What was the range that the Death Star needed in order for its super weapon to be effective, but without being so close that they risk the station being damaged by debris? How well were the people on Alderann able to see it? Could they see it as well as we can see our moon when its full, or would it be much larger?
shareI copied this pretty good answer from Quora:
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This is an interesting question, as tends to happen when you destroy a planet. But unfortunately we can’t ever answer this question because no one’s dedicated enough to have gathered the necessary infor– what am I saying? Of course they have!
Wookipedia estimates the optimal operation range of the Death Star at 2 million km, which is almost twice the distance from the Earth to Mars. The Death Star might get hit by a bit of debris, but nothing major.
Hold on. 2 million km?
That is not how far away the planet was in the movie. That looks like the size of the Earth from the moon, about. How big is Alderaan? 12500 km is its diameter.
That’s… pretty much the diameter of the Earth. How far is the moon from Earth? Only 400,000 km.
What about the Death Star? 120 km in diameter.
Okay, so you see the moon? Up in the sky? (If you don’t, just wait, it should there in a week or two) Shrink it down by a factor of ten. If you blew up the Earth, what are the odds that something would hit it?
To be honest, I really don’t know, but it doesn’t seem that high. And if the steel is strong enough to withstand the gravitational effects of the mass of the ship and survive a damn Star Destroyer crashing into it, I think it’s going to be fine. You could try moving closer, but there really is some degree of randomness to the explosion, as far as I can tell. The Death Star was certainly at a safe distance, and probably could have been moved a lot closer. I’m not sure exactly how close, but at a certain point the gravity of Alderaan would also start to have wonky effects on the station.
https://qr.ae/TUtZA8
Wookipedia estimates the optimal operation range of the Death Star at 2 million km, which is almost twice the distance from the Earth to Mars.
Short Comment:
My conclusion is that the Death Star would fire on the moon at a distance of only a few thousand kilometes more than the distance of 72,000 to 25,080,500 kilometers between the centers of the planet and the moon.
Long Comment:
The Moon of Yavin was a giant, approximately Earth sized moon orbiting a gas giant planet in the Yavin system. (I am a little uncertain whether Yavin was the name of the star, and the planet was Yavn IV, and the moon was Yavin IV something, or if Yavin was the name of the planet and Yavin IV was the name of the moon. https://moviechat.org/tt0076759/Star-Wars-Episode-IV-A-New-Hope/58c7334d5ec57f0478f88754/Yavin-IV-Star-Planet-or-Moon).
What is the size range of giant planets?
I am not certain of the minimum diameter of giant planets.
The Earth, a terrestrial planet, has a radius of 6,371 kilomaters, and a diameter of 12,742 kilometers.
The giant planet with the smallest size in our solar system is Neptune, with a radius of about 24,764 kilometers and a diameter of 49,528 kilometers. And in other star systems the largest terrestrial type planet or the smallest giant planet might have a radius of about 12,000 kilometers and diameter of about 24,000 kilometers, or somewhere about there.
The largest giant planet in our solar system is Jupiter, with a radius of 69,911 kilometers and a diameter of 139,822 Kilometers.
The mass of Jupiter is about 317.8 time the mass of Earth. It is possible for giant planets to have several times the mass of Jupiter, The dividing line between the most massive giant planets and the least massive brown dwarfs (the objects intermediate between planets and stars) is about 13 times the mass of Jupiter or about 4,131.4 time the mass of Earth.
But giant planets don't get much larger than Jupiter, no matter how massive they get. Their increased mass and gravity compresses their matter more and more, so giant planets don't get to have more than 15 percent larger radius and diameter than Jupiter, very roughly about a radius of about 80,500 kilometers and a diameter of about 161,000 kilometers.
So the radius of a giant planet should be in the range of about 12,000 to 80,500 kilometers.
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Scienctific discussions of the possibility of life on large exomoons orbiting giant exomplanets in other star systems have introduced the concept of a "habitable edge" around a gas giant planet. Moons orbiting closer to the planet than the habitable edge would get so much light reflected from their planets and get so much tidal heating - in addition to the light they receive from their stars - that they would become too hot and suffer from runaway greenhouse effects and become uninhabitable
The potentially habitable exomoons orbiting exoplanets would receive a lot of cosmic rays and stellar wind radiation, which would tend to slowly strip away their atmospheres, unless they were protected by magnetic fields which would divert the charged particles. Many or most of the potentially habitable exomoons wouldn't have their own magnetic fields. Thus those habitable moons wold need to be within the magnetic fields of their planets to be protected from cosmic rays and stellar wind.
