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As far as I know, for light and particles taking special relativity into account:

\begin{align} E^2 &= (T + m_0c^2)^2\\ &= p^2 c^2 + m_0^2 c^4 &\text{ (particles)}\\[1.5em] E &= p c & \text{ (photons)}\\[1.5em] F &= \frac{d\,p}{dt\phantom\,} \ne ma.^† \end{align}

If I have a bottle of hydrogen or xenon and 100% efficient and massless ion engine and light to electricity converters, I can accelerate away from a laser beam both by absorbing their momentum and by using their energy to accelerate ions back towards the source of the laser.

I think but am not sure that it is difficult to impossible to accelerate directly into the beam because 1) this comment and 2) a given amount of energy imparts more momentum to a photon than to a particle with nonzero rest mass $m_0$.

Questions:

  1. Is that right? Even with 100% efficient and massless light to energy converters and ion engines, I can never accelerate directly into a beam of light?

  2. If so, for a given particle energy $T$ and rest mass $m_0$ what is the highest angle at which I can accelerate in the half-space (hemisphere) towards the laser beam, if any? Or can I only accelerate into the half-space away from it?

†ref

uhoh
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  • no prob! Sadly, I find the moderation here quite objectable, so to avoid me wasting emotional energy in the future, I'll delete my account on this site; it's been an honor :) –  Oct 28 '20 at 15:40
  • @MarcusMüller thanks for you candor. I find the moderation here to be excellent, even exemplary Stack Exchange moderation, and fully adapted to the site's dedication to being welcoming to new users balanced with keeping things cordial and focused on the exploration of aspects of space exploration as well as on space itself. – uhoh Oct 28 '20 at 20:03
  • @MarcusMüller If you feel the site could be improved why not express something in meta? When humans are involved there's always room for improvement, – uhoh Oct 28 '20 at 20:07
  • the moderator in question just changed the wording of a question, thus clearly invalidating my answer, then without as much as a warning deleted my answer. Then I asked in a comment to the question whether, if he was as unsure about the change as he expressed to be, it was a careful moderation choice to just delete my answer instead of just downvoting it. And he just kept deleting my comments. So, nope, sorry, not wasting any effort on that one – he's the elected moderator, not gonna change him, so leaving this community :) –  Oct 28 '20 at 20:17
  • @MarcusMüller okay, there might have been some additional considerations that would come to light in a meta interaction. Moderators work in a different and larger information space and broader responsibility space than the rest of us. Anyway, if you have any thoughts on Have deep-space spacecraft always used some form of spread-spectrum for data downlink? before you go it would be great to hear them, I'm still confused on the definition of what modulations do or don't count as "spread spectrum". It might be more of an issue of terminology... – uhoh Oct 28 '20 at 20:32
  • I'm honestly confused, this is a different thing altogether? –  Oct 28 '20 at 20:45
  • @MarcusMüller yes it is orthogonal in terms of topic. I just ran across your profile yesterday for the first time and thought "Oh great! a radio person!" which is why I made this long list. The next day you're talking about leaving and I'm thinking "Oh no, all those potential answers disappearing..." The spread-spectrum thing has been puzzling me for a long time and I was hoping you might be able to shed some light on that. I see SE's goal as simply to generate good answers, and this question needs one! – uhoh Oct 28 '20 at 20:56
  • @MarcusMüller but also I'm hoping that is a metaphor for SE in general and this site as well; nothing is perfect here because it's completely open to the internet and a planet full of heterogeneous people; when things feel even more imperfect than usual one can always just move on to the next unanswered question, or in my case, to writing one :-) – uhoh Oct 28 '20 at 21:00
  • @MarcusMüller oh I just ran across the page you are talking about. Ya that sudden deletion does seem uncharacteristic for the site. I definitely don't think that that's worth leaving the site over, and do think it's worth exploring in meta. If you like I can write a meta question about it. But if "you got angry and violated the terms of engagement (code of conduct)" will be the answer, then that's exactly how SE now works in order to accommodate being open to the entire internet. We do need to remain cordial at all times, sometimes even against our will. :-) – uhoh Oct 28 '20 at 21:30
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    not angry, just not willing to invest effort –  Oct 28 '20 at 21:33

1 Answers1

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Because you are making use of fuel (reaction mass), this can only work for a finite time, but it must be possible for a while. We could imagine that we have a "largish" ship so the energy we get from the source imparts a negligible momentum. Then we could use that energy to push off from the bulk of the ship to accelerate toward the energy source. Done.

But it should work well for more realistic setups as well. As an example, I assume the ship is "large" enough that the xenon exhaust is a minor fraction of the total mass.

I receive 1MJ of photons. How hard does it "push" the ship?

$$dp = \frac{E}{c} = 0.0033 \text{kg m/s}$$

An engine can generate a relative velocity with xenon of 20 km/s. Most of the energy will go to the exhaust. How much Xenon can be accelerated from that energy with 100% efficiency?

$$m = \frac{2E}{v^2} = 0.005\text{kg}$$ $$dp = 0.005\text{kg}\ 20\text{km/s} = 100\text{kg m/s}$$

Since this is bigger, we can go in any direction.

The numbers aren't exact even with perfect efficiency (100% of the energy won't go to the exhaust, the engine isn't impulsive so some losses with $dp$, etc.) but the difference easily covers those caveats.

BowlOfRed
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