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Question Number 97885 by  M±th+et+s last updated on 10/Jun/20
hello every one  how do they calculated the universe old  wich is 13.8 billion years
$${hello}\:{every}\:{one} \\ $$$${how}\:{do}\:{they}\:{calculated}\:{the}\:{universe}\:{old} \\ $$$${wich}\:{is}\:\mathrm{13}.\mathrm{8}\:{billion}\:{years} \\ $$
Commented by EmericGent last updated on 10/Jun/20
One way is use the density in function of time and see when the density reach Planck's limit
Commented by  M±th+et+s last updated on 10/Jun/20
thanx for all
$${thanx}\:{for}\:{all}\: \\ $$
Answered by smridha last updated on 10/Jun/20
you can prove this by introducing  Hubble constant(H_0 )...  but the fact is our universe is  expanding, not in constant rate  it is accelarating so age  of universe cannot determine  perfectly ,this is just a theoritical  value...  well I can prove this...
$$\boldsymbol{{you}}\:\boldsymbol{{can}}\:\boldsymbol{{prove}}\:\boldsymbol{{this}}\:\boldsymbol{{by}}\:\boldsymbol{{introducing}} \\ $$$$\boldsymbol{{Hubble}}\:\boldsymbol{{constant}}\left(\boldsymbol{{H}}_{\mathrm{0}} \right)… \\ $$$$\boldsymbol{{but}}\:\boldsymbol{{the}}\:\boldsymbol{{fact}}\:\boldsymbol{{is}}\:\boldsymbol{{our}}\:\boldsymbol{{universe}}\:\boldsymbol{{is}} \\ $$$$\boldsymbol{{expanding}},\:\boldsymbol{{not}}\:\boldsymbol{{in}}\:\boldsymbol{{constant}}\:\boldsymbol{{rate}} \\ $$$$\boldsymbol{{it}}\:\boldsymbol{{is}}\:\boldsymbol{{accelarating}}\:\boldsymbol{{so}}\:\boldsymbol{{age}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{universe}}\:\boldsymbol{{cannot}}\:\boldsymbol{{determine}} \\ $$$$\boldsymbol{{perfectly}}\:,\boldsymbol{{this}}\:\boldsymbol{{is}}\:\boldsymbol{{just}}\:\boldsymbol{{a}}\:\boldsymbol{{theoritical}} \\ $$$$\boldsymbol{{value}}… \\ $$$$\boldsymbol{{well}}\:\boldsymbol{{I}}\:\boldsymbol{{can}}\:\boldsymbol{{prove}}\:\boldsymbol{{this}}… \\ $$
Commented by  M±th+et+s last updated on 10/Jun/20
sir you mean this rule  t_0 =(2/3)×(1/(H_0 (√Ω_v_0  )))sinh^(−1) ((√((3Ω_v_0  )/(2(1+q_0 ))))  and i hope if you have a time show the  prove and thank you.
$${sir}\:{you}\:{mean}\:{this}\:{rule} \\ $$$${t}_{\mathrm{0}} =\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{1}}{{H}_{\mathrm{0}} \sqrt{\Omega_{{v}_{\mathrm{0}} } }}{sinh}^{−\mathrm{1}} \left(\sqrt{\frac{\mathrm{3}\Omega_{{v}_{\mathrm{0}} } }{\mathrm{2}\left(\mathrm{1}+{q}_{\mathrm{0}} \right.}}\right) \\ $$$${and}\:{i}\:{hope}\:{if}\:{you}\:{have}\:{a}\:{time}\:{show}\:{the} \\ $$$${prove}\:{and}\:{thank}\:{you}. \\ $$
Commented by smridha last updated on 10/Jun/20
its well but you can also determine  it in easiest way like..  (1/H_0 )=age of the universe  H_0 =((73km/s)/(1Mpc)) it means if the  distant bet^n  two galaxyies is  1Mpc then the relative velocity  of moving away from one to other  is 73km/s.  so you can see imedeately that  distant and velocity is proportional  and the proportionality constant  is H_0 ..this is called Hubble′s law.
