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Like a Crookes Radiometer, could a satellite have a stiff vain to maneuver? With a white side to let light pass and the black side capture light radiation be enough provide radiation pressure to keep it in deep orbit?

Solar powered servos could be used to change the pitch of the sail.

I understand the principals are different since in a Crookes Radiometer uses gas expansion to move and a solar sail uses solar radiation pressure

Where this differs from a solar sail is that in this model the sail is firm and flat. One side to capture solar radiation and propel and the other side passive like the radiometer. It differs from a radiometer because it is a solar sail but could rotate sideways to let light pass or have a transparent side while moving towards the Sun and then reverse to use the Sun while traveling away for propulsion.

What satellite has the highest orbit around the Earth?

Can orbital maneuvers be performed by a solar sail to correct eccentricity?

Can a Solar Cell/Sail Powered Satellite orbit both the Moon and Earth rendezvously?

enter image description here

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The drawing shows a Crookes Radiometer.

They seem to spin nicely in even a little bit of sunlight. The common explanation is light pressure on the black vanes.

Unfortunately, they don’t work that way. Photons bouncing off the white side transfer more momentum than ones absorbed by the black: of the mechanism was light pressure, they’d turn the other way. A clue to the correct mechanism is that they don’t work in a full vacuum. It’s probably something to do with the residual gas and the black side being hotter.

Satellites are in much deeper vacuum than a Crookes radiometer bulb. Whatever the mechanism, it won’t be big for a satellite.

But there’s still some potential for using light pressure for various operations. There have been experiments with several kinds of “sails” to gather and use it.

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  • $\begingroup$ Bob Jacobsen, you're right on the money with the mechanism for a Crooke's radiometer. The black side is warmer so the atoms there are vibrating a bit more energetically. When molecules (or atoms) of the gas collide with the black side's surface they come off a bit faster than when they collide with the white side, so there's more momentum exchange on the black side and a net torque. $\endgroup$
    – Tom Spilker
    Commented May 6, 2018 at 19:29
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    $\begingroup$ A Crookes Radiometer was one of my most memorable gifts as a little kid. The fact that sunlight would push the black side more than the white side of each vane proved that atoms exist, or at least so said the back of the package. I was seeing atoms! Changed my life. $\endgroup$
    – uhoh
    Commented May 7, 2018 at 1:16
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    $\begingroup$ @uhoh this website changed mine. $\endgroup$
    – Muze
    Commented May 7, 2018 at 2:13
  • $\begingroup$ There's a nice write up in these two Science for Dessert blogposts: The Crookes Radiometer Part 1 and Part 2. $\endgroup$
    – uhoh
    Commented May 7, 2018 at 2:37
  • $\begingroup$ +1 - this is the right answer. The primary mechanism of action of the Crookes tube does not exist in the hard vacuum of space. I really am curious to see how long it takes for the (erroneous) "radiation pressure" theory for the Crookes radiometer to finally die. $\endgroup$
    – J...
    Commented May 7, 2018 at 20:33
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The Mariner 3 and 4 Mars flyby probes had angled vanes at the ends of their solar panel arms which provided passive stabilization of the spacecraft from solar radiation pressure:

enter image description here

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    $\begingroup$ Oh, that's clever. If the craft tilts, then one vane's apparent area to the sun increases, so getting more pressure, and the opposing vane's apparent area decreases, getting less pressure. $\endgroup$
    – Wayne Conrad
    Commented May 6, 2018 at 20:16
  • $\begingroup$ Yup. Apparently it didn't work very well, however. $\endgroup$
    – Russell Borogove
    Commented May 6, 2018 at 23:03
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    $\begingroup$ @RussellBorogove I've just asked What is the principle behind Mariner 4's “Solar Pressure Vanes”? In what case(s) would they be effective? $\endgroup$
    – uhoh
    Commented May 7, 2018 at 0:57
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    $\begingroup$ @uhoh You asked exactly the question I was going to ask. But better than I would have been able to ask it. $\endgroup$
    – Wayne Conrad
    Commented May 7, 2018 at 1:36
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    $\begingroup$ @DohnJoe, it's not that radiation pressure was used to stabilize the spacecraft, but rather that radiation pressure was the strongest unstabilizing force on the spacecraft and they optimized the spacecraft pointing to get the torque from the force to be as close to 0 as possible. The radiation pressure wasn't a solution, it was a problem. $\endgroup$
    – NeutronStar
    Commented May 7, 2018 at 15:40
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This is exactly what we call a solar sail. This works for orbit maintenance if the orbit isn't too low. If it's too low, the total impulse (force times time) lost to drag over one orbit is greater than the light-pressure (https://en.wikipedia.org/wiki/Radiation_pressure) impulse over one orbit, and the orbit still decays, just slower.

Solar sails have the disadvantage that they require a large area to produce much force. If you turn a perfectly-reflecting sail face-on to the sun at 1 AU distance, the force you get on the sail is 4.5 millionths of a Newton per square meter.

