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Nonrelativistic solution
The variables used will be
$x$ for the distance travelled
$v$ for velocity
$a$ for acceleration ($1~\mathrm{g}$)
$t$ for the time
$c$ for the speed of light.
Non braking
Assuming the velocity you arrive at does not matter we take the equation
$$x = \frac12 a t^2\ .$$
Solve for $t$:
$$t = \sqrt{\frac{2x}{a}}\ .$$
(Let’s ...
78
Technically, yes
While Voyager 1 lacks the velocity necessary to escape the Milky Way galaxy, it doesn't actually need to. Because the Milky Way galaxy itself will collide and begin to merge with the Andromeda galaxy within about 4.5 billion years. It's unlikely any objects within either galaxy will collide with something in the other. But it's pretty ...
74
no.
Voyager 1 is currently orbiting the center of the Milky Way, which has an escape velocity of $550 \ \text{km}\ \text{s}^{-1}$ at the Sun's position, while the Sun orbits at $\sim 220 \ \text{km}\ \text{s}^{-1}$. Voyager was ejected at $\sim 17 \ \text{km}\ \text{s}^{-1}$, like @user438383 said in a comment, and in the prograde direction, which means, at ...
43
Velocity relative to what? There's no central universal point to measure velocity at, so your answer is likely going to change based on your frame of reference.
New Horizons did indeed have the fasted launch velocity of any spacecraft that has left Earth (relative to Earth):
After three years of construction, and several delays at the launch site, New ...
39
It is not only how fast the airfoil has to travel, but also how large the airfoil must be to even have fluid-dynamics-like behavior. Because of the low density of particles in the interstellar medium, a normal-sized wing will not act as an airfoil. It will be more like bouncing tennis balls off the wing every so often.
The Knudsen number quantifies when ...
38
Spooky
This one is subjective. To some, just finding an abandoned spaceship would be spooky. I'll say there's probably not a lot that has to happen to evoke this feeling.
Rusted
Actually, unless your spaceship never had a breathable atmosphere or the atmosphere was vented before the spaceship was abandoned, rust is totally possible on the inside and ...
33
Voyagers are still active, and albeit they don't have the power required to run all the scientific equipment onboard and some of it stopped working by now, they still transmit telemetry data streams towards the Earth that is picked up by NASA JPL's 70-meter antenna at Goldstone, California, part of the Deep Space Network. Quoting from Wikipedia on Voyager ...
32
Does this logic make sense? Has anyone thought of this before?
Yes, it's been considered. In the literature it's known as the "incentive trap".
There are a couple of academic papers on it, notably Andrew Kennedy's 2006 Interstellar Travel - The Wait Calculation and the Incentive Trap of Progress and René Heller's Relativistic generalization of the ...
25
Why the Pioneers didn't last as long:
The Pioneers were a low-budget mission just to test if flying to the outer planets was feasible
They used a smaller radio transmitter (8 W vs. 23 W) and antenna (2.7 vs 3.6 m diameter) so their signals are weaker
The Pioneers used a smaller, earlier design Radioisotope thermoelectric generator as their power source (...
23
The speed of the probe doesn't change with regard to the assisting body. It is direction that is changed.
If a hyperbolic orbit about the sun comes in with a Vinfinity of 5 km/s, it will exit with a Vinfinity of 5 km/s.
Unless it happens to swing by a planet. From the planet's point of view incoming and outgoing speed are also the same. Again, it's ...
23
The most fuel efficient way to leave the solar system at present, is to launch into a trajectory that (like that used for Gallileo) may well involve one or several gravity assists from Earth or Venus, but which eventually gets you to Jupiter. If you can get to Jupiter you can almost certainly do so in such a way as get a slingshot into a solar escape ...
22
The expression $v_e = \sqrt{\frac{2Vq}{m}}$ is a non-relativistic approximation. This is quite valid when the exhaust velocity is small compared to the speed of light, which is the case for ion thrusters made to date (exhaust velocity is on the order of $10^{-4}c$). A more precise expression is $${v_e}^2\left(1+\frac{2Vq}{mc^2}\right) = \frac{2Vq}m$$
No ...
20
It's theoretically possible to collect fuel from near empty space, the bussard ramjet is an example of an engine designed to do just that. The principle is that you use magnetic fields to collect and concentrate hydrogen atoms from the near vacuum of space, and then a fusion rocket would turn some of this into propulsion for speed and a fusion reactor would ...
19
Zero.
Voyager 1 has left the solar system, and is therefore an interstellar spacecraft. I'm not sure what qualifies a ship, but there is no reason why it would take any humans. Nor do yachts (or cars) need humans for navigation, for that matter.
Interstellar space is particularly dull. You'll be travelling for many years with absolutely nothing ...
19
The core of your question is about real, "normal" engine exhaust velocities. The fastest we get so far from practical, in-production engines is about 4,440 m/s, Space Shuttle main engines with liquid oxygen and liquid hydrogen as propellants, producing water as the exhaust product (https://en.wikipedia.org/wiki/Specific_impulse). That speed is limited by the ...
