People have already correctly noted the extreme emptiness of space and the careful mission planning, but there's another fundamental reason why a probe like Voyager isn't going to start orbiting something (that it isn't already orbiting, like the center of the galaxy).

Newtonian orbits are what's called "conservative". That means they don't gain or lose any energy during the orbit, they just exchange kinetic energy (the energy something moving has) for gravitational potential energy (the extra energy something gets from going uphill against gravity) and back again.

One of the effects this conservation of energy has is that if a probe falls into the gravity well of a celestial body of some sort, the probe will just exchange potential energy for kinetic as it falls into the gravity well, and then exchange kinetic back to potential as it flies away out of it. If it fell towards the celestial body from a very large distance (where the gravity of the celestial body was effectively zero) and had some initial speed, then it wasn't initially gravitationally bound to that celestial object and it won't be gravitationally bound to it in the end, either. It has enough total energy (kinetic plus potential) that it will simply fly away from the celestial body just like it flew towards it and won't go into orbit!

Now, if the probe fires its thrusters, or if it interacts with the planets atmosphere, or if it interacts with a third body, then it is still possible for it to go into orbit of the planet. But the first takes active intervention by the mission controllers, the second requires incredibly precise flying to interact just right with the atmosphere so as not to burn up (and it would come around and interact repeatedly until its orbit did decay), and the third requires an even more improbable and specific three-body interaction where the two-body interaction is already fantastically unlikely.

Unfortunately, quantum entanglement transmits no information and cannot be used directly for telecommunication.

It can, however, be used to help with encryption, which in turn aids (conventional, light speed or slower) communication.

EDIT: I see below someone already mentioned this and you responded to it. Unfortunately, the NCT is still entirely preserved with the work that the 2022 Nobel Prize in Physics was awarded for, though I have seen this mis-representation in popsci articles before. Violations of Bell's inequality are related to, but not equivalent to, violations of the NCT and demonstrating a violation of Bell's inequality is not the same as demonstrating a violation of the NCT. Indeed, the NCT is entirely compatible with those results and remains entirely unchanged by them.

It's fairly simple. In the absence of much pressure outside the rocket (which is the case when the rocket is at a suitably high altitude), the hot gasses escaping from the rocket simply keep expanding. For a deeper look as to why this occurs, you will want to look into the kinetic theory of gases.

They glow either because they are still quite hot (very near the rocket) or because they are high enough up that they are illuminated by the sun even when the sun is below the horizon from the ground.

First, be careful with your Lorentz factor (γ). You are missing a sign on an exponent there, which is pretty critical in this case. We usually write

γ = ( 1 - ( v / c )^2 )^**-**1/2

and so γ diverges in the limit where v->c, and then you can see that the Lorentz transformations are not defined at v=c. But we shouldn't get too hung up on this, as this doesn't really address your real question:

>I would suggest that that's a limitation of the formulation, not necessarily a reflection of reality.

And to do that, we should step back from the math for a second and think carefully about applicability. Even if we have a quantitative description of a phenomena that gives a real, non-divergent answer we must be very careful that it is actually applicable to a given situation so as not to over-extend a model. Not all answers given by an equation are correct: sometimes we're just doing math and not physics.

In this case, we build a Lorentz transform by comparing two valid inertial reference frames. One of the postulates we use to construct one such frame is that the speed of light is invariant for all observers in any frame, which leads to the Lorentz transformations. However, if we try to construct such a frame at v=c we encounter a paradox: light moving parallel to this frame must be moving at c and also must be stationary in the frame. This cannot be, so we cannot construct the frame and without the frame the Lorentz transformations are meaningless (and also undefined as the Lorentz factor is undefined at v=c).

As such, in this case, it is quite the opposite: that the Lorentz factor is undefined at c is not an artifact of the mathematics, but a reflection of something fundamental to relativity.

