I was wondering if it is possible for a fighter jet to fly around the world and stay in daylight? For the Southern and Northern Hemisphere, the time and speed of daylight is different during seasons. So if not at the equator, would it be possible at the Hemisphere with different seasons?
Even near the equinox, when the day length is essentially the same over the entire world, this is possible.
At the equator, not so much; you'd have to average around Mach 1.5, including slowdowns for aerial refueling, to "make the sun stand still", though if you start at dawn and only need to get back by dusk, you gain another 12(ish) hours -- which, however, would still require an average speed of about 1000 km/h. Possible, but having aerial tankers in the right places at the right times, over potentially hostile territory complicates things, not to mention the greatly extended flight path needed to avoid overflying places that don't permit it pushing the required average speed back up to the 1300 km/h range.
But if you fly far enough north or south, you could do this in a Cessna, providing only that you could somehow carry twenty-four hours of fuel. Seems kind of like cheating, like those grade school riddles where you walk an hour south, an hour west, and an hour north and return to your starting point.
But in a fighter jet, with aerial refueling over the South Atlantic and South Pacific, you could circumnavigate at around the 45th parallel without having to overfly anywhere too hostile -- and given 36 hours to fly, only need to average around 600 km/h, which is well below "jet fighter" speed.
You can stay in perpetual daylight with a regular jetliner.
- During northern summer, you operate out of Iceland. You take off in the evening, circumnavigate the north pole and land back in Iceland in the morning. The trip is only 5000km, but you have to stretch it up to 12h depending on season.
- During northern winter, you operate out of New Zealand and circumnavigate the south pole every night, a trip of 8000km. You also have to stretch it up to 12h depending on season.
- On spring equinox, you fly from New Zealand to Iceland, a distance of 17700km along the westbound route (AKL-NRT-KEF). You have 12h from sunrise to sunset and you gain another 13h time shift by flying west. 17700km in 25h is easily doable, even with a fuel stop.
- On fall equinox, you fly from Iceland to New Zealand, a distance of 16800km along the westbound route (KEF-AKL). You have 12h from sunrise to sunset and you gain another 11h time shift by flying west. 16800km in 23h is easily doable, even with a fuel stop along the way.
A jet fighter is ill suited for this mission, it lacks range and endurance. Use a random jetliner with >12h endurance and >9000km range.
If you use the FAI definition for setting round the world speed records the rule states a trip minimum of 22,847 miles and all longitude lines must be crossed below 66deg latitude. If you start at sunrise on the longest day of the year at 66deg you get 24hr for a full day plus 20hr of daylight to sundown, or 44hr.
22,847mi/44hr is 519mph ground speed. If you can avoid head winds this is doable in private jets, as well as commercial and military jets. You may not even need to refuel in the air if you have extra tankage.
If you time this correctly, starting just past dawn near the equinox, then you have 24+12 = 36 hours.
This is less of a problem than other answers suggest. The around the world (crossing the equator) record is currently held by a Concorde flight with a time of ~33 hours, which is easily fast enough. I can't find exact times for every stop, but I think they may have stayed in daylight the whole way based on start/end times. Also they were supposedly only airborne for ~25 hours, maybe the Concorde is quite slow to refuel? But that is good if you only care about yourself and not the plane, as probably having a bunch of Concordes and switching planes instead of refueling would cut off several hours.
(Per Bianfable in comments, this is not so much the time spent at each individual refueling stop but the number of refueling stops--so you will need quite a few Concordes to really get to that minimum time. If my math is right you can theoretically get the minimum time with only four Concordes, but that also requires some of them to fly multiple legs, i.e. they would fly an early leg and then turn around and fly the other direction to meet you for a later leg....)
This is poorly documented, but what little documentation I'm finding suggests that the previous record for this was a hair over 36 hours in a Gulf Stream which is also very nearly fast enough, just in case you don't have a Concorde to hand. (It makes sense that a Gulf Stream or other business jet would be good for this, since they are basically for rich people who want to get places in a hurry without having to stop too much along the way.)