18
We currently cannot track Pioneer 10 or 11.
Someone on the XKCD forum calculated how much radiation the Voyager probes emit besides their radio transmissions. The heat they give off is emitted as infrared light:
We have a power source of 420 W at 1.78×1010 km, which gives a brightness of 1×10-19 Wm-2, or an apparent magnitude of 28. That is just ...
18
Voyager 1 and 2 are still in the "neighborhood" of our solar system and very close to our Sun compared to any other star. They are roughly three times farther from the Sun than Neptune and Pluto and so already past the Kuiper belt where New Horizons is currently traveling.
As the diagram below shows, the Voyagers have passed the boundary where the ...
17
The total antimatter in the van Allen belts is estimated to be 160 nanograms. Annihilating that with matter would produce a whopping 8 kW-hr of energy. A quarter of a gallon of gasoline has that much energy. The star ship would be better off getting a quick spurt from a gas station pump before heading out.
16
Hefty gravity wells can give a healthy Oberth benefit. Doing a burn deep in Neptune's well makes sense. Suggesting an Oberth maneuver near a Pluto sized object is pretty silly. Don't know if Randall Munroe knows this. Maybe that's part of his joke.
Heading all the way back from the Kuiper belt to the inner solar system take 30 years. Then back out another ...
16
You are forgetting Pioneer 10, Pioneer 11, and New Horizons. Pioneers 10 and 11 respectively operated for 28 years and 16 years after completing their primary missions. New Horizons, which has yet to perform its primary mission (Pluto flyby in July 2015) or secondary mission (TBD flyby of a Kuiper belt object) will reach the heliopause in about 2047.
No ...
16
No, the power collected by solar panels is reduced by the square of the distance from the light source.
At the Earth's distance from the sun, the energy of sunlight is about 1300 watts per square meter, of which something like ~30% can be converted to electricity by solar panels. Once the sun is far enough away to be "just another star", the total ...
15
There are incredible, mindboggling distances involved in merely reaching an exoplanet. Alpha Centauri Bb, the closest known exoplanet, is 4.365 light years away. That's 41,295,000,000,000 km (25,660,000,000,000 mi), or 276,000 AU (the distance from the Earth to the Sun).
Voyager 1 has left most of our solar system behind and is traveling a blistering 17.3 ...
15
Currently functional and proven technology is limited to basically no interstellar travel at all. To reach one of our stellar neighbors (like Proxima Centauri), one of the fastest space probes we have now, New Horizons, would take 54000 years.
There are multiple proposed methods of sending spacecraft interstellar distances (in shorter time spans) such as:
...
14
There's no reason a Von Neumann probe could not be built once a civilization reaches the appropriate technology level, it's a matter of desire. When a civilization becomes advanced enough all it needs to build anything is a supply of matter or energy, as the one can be used to make the other.
When you say "the absence of Von Neumann probes" I suspect that ...
14
There is an answer on wikipedia: Rogue planet:
It is calculated that, for an Earth-sized object at a kilobar hydrogen atmospheric pressures in which a convective gas adiabat has formed, geothermal energy from residual core radioisotope decay will be sufficient to heat the surface to temperatures above the melting point of water.[13] Thus, it is proposed ...
14
Lagrange points do exist between stars. In case of single stars, they are too far away from the stars to have any practical effect.
However, in case of the binary stars, the Roche Lobe has its apex located at L1.
"RochePotential color" by SamuelHon - Own work. Licensed under CC BY-SA 4.0 via Commons.
In case a star's surface extends beyond the Roche Lobe, ...
14
Accumulating 0.1c (30000 km/s) with gravity turns alone within the bounds of Solar system isn't possible. Reason is: system escape velocity (sometimes referred to as third cosmic velocity) is about 42km/s (at Earth orbit, and the farther the lower). Once craft reaches this speed, it still can accumulate a bit more with right escape path, but generally not ...
13
I would like to firstly echo the suggestion to read Project Rho. Throughout the entire site, there is a tremendous amount of hard science and it is all deeply entertaining.
http://www.projectrho.com/public_html/rocket/spacegunexotic.php
In short, a space war would look more like the Cold War than any other war we've known. With nuclear ICBMs, we ...
13
Do we have the knowledge, technology and resources to colonize it?
Simply put, no.
First off, you need to forget about knowledge, technology and resources and look to biology, sociology, and psychology. How many people would be needed to create a self-sufficient modern colony? The number is rather large. It's not 100 people, or even 1,000. It's at least 14,...
13
Is it pure luck that the voyager 1 survived to travel beyond our solar system in interstellar space?
It can't be pure luck, seeing as how both Voyager spacecraft are still operating today. If it were just one, you might chalk it up to luck. Both still working means they must have been built really well. Which they were.
It is essential of course that they are nuclear powered, and also that we have really big antennas on Earth with which to talk to them. ...
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