It's a subtle difference and one we should be careful to distinguish: the lack of a valid reference frame for the photon means that it does not make sense to talk about the passage of time from the photon's perspective. Without such a reference frame, something moving at c (such as the postulated massless neutrino) cannot change, which would also be true if the elapsed time was 0, though that is not the case here.

But lacking a valid reference frame is not the same as saying the elapsed time (or distance) for a massless particle between its creation and some later time (from our perspective) is zero. Talking about elapsed time at all for a massless particle from its perspective doesn't make sense. If you are familiar with coding, it's vaguely analogous to the difference between a value being 0 (a real number that can be found on the number line) and NULL (a value that is not a number at all).

Saying "time does not pass" is kind of ambiguous and I wouldn't describe it as wrong per se, though without clarification it might lead someone to think that it means that "the amount of time is 0" rather than "it does not make sense to ask how much time has passed, as the photon lacks a valid reference frame in which time could pass in".

It doesn't really make sense to ask "how much time has passed from the perspective of a photon", because we can't build something called a "reference frame" for the photon.

Whenever we talk about special relativistic time dilation we must do so by comparing the rate that time is passing in two different reference frames. If I am moving along with you, we are in the same reference frame, but if we are moving relative to each other, then we are different ones. You can think of a reference frame as being a way of describing the universe from your perspective, and when we talk about time dilation or length contraction we have to have two reference frames to compare together. Time always passes normally and distances are always the same in your own reference frame: you won't see your own clocks ticking slow or fast or your own rulers changing length, but you will see that your clocks disagree with those of someone who is moving relative to you and that you and that same person will disagree on how long your rulers are.

Time dilation and length contraction can be thought of as consequences of one basic fact about the universe: all observers, no matter how they are moving, will agree on how fast light is moving. If you're moving away from me at 100 mph and you shine a laser at me, you will measure the light leaving the laser as moving at c. I will measure the light from your laser as moving at c as well, not c-100 mph. In order to agree on how fast light is moving while we are moving relative to each other, we must disagree on how fast our clocks are ticking and how long our rulers are.

But if we were, hypothetically, to be moving relative to each other at c, we would encounter a paradox: light moving parallel to that reference frame would have to be both moving at c (as it must be in all valid reference frames) and be stationary at the same time. This is a contradiction, so we cannot construct a reference frame for the photon, and without a reference frame it doesn't really make sense to talk about time dilation or length contraction.

What we can say, however, is that as something moves arbitrarily close to c that the time it would see pass while traveling between two points would get arbitrarily close to zero and the distance between those points would as well. People often make the slight error of thinking that because the limit goes to zero here that the answer is that it is zero when v = c, but it's more precise to say that the limit approaches zero as v approaches c, but does not exist at v = c. Sort of like how 1/x gets arbitrarily large as x approaches 0 from the positive side, but 1/x does not actually exist when x = 0.

The speed of light is directly related to the permittivity (ε_0) and permeability (μ_0) of free space, via

c = ( ε_0 μ_0 )^1/2

as a consequence of building the wave equation from Maxwell's equations. Though whether this answer is in any way satisfying depends on whether one considers the speed of light or these other EM properties of free space to be more fundamental (and, in general, we usually define ε_0 and μ_0 with c as well, simply by re-arranging the equation above). But changing c would require changing one or both of these other fundamental constants as well.

My personal favorite answer, though, is when you ask someone who does GR or cosmology research about why the speed of light is what it is and they look at you like you have three heads and say "I don't know what you mean, the speed of light is exactly dimensionless 1".

Those calculations assume a lossless atmosphere and that the only attenuation is geometric. Adding in attenuation leads to full thermalization surprisingly close to the photosphere.

Of course, if there were a medium to transport that sound, then it would effectively mean that the sun were just a much larger star, and that medium itself would be turbulent and noisy.

Judging from this graph the temperature would be around 300K where the pressure is ~5 Atm. Pressures of ~5 Atm are found underwater on earth at depths of ~150 feet or so, which is routinely achieved by divers, including saturation divers who live at depths like that (or greater) for weeks at a time.

