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