$$\boldsymbol{{its}}\:\boldsymbol{{well}}\:\boldsymbol{{but}}\:\boldsymbol{{you}}\:\boldsymbol{{can}}\:\boldsymbol{{also}}\:\boldsymbol{{determine}} \\ $$$$\boldsymbol{{it}}\:\boldsymbol{{in}}\:\boldsymbol{{easiest}}\:\boldsymbol{{way}}\:\boldsymbol{{like}}.. \\ $$$$\frac{\mathrm{1}}{\boldsymbol{{H}}_{\mathrm{0}} }=\boldsymbol{{age}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{universe}} \\ $$$${H}_{\mathrm{0}} =\frac{\mathrm{73}\boldsymbol{{km}}/\boldsymbol{{s}}}{\mathrm{1}\boldsymbol{{Mpc}}}\:\boldsymbol{{it}}\:\boldsymbol{{means}}\:\boldsymbol{{if}}\:\boldsymbol{{the}} \\ $$$$\boldsymbol{{distant}}\:\boldsymbol{{bet}}^{\boldsymbol{{n}}} \:\boldsymbol{{two}}\:\boldsymbol{{galaxyies}}\:\boldsymbol{{is}} \\ $$$$\mathrm{1}\boldsymbol{{Mpc}}\:\boldsymbol{{then}}\:\boldsymbol{{the}}\:\boldsymbol{{relative}}\:\boldsymbol{{velocity}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{moving}}\:\boldsymbol{{away}}\:\boldsymbol{{from}}\:\boldsymbol{{one}}\:\boldsymbol{{to}}\:\boldsymbol{{other}} \\ $$$$\boldsymbol{{is}}\:\mathrm{73}\boldsymbol{{km}}/\boldsymbol{{s}}. \\ $$$$\boldsymbol{{so}}\:\boldsymbol{{you}}\:\boldsymbol{{can}}\:\boldsymbol{{see}}\:\boldsymbol{{imedeately}}\:\boldsymbol{{that}} \\ $$$$\boldsymbol{{distant}}\:\boldsymbol{{and}}\:\boldsymbol{{velocity}}\:\boldsymbol{{is}}\:\boldsymbol{{proportional}} \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{the}}\:\boldsymbol{{proportionality}}\:\boldsymbol{{constant}} \\ $$$$\boldsymbol{{is}}\:\boldsymbol{{H}}_{\mathrm{0}} ..\boldsymbol{{this}}\:\boldsymbol{{is}}\:\boldsymbol{{called}}\:\boldsymbol{{H}}{ubble}'\boldsymbol{{s}}\:\boldsymbol{{law}}. \\ $$
Commented by smridha last updated on 10/Jun/20
thank you...
$${th}\boldsymbol{{ank}}\:\boldsymbol{{you}}… \\ $$
Commented by  M±th+et+s last updated on 10/Jun/20
god bless you sir
$${god}\:{bless}\:{you}\:{sir} \\ $$
Answered by Rio Michael last updated on 10/Jun/20
The truth is that we cannot actually determine  the actual age of the universe due to its expanding  nature. Astronomers tell us that the universe is  about 13.7 to 13.8 billion years. They do calculations  − Based on the oldest star(methusela star).  − by measuring the rate at which the universe is   expanding from the big bang start point.
$$\mathrm{The}\:\mathrm{truth}\:\mathrm{is}\:\mathrm{that}\:\mathrm{we}\:\mathrm{cannot}\:\mathrm{actually}\:\mathrm{determine} \\ $$$$\mathrm{the}\:\mathrm{actual}\:\mathrm{age}\:\mathrm{of}\:\mathrm{the}\:\mathrm{universe}\:\mathrm{due}\:\mathrm{to}\:\mathrm{its}\:\mathrm{expanding} \\ $$$$\mathrm{nature}.\:\mathrm{Astronomers}\:\mathrm{tell}\:\mathrm{us}\:\mathrm{that}\:\mathrm{the}\:\mathrm{universe}\:\mathrm{is} \\ $$$$\mathrm{about}\:\mathrm{13}.\mathrm{7}\:\mathrm{to}\:\mathrm{13}.\mathrm{8}\:\mathrm{billion}\:\mathrm{years}.\:\mathrm{They}\:\mathrm{do}\:\mathrm{calculations} \\ $$$$−\:\mathrm{Based}\:\mathrm{on}\:\mathrm{the}\:\mathrm{oldest}\:\mathrm{star}\left(\mathrm{methusela}\:\mathrm{star}\right). \\ $$$$−\:\mathrm{by}\:\mathrm{measuring}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{at}\:\mathrm{which}\:\mathrm{the}\:\mathrm{universe}\:\mathrm{is}\: \\ $$$$\mathrm{expanding}\:\mathrm{from}\:\mathrm{the}\:\mathrm{big}\:\mathrm{bang}\:\mathrm{start}\:\mathrm{point}.\: \\ $$

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