Science indicates that Tatooine is much more likely to orbit both stars than one of them according to the way it is depicted in the movies. Astronomers often call circumbinary planets that orbit around two stars "Tatooines" - it probably seems obvious to many that the special effects of the two suns showing them both the same size prove that Tatooine almost certainly orbits around both of its suns.
In fact, If George Lucas himself told me Tatooine orbits only one of its suns and the other one is much farther away, I would say "Phooey, you're wrong, Tatooine must orbit both its suns as a circumbinary planet".
Multiple and binary star systems tend to have a "Hierarchical" structure. Each additional star or pair of stars in the system usually is separated by much greater distances than the inner stars.
There might be 2 stars separated by 1 distance unit and then another star or close pair of stars separated by 20 distance units and maybe an even father star or close pair of stars at 300 distance units, for example.
If a planet orbiting a star or close pair of stars in a system has a stable orbit any other star or pair of stars would have to orbit at least ten times the distance that the planet orbits.
1) If Tatooine orbits both stars.
In the movies the two suns of Tatooine seem to have the same apparent size and very similar colors. Similar colors indicate similar temperatures. Basically they appear to be twins with the same sizes, masses, temperatures, and brightness.
If they are at the same distance from Tatooine and Tatooine orbits around both of them as a circumbinary planet, that is.
The twin suns of Tatooine might be about the same size as the Sun - about 800,000 miles in diameter - and orbit each other at about 5,000,000 to 10,000,000 miles distance, about 6.25 to 12.5 times their diameters. And Tatooine might orbit them at about 1.19 times earth's distance from the sun, and thus about 110,670,000 million miles.
I have suggested that the twin suns of Tatooine might be separated by about 6.25 to 12.5 times their diameters, but in the movies they are usually shown separated by about two to four times their diameters. Two stars with masses similar to Earth's sun orbiting at about five to ten million miles would orbit each other in a period of a few days, I think. Thus as seen from Tatooine the stars would be appear to be separated by about two to four times their diameters every few days.
So it would not be very improbable for them to be seen at such an apparent angular separation in several different scenes years apart.
If the twin suns of Tatooine are also twins of Earth's sun, it would be quite probable that the Tatooine system had lasted for the billions of years needed for large multi celled organisms to evolve on Tatooine.
2) If Tatooine orbits only one of the stars.
And what if Tatooine orbits around one of the suns and the other sun is many times farther away? We might suppose that the closer star orbited by Tatooine is similar to Earth's sun. Thus Tatooine might orbit it about 93,000,000 miles away.
If the other sun has to be at least ten times as far as Tatooine for Tatooine to have a stable orbit, then it should be at least 930,000,000 miles from the star Tatooine orbits and possibly many times that distance.
If Tatooine orbits at a distance of 93,000,000 miles and the farther sun orbits at a distance of 930,000,000 miles from the sun Tatooine orbits, during the Tatooine year the distance between Tatooine and the outer sun will vary between 837,000,000 miles and 1,023,000,000 miles - if Tatooine orbits in the same plane as the two stars orbit each other, which is to be desired. Thus the outer sun will be 1.222 times the distance from Tatooine when it is farthest than when it is nearest, and the apparent diameter of the outer sun will vary noticeably. Actually the two orbits will be somewhat elliptical and the difference will be more than that.
The effect of the outer sun varying in apparent diameter during a Tatooine year can be reduced until it is no longer noticeable by moving the outer sun farther and farther away from Tatooine.
If the outer sun is at least ten times farther from the inner sun than Tatooine is, it will have to have at least ten times the physical diameter of the inner sun to have the same apparent diameter.
But all main sequence stars with similar colors and spectral types have similar diameters. If the inner sun of Tatooine is a nice main sequence dwarf star of luminosity class V that can shine with reasonably steady brightness for the billions of years needed for multi celled life to evolve on Tatooine, the outer sun with a similar temperature but ten times the diameter must not be a main sequence star.
