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Assume it could withstand extreme temperatures in either direction. I'm mainly curious what would happen to its circuits as it approached the speed of light.

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    $\begingroup$ Make the circuits light based , not electron based, photons work fine at the speed of light $\endgroup$ – user81619 Jul 23 '15 at 20:48
  • $\begingroup$ Related: physics.stackexchange.com/q/23576/2451 $\endgroup$ – Qmechanic Apr 15 '16 at 10:31
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The relativistic determining factor would be acceleration, not speed. According to the axioms of relativity, an object moving at constant speed cannot be distinguished from an object at rest in another inertial frame; at high constant speed the satellite will still think it's at rest.

The practical limit on speed would be determined by the density of the interstellar medium; move fast enough and the "upwind" side of the spacecraft would start to intercept a lot of matter and get hot.

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  • $\begingroup$ Not just hot... micron-sized dust particles, which are ubiquitous in the interplanetary and interstellar medium, would ablate the entire spacecraft away... $\endgroup$ – honeste_vivere Apr 15 '16 at 20:43
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There is another speed limit, though

The problem with ultra-high speeds could be the doppler beamed and boosted cosmic microwave background (CMB), which may well fry your circuitry.

I don't know enough about radiation shielding to give you an exact number where problems would begin. This limit would still apply even should the spacecraft be moving through an incredibly sparse medium.

Let's assume that the problems for the spacecraft would begin once it is illuminated by hard X-rays. For the CMB to be boosted to X-ray frequencies requires a redshift $z \sim 10^{7}$ ($z \sim 2\gamma$ here), making the CMB a blackbody at $3\times10^{7}$ K. The necessary speed is given by $$z^2 = \frac{c+v}{c-v}$$

A quick calculation gives $v \simeq 0.99999999999998c$ (or $\gamma \simeq 5 \times 10^{6}$).

At this speed the specific intensity of the CMB in the direction of motion is also boosted by a factor of $z^3$ to reach $3.7\times10^{-18} \times 10^{21} = 3700$ W m$^{-2}$ sr$^{-1}$ Hz$^{-1}$. This is 11 orders of magnitude brighter than the surface of the Sun, but the radiation will be in the form of a narrow X-ray spot on the sky of diameter $\sim 2/(1-v^2/c^2)^{-1/2} = 2\times10^{-5}$ degrees in diameter.

In fact, if you think about it, if you were to direct your spacecraft directly towards a star at relativistic speeds, then you would encounter a very similar problem. However, because the radiation field of the star is already in the visible band, the problems would occur at redshifts of $\sim 10^{4}$ and therefore at speeds of $\sim 0.99999998c$.

A recent paper by Yurstever & Wilkinson (2015) approaches this problem in a very similar way. They argue that inelastic X-ray scattering (and therefore heating of the spaceship) can be alleviated in some way but that pair production on nuclei in the hull of a ship will unavoidably take place when photon energies of around $10kT > 1 MeV$ are reached, or $T \sim 10^{9}$K, which leads to $\gamma \sim 2\times 10^{8}$.

These authors also conclude though that interstellar dust is the main problem "a single grain of cosmic dust with a mass of $10^{-14}$g at $\gamma=10^8$ has the impact energy of close-to 24kg of TNT". This equates to a typical interstellar grain sizes of 0.1 micron, with typical densities of a few g/cm$^3$. However, interstellar dust grains have been collected of 20 micron size ($10^{-7}$g), which gives an impact energy like a tonne of TNT (4.2 GJ) when $\gamma=500$.

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    $\begingroup$ Nice, but I would have said something like 1 - 2e-14 or 1 - 2e-7, rather than string a bunch of 9s and make me count them :) $\endgroup$ – Mike Dunlavey Jul 27 '15 at 12:53
  • $\begingroup$ I forgot about the CMB and wouldn't have thought of starlight. However there are "only" $10^9$ CMB photons per baryon in this part of the universe, so the interstellar medium does become a problem first. $\endgroup$ – rob Jul 29 '15 at 23:52
  • $\begingroup$ The energy absorbed at the point the CMB becomes x-rays makes the surface of the sun look chilly, it would overheat much sooner. $\endgroup$ – Kevin Kostlan Jul 10 '16 at 4:48
  • $\begingroup$ @KevinKostlan That is exactly what the last paragraph of my answer , and the paper it refers to, addresses. They argue that X-rays are likely not a problem and that only when pair production kicks in does the heating become unavoidable. $\endgroup$ – Rob Jeffries Jul 10 '16 at 5:33
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    $\begingroup$ @KevinKostlan The only way the X-rays can heat is if they are absorbed or inelastically scattered. The calculations (and my answer) specifically say that X-ray scattering (i.e. the Compton effect) is ignored - the idea that being that if you can build a spaceship to go at $>0.9999c$, then you will have figured out a way to disperse heat. But you cannot disperse momentum. $\endgroup$ – Rob Jeffries Jul 10 '16 at 14:59
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Potentials do not have retarded time effects. If electron is removed from the sun its effect on the potential on esrth is immediate . So the electronics will be likely tip top. The limit of speed nowadays in space is set by the rocket gas engines that they use. Basically they use the chemical bonds energy to accelerate and push gas outside.

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protected by Qmechanic Jul 10 '16 at 16:21

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