Latitude and Longitude LAX-SYD flight
 

My flight LAX to SYD leaves at 10.40 pm and is about 15 hours. My question is: how can I know in advance what latitude/longitude I will be at a certain time -- say 5 am Pacific time? The second question ties to the first one -- what time would the sun set on this flight.

The crazy thing is we leave on a Thursday at 10.40 pm or 8.40 PM HNL time. So, we won't be able to see the sunset (LAX's Friday sunset around HNL) for sure. Fiji, the sunsets at just past 6 pm, we will miss that as well and within four or so hours, we would be in SYD and would have missed the Friday's sunset in SYD as well. My wild guess is that the sunset should be around 6 am Los Angeles time on this flight.

No sunset - you depart after dark and most/all of the flight is at night. Depending on time of year you might have sunrise before landing (or might not).

This will give you the best advance approximation possible that I'm aware of, just enter the requested parameters. There will be a slider to see how things change over the course of the flight:

http://sunflight.net

For real-time position information during flight, though, the seatback monitor will have a flight map option that shows the current aircraft position along the Earth and with corresponding daylight & nighttime shadow across the globe illustrated.

Easiest way is to go find your flight number at FlightAware and look up a few days of your flight. Look at the map and look up the track log. Compare.

But let me simplify it for a rough "calculation". LAX is 34N118W and UTC-8. SYD is 34S151E and UTC+10 (+11 DST). Let's chop the 15 hours into 3 chunks of 5 hours. That's six 15-degree time zones to cross, and every 5 hours you cross two time zones.

You leave LAX at 11 pm Thu PST.
Five hours later you're roughly at 10N150W. It's 2 am Fri HST.
Five more hours later you're roughly at 10S180. 5 am Fri UTC-12 becomes 5 am Sat UTC+12.
Five more hours later you arrive SYD at 8 am AEST or 9 am AEDT Sat.

Sunrise should be somewhere after 10-hour mark. You don't have daytime Friday. You don't have Friday's sunrise or sunset.

I sent OP a very detailed rwy to rwy calculation based on some guesses for anticipated cruising altitudes and speed, typical wind conditions, etc, etc. Waiting to hear back if it jived with his in-flight map. Actually, guess I could check his flight on FlightAware myself