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I'm working on a somewhat* hard scifi story set in a solar system that contains a hot jupiter. Frankly building a large station in the shade (?) of the L2 point of the hot jupiter sounds metal, and I'm trying to think of why someone might want to build one.

Premise for the station

My tenuous thought so far, is to have the shaded L2 station specialize in sending mining drones to the nearby L4 and L5 points and mine carbonaceous asteroids that accumulate there. Then use the high levels of solar power, to refine those into carbon nanotubes via laser ablation for spacecraft production. The L2 station serves as a dropoff point for those drones, and holds a significant sophont crew for their repair/maintence (electronics being subject to high wear and tear this close to the sun) and merchandising refined products. Power could be beamed from satellites orbiting the hot jupiter in a sun-synchronous orbit.

Setting Schpiel

There are at least two other habitable planets/moons elsewhere in the system, and technology wise a somewhat more advanced than us (none human). The basic premise is a worldbuilding project wherein the solar system, planets and other conditions conspire to make expansion into space significantly easier than here (more readily available mining locations, compact system, lower gravities, etc.). But the short of it: they have a larger space economy, but not too significantly greater tech.

Questions

I'm not an astronomer or a chemist, is there any egregious misunderstandings on my part? Would a hot jupiter L2 actually provide a shelter from a sun for the station?

Research indicates that hot jupiters suffer from significant atmospheric loss, creating an almost comet-like plume. See this question. I'm guessing any station at L2 will be squarely within this, would that be detrimental, beneficial, neither? What would the view look like from the station?

Some numbers for anyone curious

Star: 0.8 Solar Mass Orange Dwarf

Hot Jupiter: 1 Jupiter mass, 0.06 AU from the star, 6.1 orbital period, near circular orbit

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  • $\begingroup$ I very much doubt the hot Jupiter covers enough sky. $\endgroup$ Dec 3, 2022 at 5:42
  • $\begingroup$ I'm not sure it would be necessary, even if it were to work. What's to stop the station working in full view of the sun, with an appropriate heat shield? It could be stationed at L4/L5, for instance. $\endgroup$ Dec 3, 2022 at 13:44

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Using formula given here I've estimated L2 to be at 660000 km from your planet. Given that Jupiter's radius is 70000 km, and hot jupiters tend to be even bigger due to expansion of overheated atmosphere, your station may be very close to or inside said atmosphere, and close to radiation belts.

Try to make spreadsheet with maths that'll help you play with exact numbers, maybe better combination exists. Remember that carbon asteroids can dominate everywhere below snow line, so maybe your jupiter doesn't need to be hot. Planets umbra won't be a problem - Earth's umbra doesn't reach L2, but hot jupiter should cover its L2 completely due to its low density and big radius.

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  • $\begingroup$ Thank you that helps, especially pointing out that the atmospheric expansion would be relevant. I made a copy of a spreadsheet from a similar L2 shading question and substituted values for known hot jupiter (en.wikipedia.org/wiki/HAT-P-1b). It wasn't quite 100% covered, but scaling the planet up a bit I was able to get it reasonably close. This is probably simplistic, but I think reasonable enough for the setting. docs.google.com/spreadsheets/d/… $\endgroup$
    – Wavedash
    Dec 3, 2022 at 17:36
  • $\begingroup$ Just wanted to update this since I went back and tried to do this more precisely with python. And found I made a mistake. As it happens if you increase the planet's mass it doesn't work -- because it also pushes out the l2 distance. Somewhat counter-intuitively, using HAT-P-1b as an example again, you want a lower mass. You get a permanent eclipse at 0.75% of its actual mass. $\endgroup$
    – Wavedash
    Dec 8, 2022 at 21:37
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I went back and re-did this a bit more precisely and wanted to share how in case it helps with similar L2 shading questions.(I still want to leave ZuOverture's answer since credit is due, and it also pushed me to use an existing hot jupiter system since they have odd characteristics).