So definitely survivable, and even comfortable. Neglecting the chemical environment and the wind, of course. But you can be protected from a harsh chemical environment with some pretty simple coverings and depending on the variability of the wind you might be able to ride along with it in a way that's not too uncomfortable.

In order to do that you would have to break the symmetry somehow. One or both of you would need to change frames either by proper acceleration or by moving near a large mass.

In the case that only one person spends time in two reference frames, the latter will have had less time pass by their clock than the stationary person.

If you accelerate in a symmetric fashion — you both turn around at the same time and in the same way and head back together), you will find that you both actually agree on how much time has passed.

More fundamentally, there is no absolute speed whatsoever. Both of you are equally justified in saying you are stationary and the other one is moving at 0.995c and the universe will agree with both of you.

Nope, kinematic time dilation is symmetric. Your watch is running slow compared to theirs from their perspective and theirs is running slow from yours.

Similarly, there is no way to say which one of you is stationary and which is moving at 0.995c, because you are both justified in saying you are the stationary one and the other person is moving. Motion is relative and there is no absolute motion or sense of absolute stillness.

One complication: due to kinematic redshifting/blueshifting you may observe the other person’s clock as running slower (if they are moving away from you) or faster (if they are moving towards you) than the time dilation calculation would predict, but that’s just an apparent effect. When they are moving right by you you will observe only the time dilation itself, and you will still find the time dilation present at all times when you account for the apparent kinematic effects.

Maybe a bit, though there are some very notable differences between the refresh rate of a monitor and what time dilation is like that you should be very cautious with.

First, refresh rate on a monitor reduces the number of discrete images the monitor displays per unit time. Time itself is continuous and not broken into fixed steps like that, as near as we can tell and we don't have any reason to think otherwise (note: you may have heard that Planck time is something like a discretization of time, but this is not the case. Planck time is a unit like seconds or decades and while some interesting physical phenomena are predicted to occur or have occurred over timescales similar to 1 Planck time it is not a discretization of time). With time dilation there's no stuttering or anything like that.

Second, the stuff displayed on the monitor is often flowing at the same rate, just with fewer frames. If I play a video game and it takes me 1 second for my character to run across the screen, that will occur in 120 frames at 120 Hz and 60 frames at 60 Hz, so that both take 1 second, but one is "smoother" as it has finer steps between each frame. Time dilation actually slows everything down relative to another reference frame. If it took my character 1 second to run across my screen from my perspective, it will take my character 10 seconds to run across my screen from the perspective of someone flying by me at 0.995c (even after kinematic redshifting is accounted for). Time dilation actually changes the speed at which time flows in one frame relative to another. It's not changing how long stuff takes in my reference frame, but how fast time itself is passing in my reference frame relative to a different reference frame.

Lastly, time always passes at the same rate in your reference frame: 1 second per second. Time dilation only make sense to talk about relative to another reference frame. If you're running by me at 0.995c, we will each calculate the other's watch as running ten times slower while seeing our own working fine, and that means we will disagree on whose watch is running slow. There is no absolute speed, so either of us can say we are stationary and it's the other one that's moving and be equally correct. Frame rate issues with a monitor are absolute as measured by the number of frames per unit time (in the monitor's reference frame, I suppose). Conversely, If I am very near a large mass and you are far from it we will both agree that my watch is running slow, but the fact that time is passing slower for me still only makes sense when compared to someone in a different location. In that case we know objectively who is closer to the mass so that gravitational time dilation is still relative, but is absolute in the sense that we can say for sure who is closer to the mass.

So yeah, kinda, but time dilation is different from lag that you'd have to be very careful in using that analogy. That said, all analogies are imperfect and the trick is knowing how and where they are applicable and where they aren't.

It doesn't seem unreasonable that we could have used the notation differently as well. There's no fundamental reason why a prime has to be a space derivative and a tittle a time derivative. It might make communication a little tricky at first, but the meaning should be made clear by context (and if it isn't, we probably would want to use more specific notation anyway).