MAGNETIC SHIELDING OF EXOMOONS BEYOND THE CIRCUMPLANETARY HABITABLE EDGE
Rene Heller ´ 1 and Jorge I. Zuluaga2 (2013)
https://iopscience.iop.org/article/10.1088/2041-8205/776/2/L33/pdf
Calculates that a moon of a Jupiter like planet would be beyond the circumplanetary habitable edge but within the shielding of the planetary magnetic field ar a distance of between 5 and 20 planetary radii. A giant planet should have a radius roughly in the range of about 12,000 to 80,500 kilometers. So a habitable moon could orbit the smallest size giant planet between the distances of about 60,000 and 240,000 kilometers. And a habitable moon could orbit the largest size giant planet at a distance between 402,500 and 1,610,000 kilometers.
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But they say that Mars sized exomoons orbiting Neptune sized planets would be either too close, inside the habitable edge, and suffer runaway greenhouse effects, or else be outside the planetary magnetic field.
Mars-sized exomoons of Neptune-sized exoplanets in the stellar HZ of K stars will hardly be affected by planetary magnetospheres if these moons are habitable from an illumination and tidal heating point of view
But exomoons orbiting Jupiter sized planets can have safe orbits.
Saturn-like planets have stronger fields, and Jupiter-like planets could coat close-in habitable moons soon after formation. Moons at distances between about 5 and 20 planetary radii from a giant planet can be habitable from an illumination and tidal heating point of view, but still the planetary magnetosphere would critically influence their
habitability.
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So if the moon had its own magnetic field, it could orbit a very small giant planet at a distance of 60,000 kilometers, outside the magnetic field of the planet, and still be protected.
So a large, Earth sized, habitable moon with its own magnetic field could orbit a very gigantic giant planet far outside of the protective magnetic field of the planet. It could orbit as far out as the planet's gravity could keep it in orbit, as far as the planet's Hill sphere extended.
At Earth's distance from the Sun, its Hill radius is approximately 1,500,000 kilometers. Jupiter's Hill radius is approximately 50,000,000 kilometers. But Jupiter is about 5.2044 times as far from the Sun as Earth is, and would have a much smaller Hill radius if it was as close to the Sun as Earth is, and had a moon as warm as the Earth. If JUpiter ws as close to the Sun as Earth is the Hill radius of Jupiter would be much smaller, and even a giant planet with 13 times the mass of Jupiter wouldn't have a Hill a radius of 50,000,000 kilometers that close to the Sun.
The Hill sphere is only an approximation, and other forces (such as radiation pressure or the Yarkovsky effect) can eventually perturb an object out of the sphere. This third object should also be of small enough mass that it introduces no additional complications through its own gravity. Detailed numerical calculations show that orbits at or just within the Hill sphere are not stable in the long term; it appears that stable satellite orbits exist only inside 1/2 to 1/3 of the Hill radius.
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So if the true region of longer term stability is about 1/3 to 1/2 the Hill radius no moon of a giant planet orbiting its star at about the Earth's distance from the Sun should have an orbit more than about 16,666,666 to 25,000,000 kilometers from the planet.
So my rough calculations indicate the distance between the center of the moon and the center of the giant planet should be between about 60,000 and 25,000,000 kilometers.
And when the Death Star was approaching, the moon was on the other side of the planet. So the distance betweent he moon and the Death Star was 60,000 to 25,000,000 kilometers, plus one radius of the giant planet, or about 12,000 to 80,500 kilometers, for a total of about 72,000 to 25,080,500 kilometers, plus the unknown distance between the planet and the approaching Death Star.
I believe the Death Star was said to be orbiting the planet as it maneuvered to get a clear shot at the moon, and that implies that the Death Star was close to the planet. Thus I believe that when the Death Star got a clear line of sight to the moon, it would have been onlly a ltttle farther from the moon than the distance between the centers of the planet and the moon.
My conclusion is that the Death Star would fire on the moon at a distance of only a few thousand kilometes more than the distance of 72,000 to 25,080,500 kilometers between the centers of the planet and the moon.
Um, the only planet that was destroyed was Alderan. It's even said by Tarkin in the movie.
shareI thought of another way to calculate the distance.
If the planet Yavinandits moon Yavin Four are seen in the same scene, the realtive apparent diameters are a clue to actual relativve sizes. Of course one of them might bemuch closer than the other, but it is a clue.
And in scenes on the Death Star Bridge, a computer displays an image of the planet Yavin with Yavin Four seen through the planet Yavin. Since this seems to a targeting display, it would show the angulardiameters of both worlds, and not their actual diameters. Since Yavin Four is beyond Yavin and farther frm the death Star, it should appear to have smaller diameter relative to Yavin than it actually does.
Thus Yavin Four must be somewhat larger relative to Yavin than is shown in the targeting screen. How much larger will depend on how farther than Yavin it is from the Death Star. If it is twice as far from the Death Star as Yavin is, its relative size will be twice as great as seen on the screen.
