Also, would there be any difference between shadows cast by the exhaust from a rocket as opposed to the flame from a rocket?
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6$\begingroup$ NASA photo of shuttle launch that addresses question: apod.nasa.gov/apod/ap110525.html $\endgroup$– AdamCommented Jan 9 at 16:56
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1$\begingroup$ And also another APOD: apod.nasa.gov/apod/ap111127.html $\endgroup$– RuslanCommented Jan 10 at 7:52
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6$\begingroup$ Does this answer your question? Are rocket exhaust flames ever opaque? $\endgroup$– Alex RobinsonCommented Jan 10 at 10:47
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$\begingroup$ @AlexRobinson - do we assume that opaque and casting a shadow are the same thing? Some of the answers here discuss the refraction properties of transparent materials or gases which reduces light transmission in a linear direction thus creating a shadow. $\endgroup$– Steve PembertonCommented Jan 15 at 23:50
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4 Answers
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The exhaust (including the flame) flame will either absorb or redirect the sunlight that passes through it. You can see this in the photo below. Either way, it is likely that, under the right circumstances, it will cast a sunlight shadow.
However, if the flame is very bright relative to the sun where the sunlight shadow is being cast, then the sunlight shadow would likely be washed out by the brightness of the flame.
Recent photo of Falcon Heavy by John Kraus
Also, if the surface was too far away then the shadow would not be very sharp.
A SpaceX Falcon 9 rocket creates its own shadow in the clouds. (ref)
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I agree with @phil1008’s answer, but will amplify it to “YES, always”. Shadows may be difficult to detect if the contrast is low (for instance, added light from the exhaust itself) but light passing around the exhaust will always be brighter than light which has passed through the exhaust unless the exhaust is completely uniform and has exactly the same refractive index as the ambient air. This restriction is obviously not the case with rocket exhaust
Even the best optical glass casts a shadow. Try it with your glasses. It doesn’t matter if the lens is convergent (far sighted) or divergent (near sighted). The only theoretical exception is a converging lens exactly 2 focal lengths from the screen. A flat plate of optical glass will cast a shadow due to surface and internal reflection.
Credit: Nataliia Yankovets
Shadows cast by transparent structures are due to refraction which causes concentration or dispersion of light. But even if refracted light is concentrated, it does not erase the border of the shadow as illustrated by the area highlighted by the red rectangle.
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5$\begingroup$ I don't like calling those things shadows as they are not absorbing - they conserve energy. It's better to call the effect "caustics" cf. the grayscale image of Alan Turing made from shaped glass in my answer to What is this wavy light coming through my blinds? $\endgroup$– uhohCommented Jan 10 at 8:42
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1$\begingroup$ @uhoh one could argue that in a general sense, a caustic just casts a specific type of shadow. Going back to the question, most of the visible electromagnetic energy incident on a rocket plume is not absorbed either, it's scattered. But just like any other cloud, it will cast a shadow if it is optically thick enough (not because of absorption but because of scattering). $\endgroup$– RyanCommented Jan 11 at 4:24
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2$\begingroup$ @Ryan Hmm... I wanted to reply "One can also argue that apples are oranges" but you make an interesting point that gives me pause. That there's only a binary choice is a false one; there's a whole continuum. If I hold a small mirror in a beam of light, I would say it casts a shadow even thought there's no absorption - just the opposite. And a few tens of cm of snow is pretty much opaque even if it's pure, (nearly) transparent ice crystals. $\endgroup$– uhohCommented Jan 11 at 5:52
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3$\begingroup$ Using these definitions the sky casts a shadow on the Earth, since only about half of the solar constant reaches the Earth's surface. Although I don't think I have ever heard anyone describe it as a shadow. Interesting way to think about it though, here we are sitting in the shadow of our atmosphere. Maybe from now on if someone asks me what the temperature is in the shade I will ask them to clarify exactly which shade they are referring to, atmosphere only, or atmosphere plus structure. I'm guessing I would get some funny looks. $\endgroup$ Commented Jan 11 at 19:20
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There are actually two different effects at play:
If it's bright, it'll cast a shadow. When something hot is a good emitter of light at certain wavelengths, it is just as effective an absorber of these same wavelengths. If that were not the case, you could reduce entropy, and our universe does not like that.
If it bends light, it'll cast a shadow. That's what the other answers have said already. Light that is bend gets effectively moved around within the shadow image, yielding light and dark areas. And we call the dark areas the shadow. There will be bright spots as well that form a caustics pattern, most likely both within the shadow region and without, but dark regions there will be.
Now, applying this to rocket exhausts, we find that kerosene and solid fuel rockets fly with a very bright flame due to all the soot/aluminum particles contained in the hot exhaust stream. These flames absorb virtually all ambient light because they are so bright themselves.
Other rocket fuels do not produces as bright a flame, most prominently hydrogen/oxygen rockets. And, just as thermodynamics suggest, their exhaust is also almost perfectly transparent. However, it is hot, and it is moving fast. It's also comprised of molecules significantly lighter than the average air molecule (H2 as well as H2O since hydrolox engines burn on the fuel rich side). As such, they are significantly less dense optically. And they produce strong turbulence and shock waves at the air/exhaust boundary, which in turn lead to regions of high/low pressure, which also modulates the optical density of the medium. As such, they bend light quite effectively in all directions, again producing a shadow according to effect two.
Other rocket fuel combos produce flames somewhere in between those two extremes, but they all do cast shadows.
answered Jan 10 at 16:32
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$\begingroup$ "And we call the dark areas the shadow." I think that we should call those caustics, not shadows $\endgroup$– uhohCommented Jan 10 at 20:14
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3$\begingroup$ @uhoh Well, the dark areas are strictly constrained to where the shadow would be if the object were absorbing light. The bright spots, however, are not constrained to this shadow region; they are what I would call caustics. And, as you move the shadow screen further and further back, those bright spots will eventually leave the shadow region and/or dim out, leaving only the dark shadow behind. But I guess, I'm getting dangerously close to philosophical debates here, where the only difference is different definitions of central terms... Nevertheless, caustics was the term that eluded me :-) $\endgroup$ Commented Jan 10 at 21:16
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That depends.
Smoke: Some fuel types (hydrogen, some hypergolics) produce a transparent exhaust. Others (solids) produce opaque smoke. In all cases, a shadow is produced (if there's enough light to cast a shadow).
Flame: Most fuels produce flames bright enough to produce shadows, but this depends on the amount of ambient light.
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4$\begingroup$ "transparent exhaust ... would not cast a shadow.". Not so. Transparent objects cast shadows unless they are exactly the same refractive index as air. Try it with a pair of glasses, a glass of water. Even a flat sheet of optical glass will cast a shadow due to surface reflection and internal reflection. $\endgroup$– WoodyCommented Jan 9 at 20:40
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1$\begingroup$ @Hobbes you can change it back; caustics are caustics and shadows are shadows and never the twain shall meet. $\endgroup$– uhohCommented Jan 10 at 11:21