What is the true time when the sun is directly over Perth given that the W.A. time is taken from Southern Cross

Question

What is the true time in Perth western Australia when the sun directly overhead, given that the state time is calculated at Southern Cross.

Answer 1

I find the statement that time in Western Australia is based the location of Southern Cross somewhat speculative. Some supportive evidence would improve the question.

Given the history of British colonization of Western Australia, Southern Cross was established many years after the initial two settlements of Albany and Perth.

Albany was initially established as a military outpost in 1826.

Perth was establish in 1829, initially called the Swan River Colony. It was established as the seat of colonial administration & eventually government for the then colony and still remains so.

Southern Cross was established in 1890, some 61 years after the establishment of Perth. Government authorities in Perth would not have waited 61 years to establish a system of keeping time in Perth and the rest of the colony.

The lines of longitude (eastings) and the time difference from the Greenwich meridian for the three locations are:

\begin{array}{|c|c|c|} \hline \text{Location} & \text{Easting} & \text{Time from Greenwich}\\ \hline {Perth} & 115^o\ 51'\ 38" & 7h\ 43'\ 27" \\ \hline {Albany} & 117^o\ 52'\ 53" & 7h\ 51'\ 32" \\ \hline {Southern\ Cross} & 119^o\ 19'\ 40" & 7h\ 57'\ 19" \\ \hline \end{array}

The times are based in the Earth rotating effectively 360° in 24 hours, or at a rate of 15° per hour.

For the colonial authorities in 1829, 7 hours 43 minutes and 27 seconds would have been close enough 8 hours from the Greenwich meridian to set the time for the colony to be 8 hours ahead of Greenwich. The fact that Southern Cross is only 2 minutes 41 seconds short of 8 hours time difference from Greenwich is a coincidence.

When the Sun is directly overhead in Perth the so called "true time" is 12h 16' 33".