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Not one probe that has or will leave the Solar System (Pioneer 10, Pioneer 11, Voyager 1, Voyager 2, and New Horizons) has a Solar Power System. This leads to the question, is there a reason behind this? And secondly if a probe were to be launched out of the Solar System with a solar power system couldn't it theoretically communicate with earth indefinitely? The reasoning behind that is even billions of miles out they could turn off all systems for say 3 months, let the batteries recharge and then after the 3 months turn the power back on,communicate with it for a few days and then repeat the process.

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Solar panels for a few months in deep space are more likely to collect enough energy to transmit for seconds or minutes rather than days (my crude estimate). The trade off in weight between them and an RTG would tend to favour the RTG (again, my crude estimate). – Andrew Thompson 15 hours ago
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Can you show a link or support your premise that realistic PV cells can produce power at very low light levels? Recombination can be a problem, and it may get worse as radiation damage increases. – uhoh 15 hours ago
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You'd also need magic batteries that don't self-discharge, and magic electronics that can wake up and work when extremely cold. Rosetta had to sleep for two years because it's panels were not sufficient to warm the entire spacecrat electrically! See why-actually-did-rosetta-have-to-go-into-hibernation-for-2-5‌​-years? – uhoh 15 hours ago
    
Thanks for the answer to the first question! I just don't see a response that covers my second question. – Aaron M 3 hours ago
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Solar power generation capability drops with 1/R^2, where R is the distance between the spacecraft and the Sun. Meanwhile, the communication at a given power and comm rate also drops with 1/R^2 communicating at a given rate, where R is the distance between the spacecraft and the Earth. Together, those combine to make for a 1/R^4 drop in solar power / comm. Using solar power simply does not work beyond Jupiter. – David Hammen 2 hours ago

There isn't enough solar energy to power a spacecraft once you get a certain distance from the sun, even if you had 100% power conversion efficiency. The intensity of sunlight diminishes inversely proportional to the square of the distance from the Sun. The intensity of sunlight at Mars is half what it is at Earth, and at Jupiter it's only 5%. At the Earth's orbit the sun's intensity is about 1400 W/m2 (watts per meter squared), but at Uranus it's only 4 W/m2. Juno's solar array, which is about 70 square meters and 10%-ish efficiency, generates almost 500 Watts of power at Jupiter, but would only generate 28 Watts at Uranus, which is nowhere near what it would need to function. Pluto averages 1 W/m2, which equates to about 7 Watts. Even if you had 100% efficiency a 70m2 array would generate 70 Watts at that distance.

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The primary missions of the Voyagers, Pioneers, and New Horizons was exploration of the planets of our solar system, not beyond it. Continuous power during their approaches to our system's planets was much more important than their ability to tell us about interplanetary space. Any mass dedicated to solar panels would be mass that couldn't be spent on scientific instruments.

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Though it is worth noting that the Voyagers have given us valuable information as they pass out of the Solar System. – Phiteros 12 hours ago

In addition to a few hundred W of electrical power, an RTG produces a few kW of thermal power which is used to keep the spacecraft warm. Without heaters, the spacecraft's temperature would drop to -200 °C. It needs to be warmed up for the electronics to work well, and the thermal cycling would soon break stuff.

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Why -200°C and not less? – gerrit 8 hours ago
    
-200 was a WAG, not an exact value. – Hobbes 8 hours ago

A simple estimate, at a distance of 50 AU (1 AU is the distance earth to sun) the solar power is 1/2500 of that at earths orbit. Collecting energy for three months and use it in three days is only a factor of 30, but we need more than a factor of 2500. 3*2500 is 7500 days or more than 20 years. As others wrote, the self discharge of the batteries would be much faster than this slow charge.

The Kuiper belt goes from some 40 to 75 AU, I used 50 AU for the estimate.

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