Drag force is given by $Fd = \frac{1}{2} C_d A \rho V^2$, where $C_d$ is the drag coefficient (for orbital speeds and atmospheric densities it is usually very close to 2), A is the projected area, ρ is the atmospheric mass density, and V is the velocity. If that same square meter is face-on to the velocity vector at an altitude of 150 km, where the atmospheric density is roughly $2 \cdot 10^{-9} kg/m^3$ and the orbit velocity is ~7,820 m/s, the drag force generated would be ~0.122 N, nearly five orders of magnitude higher than the solar light pressure force.

Of course, the solar sail isn't always face-on to the sun, nor face-on to the velocity vector, but the averages over one orbit would be around 1/2 to 1/4 of the face-on values. The solar sail suffers from being in Earth's shadow a significant fraction of its orbit (unless it's in a nearly-polar orbit that is face-on to the sun) so its average force over an orbit is a smaller fraction of the face-on value than for drag—drag never turns off! So orbit maintenenance with a solar sail certainly wouldn't work at such low altitudes.

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  • $\begingroup$ Does drag use the same equation in atmosphere thin enough to not be an ideal gas? (If it does it would be nice to have a statement to that effect, and maybe a citation.) $\endgroup$
    – Nathan Tuggy
    Commented May 7, 2018 at 2:38
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    $\begingroup$ @NathanTuggy , I assume you mean thin enough not to be a collisional gas (frequent molecular collisions). Thin gases do fine with the ideal gas law, it's very dense gases where van der Waals forces come into play and the behavior deviates from ideal. But it turns out the mathematics for drag in a tenuous gas is the same for a fully collisional gas. Aerodynamicists cheat and roll up any deviations into the drag coefficient. These deviations get important at significant transitions, like subsonic to supersonic, and supersonic to hypersonic. $\endgroup$
    – Tom Spilker
    Commented May 7, 2018 at 2:49
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    $\begingroup$ @NathanTuggy , en.wikipedia.org/wiki/Drag_(physics) shows them using the same equation for low-velocity and high-velocity cases, saying that the Reynolds number is a significant part of determining the drag coefficient. It's not the best article in the world, but at least they got that part right. In all my work designing missions at JPL we always used that functional form. $\endgroup$
    – Tom Spilker
    Commented May 7, 2018 at 3:00
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could a satellite have a stiff sail like the white side to let light pass and like the black side capture light to provide enough force to keep it in orbit?

Not really.

Let's ignore the point Crooke's Radiometer works on different principles. Yes, you can use solar pressure to give your craft acceleration, and yes, changing the surface color will vary the effect magnitude.

  1. Solar sails start making sense above 1000km - below that altitude atmospheric drag outweighs light pressure. And the decay time of a satellite at 1000km goes into hundreds upon hundreds years. So, where this could work, it's no longer needed.

  2. Orbital mechanics working against you. Any prograde acceleration of the satellite extends the orbit on the opposite side of the central body. If you keep accelerating during your passes on one side, the orbit initially grows on the other side - your acceleration area becoming periapsis, the passive, dark side operation at apoapsis. But orbital mechanics makes the time of flight near apoapsis longer than near periapsis, the more eccentric the orbit the more drastic the difference. And the "dark operation" side of your probe won't be entirely passive - it will act at about half the force of the acceleration side - but acting in retrograde direction. Meaning your periapsis starts dropping! Eccentricity grows, periapsis drops faster, and soon the satellite burns up, deorbited.

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In a way, yes — the US Naval Academy cubesat ParkinsonSAT was designed with four faces asymmetrical, with solar panels offset to one side and reflective tape occupying the remaining space, creating an angular moment of solar radiation pressure, and this has succeeded in keeping the satellite spinning at a rate of several RPM for years. Apparently they have used this design in the past as well. Although the principle is different from a radiometer, the result is the same — spinning!

As for using it to change orbits, that doesn't sound even remotely practical.

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A Crookes Radiometer was one of my most memorable gifts as a little kid. The fact that sunlight would push the black side more than the white side of each vane proved that atoms exist, or at least so said the back of the package. I was seeing atoms! Changed my life.

As @BobJacobsen points out, these guys require low pressure gas to work, and they need the gas to be pretty much at rest with respect to the spacecraft, otherwise aerodynamic forces would dominate and the configuration would stop when torques due to drag on each vane balanced.

So this wouldn't work in a low density atmosphere of a planet the spacecraft were orbiting, it would have to be roughly at rest in a low pressure gas, and the forces would have to be lower than the pressure of the solar wind.

I don't think there is a situation anywhere in space where this would work.

However, on the surface of a body with a very low pressure atmosphere, such as a large asteroid or small planet or Moon, the demonstration might work. But the question is about a spacecraft or propulsion, so this doesn't apply.

Slightly related:

below: Image (GIF) of a Crookes Radiometer, from here.

enter image description here

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