And in real life there are limits on the relative sizes of a giant planet like Yavin and of a human habitable world like themoon Yavin Four.
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The mass and size range for human habitable worlds was discussed in Habitable Planets for Man, Stephen H. Dole, 1964. https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf.
Dole believed that humans wouldn't want to colonize a planet with a surface gravity higher than 1.5 Earth gravity. I note that the people on Yavin Four seem to walk like the surface gravity is not signficantly higher than on Earth. On page 53 Dole wrote that a planet with a surface gravity of 1.5 Earth gravity would have a mass of 2.35 Earth mass, a radius of 1.25 Earth radius, and an escape velocity of 15.3 kilometers per second. If theplanet was made of less dense substances than Earth, it could be little larger while still having only 1.5 times Earth's surface gravity. But there are limits to how much the density can be reduced before the planet is covered with many miles of liquid and has no exposed solid ground.
On page 54 Dole decided that a habitable planet might sometimes have an escape velocity as low as 6.25 kilometers per second and retain a breatheable atmosphere for a long time. That correspondes to 0.195 Earth mass, 0.63 Earth radius, and 0.49 the surface gravity of Earth.
So according to Dole, Human habitable worlds should have mass between 0.195 and 2.35 Earth mass and radii between 0.63 and 1.25 Earth raddi, or 4,013.73 to 7,963.75 kilometers, and thus diameters of 8,027.46 to 15,927.5 kilometers.
In this article from 2013, the habitability of exomoons, moons orbiting exoplanets in other star systems, is discussed.
https://arxiv.org/ftp/arxiv/papers/1209/1209.5323.pdf
This is a discussion of habitabiity for liquid water using life in general - not for humans in particular. aEven on Earth there are environments filled with life where unprotected humans rapidly die. Human habitable worlds would be a subset of the habitable worlds discussed in that article. In a paragraph on pages 3 and 4 the mass limits of habitable worlds are givenas orughly 0.25 to 2.0 Earth mass, which is rather similar to the mass limits of Human habitable worlds estiamted by Dole.
So Dole's diameter range of 8,027.46 to 15,927.5 kilometers seems fairly solid. Perhaps it might be extended by as much as 20 percent to a range of 6,421.968 to 19,113 kilometers.
So now the diameter range of giant planets has to be considered.
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Astronomers generally call rocky planets significantly more massive than Earth "super-Earths".
In general, super-Earths are defined by their masses, and the term does not imply temperatures, compositions, orbital properties, habitability, or environments. While sources generally agree on an upper bound of 10 Earth masses[1][3][4] (~69% of the mass of Uranus, which is the Solar System's giant planet with the least mass), the lower bound varies from 1[1] or 1.9[4] to 5,[3] with various other definitions appearing in the popular media.[5][6][7] The term "super-Earth" is also used by astronomers to refer to planets bigger than Earth-like planets (from 0.8 to 1.2 Earth-radius), but smaller than mini-Neptunes (from 2 to 4 Earth-radii).[8][9] This definition was made by the Kepler space telescope personnel.[10] Some authors further suggest that the term Super-Earth might be limited to rocky planets without a significant atmosphere, or planets that have not just atmospheres but also solid surfaces or oceans with a sharp boundary between liquid and atmosphere, which the four giant planets in the Solar System do not have.[11] Planets above 10 Earth masses are termed massive solid planets,[12] mega-Earths,[13][14] or gas giant planets,[15] depending on whether they are mostly rock and ice or mostly gas.
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A Mini-Neptune (sometimes known as a gas dwarf or transitional planet) is a planet less massive than Neptune but resembling Neptune in that it has a thick hydrogen–helium atmosphere, probably with deep layers of ice, rock or liquid oceans (made of water, ammonia, a mixture of both, or heavier volatiles).[1]
A gas dwarf is a gas planet with a rocky core that has accumulated a thick envelope of hydrogen, helium, and other volatiles, having, as a result, a total radius between 1.7 and 3.9 Earth radii (1.7–3.9 REarth). The term is used in a three-tier, metallicity-based classification regime for short-period exoplanets, which also includes the rocky, terrestrial-like planets with less than 1.7 REarth and planets greater than 3.9 REarth, namely ice giants and gas giants.[2]
And at rebel headquarters on yavin Four there was dispaly showing Yavin, Yavin Four, and the Death Star. I rather doubt that it showed the Death Star to scale, and possibly it didn't show Yavin and Yavin Four at the same scale either. But it might have show the relative distances of the Death Star, Yavin, and Yavin Four accurately.
So it seems ot me that a Star Wars fan who does photo analysis and has images from Star Wars should be able to do some kind of analysis of the ranges in the sizes and positions of the viewpoint, of VYavin, and of Yavin Four and be able to give some sort of estimate of the range at which the Death Star would have fired at Yavin Fourif it had lasted for a few more seconds.