It must have been at least a little more massive originally than the inner sun and evolved more rapidly and left the main sequence, swelling up into a sub giant star of luminosity class IV, or a giant star of Luminosity class III, or a bright giant of luminosity class II, or a supergiant of luminosity classes Ia or Ib.
But stars only remain in one of the giant phases for relatively short times, hundreds of thousands to hundreds of millions of years, and then eventually become tiny white dwarfs that would appear as star like points of light in the sky of nearby planets instead of discs.
So if the outer sun has swollen up to many times the diameter of the inner sun, and if the two stars are the same age as is usual in a double star system, it must be more massive than the inner sun. And if the outer sun is more than just a few times more massive than the inner sun, it will be going through the giant phase when the planets of the inner sun are not yet old enough to have complex native life.
The inner sun must have a mass within a relatively small range in order for Tatooine to be habitable and have complex native life, and the outer sun must have a mass within a certain range for it to be going through the giant phase before the inner sun does but after the inner sun is already old enough for Tatooine to have an oxygen atmosphere and complex native life.
The mass range between the inner sun and the outer sun will determine how many times the diameter of the outer sun in the giant phase can be relative to the diameter of the inner sun while on the main sequence.
The minimum distance between the two suns must be at least ten times the distance between the inner sun and Tatooine, and thus the outer sun in the giant phase must be at least ten times the diameter of the inner sun. But since both suns are almost certainly the same age there is an upper limit - that could be calculated - to how massive and wide the outer sun can be if the whole system is old enough for Tatooine to have an oxygen atmosphere and advanced native life forms.
Planets of single stars orbit in the equatorial planes of their stars' rotation. but in double star systems the different stars rotational planes are not necessarily in the same plane as they revolve around each other.
Thus Tatooine could orbit around the inner sun at an angle anywhere between zero degrees and ninety degrees relative to the orbits of the two stars around each other.
If the angle of Tatooine's orbit is zero degrees the two suns will be on opposite sides of Tatooine during part of the year and on the same side during another part of the year. The inner sun will eclipse the other sun once a year. And there will be a period of perhaps weeks during each year when the two suns will appear as close together in the sky as seen in several scenes set on Tatooine. And during the rest of the year the two suns will seem farther apart.
If Tatooine passes between the two suns during part of the year, and if the two suns give approximately equal amounts of light and heat to Tatooine, as their appearance indicates, Tatooine should be hot enough to kill all life during part of each year.
Places on Earth heat up during the day and cool off at night. When the days are longer than the nights at a place on Earth it heats up faster than it cools down. When the nights are longer than the days at a place on Earth it cools down faster than it heats up.
If the days are very hot on Tatooine when the two suns are seen together in the sky and it cools off during the night, how hot would it get when Tatooine is between the two suns and never cools down for weeks or months? Probably hot enough to kill all life on the planet.
A planet that orbits one star in a double star system will not overheat and kill off all life when it is between the two stars, if the outer star is far enough away that it appears much smaller than the other one, or even as a mere point of light, and gives the planet much less less light and heat than the other one. Then the planet can be habitable.
But if the outer star is close and large enough that it appears to be a twin of the star that the planet orbits, and gives that planet approximately as much heat and light as the nearer star, then it will roast and sterilize the planet once a year when the planet passes between the two stars and can't cool down at night.
And if the angle between Tatooine's orbit and the orbit of the two stars around each other is 90 degrees, the two suns will always appear almost ninety degrees apart from each other and will never seem as close together as seen in the movies.
Unless the angle between Tatooine's orbit and the orbit of the two stars is less than a few degrees from zero, the two stars will never seem as close together in the sky of Tatooine as I remember them always being depicted.
Therefore I believe that it is many times more probable that Tatooine orbits both stars in its system than orbiting only one of those stars. And an astrophysicist could calculate the probability.
And when astronomers find extra solar planets that orbit two stars - circumbinary stars - they often call them "Tatooines" - perhaps because many astronomers would naturally from the look of the special effects that show both suns the same apparent size believe that Tatooine orbits both of its suns and couldn't orbit only one of them.