-agagharị n'ọsọ na-eru nso ọsọ ìhè, ogologo ya ga-adị ka mkpụmkpụ nye onye na-ekiri ihe na-anaghị aga ebe ọ bụla.
Ihe atụ nke nsogbu:
Ụgbọelu mbara igwe nke nwere ogologo mita iri n'ezie na-aga ọsọ ọkụ okpukpu 0.9. Ogologo oge ole ka ụgbọ elu mbara igwe ahụ ga-adịru onye na-ekiri ihe na-eme n'ụwa?
Azịza:
Iji gbakọọ mkpụmkpụ ogologo, anyị na-eji usoro a:
\[ L = L_0 \sqrt{1 – \frac{v^2}{c^2}} \]
Ebe:
– \( L_0 \) bụ ogologo kwesịrị ekwesị ma ọ bụ ogologo n'ezie (mita 10),
– \( v \) bụ ọsọ nke ụgbọelu (0.9c).
Dochie ụkpụrụ ndị a maara:
\[ L = 10 \sqrt{1 - (0.9)^2} \]
\[ L = 10 \sqrt{1-0.81} \]
\[ L = 10 \sqrt{0.19} \]
\[ L = 10 \ugboro 0.436 \]
\[ L = 4.36 \ederede{ mita} \]
Ya mere, dịka ndị na-ekiri ihe na-eme n'ụwa si kwuo, ogologo nke ụgbọelu ahụ bụ mita 4.36.
Mmekọrịta Izugbe
Njiko ihe gbasara ike na-akọwa ike ndọda, ebe oke na ike na-emetụta oghere na oge.
3. Lensi ike ndọda
Anya ndọda na-eme mgbe ike ndọda nke nnukwu ihe dịka galaxy ma ọ bụ oghere ojii gbagọrọ agbagọ ìhè sitere na ihe dị anya.
Ihe atụ nke nsogbu:
Galaxy A nwere oke ibu iji gbapụ ìhè site na quasar B, nke dị n'azụ ya. Ọ bụrụ na akụkụ ntụgharị ahụ bụ sekọnd 1.5 arc, kedu oke ibu nke galaxy A? (Jiri ihe ndọda Newton G = 6.674 × 10^-11 N(m/kg)^2, ọsọ nke ìhè c = 3×10^8 m/s)
Azịza:
Enwere ike inye akụkụ nke mgbagọ θ site na usoro:
\[ \theta = \frac{4GM}{c^2 R} \]
Ebe:
– \( G \) bụ ihe ndọda ike ndọda,
– \( M \) bụ oke nke ụyọkọ kpakpando ahụ,
– \(c \) bụ ọsọ nke ìhè,
– \( R \) bụ anya kacha nso n'etiti ìhè na etiti kpakpando ahụ.
Ebe anyị chọrọ ịchọta M, anyị na-ahazi usoro ahụ:
\[ M = \frac{\theta c^2 R}{4G} \]
Were ya na R bụ mita 5×10^20 (nkezi anya nke ụyọkọ kpakpando). Gbanwee θ site na arcsekọnd gaa na radians (1 arcsekọnd = 4.848×10^-6 radians):
\[ \theta = 1.5 \ugboro 4.848 \ugboro 10^{-6} \, \text{radian} = 7.272 \ugboro 10^{-6} \, \text{radian} \]
Dochie ụkpụrụ ndị a maara:
\[ M = \frac{(7.272 \ugboro 10^{-6}) (ugboro atọ 10^8)^2 (ugboro ise 10^{20})}{4 \ugboro 6.674 \ugboro 10^{-11}} \]
\[ M = \frac{(7.272 \ugboro 10^{-6}) (ugboro 9 10^{16}) (ugboro 5 10^{20})}{26.696 \ugboro 10^{-11}} \]
\[ M = \frac{(3.2764 \ugboro 10^{31})}{26.696 \ugboro 10^{-11}} \]
\[ M = 1.227 \ugboro 10^{41} \, \text{kg} \]
Ya mere, oke nke galaxy A dị ihe dịka kilogram 1.227 × 10^ 41.
4. Mbelata Perihelion nke Mercury
Njirịta izugbe nwekwara ike ịkọwa mmalite nke okirikiri nke mbara ala Mercury nke ndị ọrụ Newtonian na-apụghị ịkọwa.
Ihe atụ nke nsogbu:
Kedu oke mgbanwe perihelion nke Mercury dịka akọwara site na njikarịcha izugbe? (Njikọ paramita A: 43 arcsekọnd kwa narị afọ)
Azịza:
Jiri data enyere ozugbo:
Dịka ozizi Einstein nke ikwu okwu gbasara njikọta (relativity) si kwuo, mgbanwe perihelion nke Mercury nke akọwara bụ sekọnd 43 arc kwa narị afọ, nke kwekọrọ na nsonaazụ ihe a hụrụ.
Mmechi:
Site n'ịmecha nsogbu na mkparịta ụka ndị a, anyị nwere ike ịhụ otú mmekọrịta Einstein si enye nghọta miri emi banyere oge, ogologo, na ike ndọda. Ozizi a agbanweghị naanị echiche sayensị anyị banyere eluigwe na ala kamakwa o nwere ojiji bara uru na teknụzụ ọgbara ọhụrụ, dị ka sistemụ GPS navigation, nke chọrọ mmezi mmekọrịta iji rụọ ọrụ nke ọma. Ịmụta na ịghọta mmekọrịta Einstein bụ nzọụkwụ dị mkpa n'ịmụbawanye n'ime ụwa dị mgbagwoju anya nke physics.
