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I am a fan Star Wars and physics, but I must admit that I do not know what the jump in hyperspace means. In short, it's a way for spaceships in the Star Wars universe to travel great distances in a very short time. It should be clear that hyperspace travel is do not at the speed of light. The light has a speed of 3 x 108 meters per second. This means that even traveling to the nearest star (Earth) would take a few years. According to Einstein's theory of special relativity, other strange things would happen, but suffice it to say that a jump into hyperspace is not just about traveling at the speed of light.
A common idea about hyperspace is that it involves additional dimensions. Traveling through this extra dimension may allow a spaceship to make a shortcut in space, so a trip that would take years would take hours. It's just a thought.
But what about something we can really measure? Can we determine the acceleration of a ship when it makes the jump into hyperspace? Oh, yes, we can totally and we will. For this analysis, I'm going to use the picture of the Millennium Falcon jumping into hyperspace at the end of The empire counter-attack. To estimate the acceleration, we can look at the angular size of the Falcon 's back as it moves away.
What's the angular size to do with it anyway? Our eyes (and cameras) do not see the size of things. Instead, they see the angular size of the objects. If you draw an imaginary line of your eye on one side of an object and then on another line on the other side of the object, you create a small corner. The angle between these two lines is the angular size.
Rhett Allain
That's why, when things go away, they seem smaller. But if you know the angular size (θ) in radians and the actual size (The), you can find the distance (r). Oh, I know what you think. This relationship only works for the arc of a circle. Yes, it's technically true. However, if the object is far enough apart, the difference between the length of the arc and the width is tiny, and we can ignore the distinction.
Now for some data. All I need to do is measure the position of the Falcon's sides and use it to calculate the angular size of each frame of the video during the hyperspace jump. Of course, there is a big problem. I do not really know the angular size at the beginning of the jump. I'm just going to have to estimate it. Let's say that the Millennium Falcon is 25 meters wide and starts 100 meters from the camera. With this, I can define the angular field of view of the scene. This gives the following plot of angular size versus time for this Falcon when it escapes.
With this angular size and the width of the Millennium Falcon, I can calculate the distance between the camera and the spacecraft.
There are a lot of things to consider in this chart. Just look at the final position, about 8000 meters. Thus, in about half a second, the Millennium Falcon goes from a position of only 100 meters to about 5 miles. Even if you consider the average speed (change of position with respect to change over time). That's about 29 thousand miles per hour (for imperial readers). No matter the units, it's a super fast speed.
Ok, but what about the acceleration? I can adapt a quadratic function to the data (as shown in the graph). This is useful since a moving object with constant acceleration will also have a quadratic for the motion equation. As the motion of an object with constant acceleration is quite common in physics courses, we attribute to this equation a special name: the kinematic equation. It gives the position of an object at different times depending on the acceleration (and initial position and speed). Here is the equation of fit with the kinematic equation for constant acceleration.
Rhett Allain
Here you can see the number of the fitting in front of the2 term should be equal to half of the acceleration. This puts the Falcon's acceleration at 33,922 meters per second squared. Ummmm … it's a super high acceleration. If you drop an object on the surface of the Earth, it will have an acceleration of 9.8 m / s.2. If you eject yourself from a fighter plane, you will have a painful acceleration of about 60 m / s.2. This spaceship jumping into hyperspace accelerates a little more than that.
What about the G force? OK, let's be clear on two points here. First, the Millennium Falcon surely has a type of inertial damper that allows people inside the ship to accelerate without dying. Second, Star wars it's not real life, so it does not matter (but it's still fun to analyze). Now for the g-force. This is a false strength. This is a way to make sure that an accelerated repository behaves like a non-accelerator repository. In this case, the false strength is essentially a measure of the acceleration of the interior of the Millennium Falcon.
The measurement of this false force is expressed in terms of the gravitational force on Earth – it is the acceleration of "g". If the ship accelerated to 9.8 m / s2it would be a false force of 1 "g." Inside the vessel, this would give the impression of an additional gravitational weight pushing you in the opposite direction to which the spacecraft is accelerating. Thus, the acceleration in the jump in hyperspace would be of a force g of 3461 g. It's an acceleration big enough to easily kill a human if you do not have something like an inertial damper.
But wait! We also have an idea of the G forces inside the Millennium Falcon during this jump. First, you can see Leia in the cockpit being thrown into her seat. Second, R2-D2 goes back and falls into an access panel. Surprisingly, there is enough data to measure the acceleration of R2 inside the ship. Here is a graph of its position as a function of time with a quadratic adjustment.
Rhett Allain
From there, it seems that there is a false internal force of 2.73 m / s2 or 0.28 g. Yes, it's much less than the acceleration seen from the outside of the ship. Obviously, the inertial dampers still work mainly.
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