>From ... Newton we get the y' and x' notation which (In my engineering school at least) specifically refers to time-based derivates.

Interesting! We used a prime for spatial derivatives and a tittle for time derivatives in my physics education when we used Newtonian notation.

Usually batteries are used for this, as they can store far more energy and if they're big enough, their maximum power is also large enough for quick charge/discharge. This means that an ultracapacitor isn't necessary for power density reasons and the battery is better for energy density reasons.

For example, a number of electric cars are already traction-limited for acceleration and capable of driving two to three times any finite speed limit they encounter, while still having a 300-400 mile range at full charge.

Conversely, late-generation Honda Insights use a small, but high efficiency motor that is used mostly to charge a battery. It turns on, runs at max efficiency charging the battery, then turns off when the battery has enough charge. The battery provides electric traction and is capable of both load-leveling (since the motor is providing more power than is usually necessary for driving at any given moment) and is capable of providing more power than the motor is in short bursts! This drivetrain is not entirely dissimilar from a diesel-electric train.

Due to ultracapacitor's low energy density, they are only good where you need extremely high power densities (higher than are generally needed by modern electric vehicles) or extremely high charge/discharge cycles. So they've been examined for public transit purposes (where they might not even be carried by the vehicle itself, but rather be installed in a fixed location and connected to the vehicle by rail or overhead lines), but they don't really make sense for cars and trucks.

Farthest you can easily see. Experienced observers in exceptional conditions can see some things that are farther away!

While the density change is only ~4% for liquid water between its minimum and maximum (under standard conditions), this can be noticeable if the floating thing is very close to neutral buoyancy.

For example, the Galileo thermometer works by having objects of (relatively) fixed density suspended in a water column. The objects densities are slightly different and such that they are all very near neutral buoyancy, so that the more dense objects will only float when the water is colder and more dense as well. This can be made into a thermometer by carefully selecting the densities of your suspended objects!

Jim Lovell is still alive. Just saying, NASA…

Before we sent humans to the moon on Apollo 11, there were a whole bunch of test flights that got progressively closer, so we could work out all the kinks and technical problems associated with landing on the moon.

The Gemini program was basically testing out basic things we would need to go to the moon: long endurance spaceflight, in-space rendezvous and formation flying, docking with another spacecraft, etc.

Then Apollo had a ton of flights before Apollo 11 (ten flights, plus the Apollo 1 disaster). Until Apollo 7 they were all uncrewed tests of the rockets, the capsules, the escape systems, etc.

Apollo 7 tested the command and service modules in space with an actual crew. They stayed in low earth orbit and did a full rundown of all the systems.

Apollo 8 carried the first humans to the moon. It was just the command and service modules with no lander, and orbited the moon before returning home.

Apollo 9 had a lunar lander as well, but stayed in low earth orbit, so the docking/undocking maneuvers could be tested and perfected and all the LM’s systems checked out.

Apollo 10 was everything but the landing, putting all the pieces together from the earlier flights and programs. They flew to the moon, orbited it, and had the first LM in lunar orbit with them, which they took down to just a few miles over the surface of the moon. It was a full dress rehearsal for the actual landing.

Artemis is just doing something similar.

Same, happy screenings to you!

I love Event Horizon. One of the very best space horror movies with just the right amount of camp.

Also, [there is a longer, far gorier version that is lost](https://en.m.wikipedia.org/wiki/Event_Horizon_(film)#Lost_footage). Like, it was finished and test-screened to the horror of the audience and studio execs and no one has seen that cut since.

Warhammer 40k nerds also consider it canon in that universe, too.

BSG is great. The new series got kind of weird at the end, but the whole thing was so well done otherwise.

Nope, scattering is a change in the direction of light due to an interaction. The inverse square law is just a geometric spreading of the light from a point source in the absence of an interaction.