My basis for the guess being the cost of deep space missions, the general lack of interest in deep space missions and the inherent cycle times between probes to particular planets.
I don't know why there would be orbiters around all of the planets at the same time. It would involve a serious committment of time and resources, and without a compelling reason I don't know why anyone would do it. It might happen by coincidence if there were multiple agencies involved, so perhaps my answer should be post-2200 rather than never.
I have no idea, but I think I've been immersed in history too much lately, because I thought, "Wait, eight planets, that doesn't sound right..." (pause, in which anyone else would say "But there are nine!") "Isn't it actually seven?"
By this do you mean when will we likely have simultaneous orbiters around all eight planets, or when we will have put orbiters around all eight planets? The latter is probably within thirty years, considering that we're only missing Uranus and Neptune. The former is going to be when it's worthwhile having permanent orbiters, and when we figure out how to actually do that with Mercury, which is an indeterminate amount of time.
How hard is it to get a long term orbiter around Mercury? How fast does the Sun perturb any satellites there? I don't foresee a long term orbiter there unless we have some reason to put one at a Lagrange point.
I'll go with never, being rather pessimistic about the prospects for impending environmental, economic, and social collapse, pandemic, class warfare, (insert your preferred, clichéd gloom & doom here) ....
Somewhat to my own surprise, I voted "Never". It's taken >50 years to get this far, and we might be at or past the peak.
Given that very soon now, the US will no longer have a manned space program, I'm feeling pretty pessimistic about the future of space exploration in general.
Mercury reason #1: Instead of using orbiters at Mercury, Robert Forward's Statite's might be used to hover such that they are constantly in the sky above the more useful polar regions.
Mercury reason #2: Some of the people commenting above wondered what need there would be to have orbiters simultaneously around each planet. One reason involves climate change here on Earth. I'm not a climatologist, but I imagine that it would be useful to understand the sun's effect on the atmospheres of each of the planets, so that we can better distinguish between the effects of the sun, and other terrestrial causes of climate change ("Beware the beast man, for he will make a desert out of his home and yours....") I'm thinking of this system-wide monitoring as taking place in a moderately far-off future where future tech makes things a bit easier. But Mercury, being atmospherically-challenged, might be the one planet where we wouldn't monitor the sun's effect - so Mercury would be the spoiler, and we'd only have 7 of 8. On the other hand, as Pluto's atmosphere resurrects itself (the atmosphere comes and goes at different points in its orbit), we might be monitoring its atmosphere instead, so we'd still have 8 orbiters around objects historically thought of as planets. And maybe we'd want to monitor the atmosphere of Titan, and maybe even Triton's too.
Alternatively: Despite Uranus' tilt, despite its rings, despite Mirada's deep canyons, and despite Uranus' other various unique features, it might be viewed as the most boring of the planets, and I can imagine a time when it is neglected while each of the other planets is being simultaneously visited.
This is fun - it's a science-based elimination game! Mercury/Venus: I like the answers people have given above, but these are the hard ones to keep funding. Hmm. But in another 2-3 funding cycles, the Decadal Surveys might think about them again. Earth: well, guaranteed. Mars: ditto. Jupiter: Juno to launch very soon. Europa if you're into the long-term payoffs (and depending where this decade's Europa/Titan fight goes; by the next 3 funding cycles, guaranteed to get them both). Saturn: Titan, Titan, Titan. And Enceladus. Frankly, you're going to have to drag people away from this one if you want them to stop looking at it. Uranus: If the Cassini crowd get another orbiter to go to Titan, we can send Cassini to Uranus for the better part of a decade. Neptune: Triton! We don't have to go to the Kuiper Belt to look at a KBO, and we can go into orbit instead of zooming by!
So all 8? Pushing it...but the ones that go to the outer Solar System in particular tend to be long-term missions. Anyway, the science will be more important than the simultaneity :)
On a more sierous note, one of the things that may just limit the amount of simultaneous deep space missions might not be the cost of the orbiters themselves or the lead times, but the amount of staff you need on the ground to guide the mission and digest the data coming back. NASA or ESA personell budgets are not infinite after all.
Here's a fast mission to explore a planet's poorly understood geology.
I once did a little research trying to figure out what sort of devices could function for extended periods in molten iron, and there are a few things, like immersion sensors, that the steel industry uses. Stevenson, like Landis, proposed Stirling coolers.
I picked 2050 because A) it's a semi-round number, and B) I enjoy being optimistic about sending unmanned stuff into space. But I certainly am not envisioning NASA (or The Big Governmental Space Agency of 2050) having 8 simultaneous orbiters.
ion engines mean cheap small probes are quite likely, and will be more and more common - also the energy cost for a mission will be less important with a SI in the tens of thousands. More countries in space, trying to get recognition means open slots will be rarer and rarer. So, really, I would have chosen 2020, but went conservative and chose 2050.
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If the question is at what time will all of them have or have had orbiters, I'll guess 2100.
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Given that very soon now, the US will no longer have a manned space program, I'm feeling pretty pessimistic about the future of space exploration in general.
Blame Mercury
Mercury reason #1: Instead of using orbiters at Mercury, Robert Forward's Statite's might be used to hover such that they are constantly in the sky above the more useful polar regions.
Mercury reason #2: Some of the people commenting above wondered what need there would be to have orbiters simultaneously around each planet. One reason involves climate change here on Earth. I'm not a climatologist, but I imagine that it would be useful to understand the sun's effect on the atmospheres of each of the planets, so that we can better distinguish between the effects of the sun, and other terrestrial causes of climate change ("Beware the beast man, for he will make a desert out of his home and yours....") I'm thinking of this system-wide monitoring as taking place in a moderately far-off future where future tech makes things a bit easier.
But Mercury, being atmospherically-challenged, might be the one planet where we wouldn't monitor the sun's effect - so Mercury would be the spoiler, and we'd only have 7 of 8. On the other hand, as Pluto's atmosphere resurrects itself (the atmosphere comes and goes at different points in its orbit), we might be monitoring its atmosphere instead, so we'd still have 8 orbiters around objects historically thought of as planets. And maybe we'd want to monitor the atmosphere of Titan, and maybe even Triton's too.
Blame Uranus
Re: Blame Uranus
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Mercury/Venus: I like the answers people have given above, but these are the hard ones to keep funding. Hmm. But in another 2-3 funding cycles, the Decadal Surveys might think about them again.
Earth: well, guaranteed.
Mars: ditto.
Jupiter: Juno to launch very soon. Europa if you're into the long-term payoffs (and depending where this decade's Europa/Titan fight goes; by the next 3 funding cycles, guaranteed to get them both).
Saturn: Titan, Titan, Titan. And Enceladus. Frankly, you're going to have to drag people away from this one if you want them to stop looking at it.
Uranus: If the Cassini crowd get another orbiter to go to Titan, we can send Cassini to Uranus for the better part of a decade.
Neptune: Triton! We don't have to go to the Kuiper Belt to look at a KBO, and we can go into orbit instead of zooming by!
So all 8? Pushing it...but the ones that go to the outer Solar System in particular tend to be long-term missions.
Anyway, the science will be more important than the simultaneity :)
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I once did a little research trying to figure out what sort of devices could function for extended periods in molten iron, and there are a few things, like immersion sensors, that the steel industry uses. Stevenson, like Landis, proposed Stirling coolers.
The spin-offs seem obvious.
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So, really, I would have chosen 2020, but went conservative and chose 2050.