Assuming, for simplification,

  • you can increase the planet's mass while keeping it's density the same then you can recalculate what the new radius should be after increasing the planets' mass

  • you assume the planet is much smaller than the star you can also calculate how far the planet's umbra extends (where a total eclipse occurs) and where the l2 point is located (as ZuOverture points out)

More practically the below Python code will let you find where this occurs given those two assumptions (using Hat-P-1b as a basis):

=import numpy as np
# Hat-p distance from the star AU to km (it has a near circular orbit)
planetary_distance = (0.05561)*1.496e+11

# Radii Involved (m)
star_radius  = 1.123*6.95700e+8 # Hat-P-b's star radius to m
giant_radius = 1.319*7.1492e+7  # Hat-P-b radius to m

# Masses involved (kg)
giant_mass   = 1.319 *(1.898e+27)
star_mass    = 1.16  *(2.0e+30)

# Calculate density given mass and radius of the planet
giant_density =  (3*giant_mass)/(4*np.pi*giant_radius**3)


# Rescale it (aiming for lagrange < umbra, i.e. have l2 be completely eclipsed)
giant_mass *= 0.75
solve_tmp = (3*giant_mass)/(4*np.pi)
giant_radius_scaled = ((1/giant_density) * solve_tmp) ** (1./3.)

# Calculate umbra and l2 distance (assuming mass of the star >> planet, which it should be)
umbra = (planetary_distance*giant_radius_scaled)/(star_radius - giant_radius_scaled)
lagrange_point2 = planetary_distance* (giant_mass/(star_mass*3)) ** (1. / 3)

print("Planetary Density: ",giant_density, "kg/m3")
print("Umbra Distance: ",umbra, "km")
print("L2 Distance: ",lagrange_point2, "km")
print("Umbra/Lagrange: ",umbra/lagrange_point2)
print("Lagrange < Umbra: ",lagrange_point2 < umbra)

Planetary Density: 712.763854273664 kg/m3

Umbra Distance: 1024668956.4167596 km

L2 Distance: 537545830.7010522 km

Umbra/Lagrange: 1.9061983144403056

Lagrange < Umbra: True

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  • $\begingroup$ Your L2 formula is off - it's /3 not *3 in the cubic root - however that doesn't make much difference. Furthermore a lot of diffuse radiation decreases your effective shadow length. The bigger point is however that your formula is estimating whether the core shadow reaches L2, but that's not where you can sit at, as L2 is dynamically unstable - you have to orbit L2 in halo orbits - making it much harder to sit in the shadow. as space station. $\endgroup$ Dec 9, 2022 at 3:21
  • $\begingroup$ A second point given the other answer - don't overestimate the effects of an outflowing atmosphere - 1. the measured radius is the measured radius. Whether the atmosphere of HAT-1b is outflowing, doesn't allow you to add a larger value to its radius, as that is already known. 2. Inflated radii of Hot Jupiters (or "super puffs") are not thought to be due to escaping atmospheres - the densities in the escaping parts of the atmosphere are too low to play a role in obscuring or shadowing, at least in the optical. In the UV that would be a different matter. $\endgroup$ Dec 9, 2022 at 3:25
  • $\begingroup$ L2 formula -- happy to correct, but I pulled the equation from here en.wikipedia.org/wiki/Lagrange_point#L2. I may have been looking at this too long but I think it checks out? I am realizing the umbra formula needs work, as you said "just" reaching the station isn't going to necessarily mean permanent solar eclipse. I think the umbral part of this formula does need work, checking checking... $\endgroup$
    – Wavedash
    Dec 9, 2022 at 4:11
  • $\begingroup$ 1. I should have explained better. I just used HAT-1b as a basis -- first set up my equations for the lagrange point and umbra, then scaled the mass (keeping the density the same and recalculating the radius ) until the lagrange < umbra condition was met. It was a starting point for some reasonable "real world" numbers, then I just messed with the mass and radii. 2. The part I used was just calculating the density of HAT-1b, not anything about escaping atmosphere. Sorry that was me being not super clear edit: more specifically this occurs at the "# rescale it" part $\endgroup$
    – Wavedash
    Dec 9, 2022 at 4:15
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    $\begingroup$ You have $r_H=a_p (m_p/m_s*3)^{1/3}$, correct is $r_H=a_p (m_p/(m_s*3))^{1/3}$. Yeah I ignored the rescaled radius as part of your argument, because your code doesn't use it to compute whether L<U. No worries. $\endgroup$ Dec 9, 2022 at 4:19

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