Mass ratio of solar-electric versus radioisotope thermo-electric power for propulsion; beyond how many AU do RTGs win?

Solar-electric propulsion has been used several times now in deep space missions. This question explores the scalability in comparison to Radioisotope thermoelectric generation or other nuclear-based sources.

Primary part

Suppose a deep-space mission where smallsats needs to be placed at several distances from the Sun in circular orbits. Each requires 1 kW of electrical power (thermal management for the coldest orbits is done with separate radioisotope heating units).

Does solar-electric always win over RTGs in terms of mass? Below 1 AU it's almost certain that solar-electric power wins, but at what distance from the Sun would the cross-over point be where, roughly speaking the two types of power systems would be similar masses?

Reasonable extrapolation and estimation are fine, we don't need a design review. I'm just wondering if these points are in the asteroid belt or the Oort cloud.

Secondary (optional) part

If the power requirement were much lower, say 1 W or 10 W, would the crossover point be roughly the same? Or does the scaling of mass with output power behave very differently for one versus the other?

Just fyi Juno had to hibernate for 2.5 years because there wasn't enough sunlight near aphelion, and the really-deep-space probes all used RTGs.

• Don't forget actual nuclear reactors, as well. Nov 26, 2019 at 8:36
• @ikrase I didn't, they're covered under "...or other nuclear-based sources." in the first sentence.
– uhoh
Nov 26, 2019 at 11:09
• @RussellBorogove that's part of the question, yes. The mass of a power generation system may not drop linearly as the output rating drops (e.g. a 1 W RTG may not be 0.001 of the mass of a 1 kW RTG), and one might drop more slowly than the other.. It doesn't have to be exactly 1 W it could be 10 W if there's more data available. This might be a more difficult part of the question to answer.
– uhoh
Nov 26, 2019 at 23:02
• @RussellBorogove I've changed to "two types of power systems". An ideal answer would identify the crossover point for a 1 W rating and a 1 kW rating. If one assumes that for both system types the mass scales the same way with power rating (as this answer does), then the two power ratings would have a crossover at the same distance from the Sun.
– uhoh
Nov 26, 2019 at 23:57
• Yes, that’s much clearer. Nov 27, 2019 at 1:30

With current technology: 4.3AU.

From wikipedia, it appears that the most powerful flight-proven RTG had a power density of 5.4W/kg. From NASA, current (as of 2017) solar technology has a power density of 100W/kg.

The power output of a solar cell drops off with the square of the distance from the sun. So, let's assume we have 1 kW at 1 AU. The mass of this cell would be:

$$m_o = \frac{1000W}{100W/kg} = 10 kg$$

The mass as we move away from the sun is $$m_{req} = m_oD^2$$, where $$D$$ is the distance from the sun in AU.

The RTG's output is constant and you'd need a mass of 185 kg to get 1 kW.

Plotting this and finding the intersection gives you 4.3 AU.

From the NASA report:

Solar Arrays: The types of solar arrays currently in use are: a) body-mounted arrays, b) deployable rigid arrays, and c) flexible fold out arrays. During the past 25 years, the specific power of solar arrays has improved from 30 W/kg to 100 W/kg. In the past decade, these advances have enabled several orbital and surface missions at Mars, as well as flyby and orbital missions to small bodies and inner planets.

Limitations: In spite of these advances, SOP solar power systems are not attractive for the following future planetary mission concepts:

1. Outer planetary missions beyond Saturn, because of limited performance capabilities at low solar irradiance and low-temperature environments;
2. Low-altitude Venus aerial and surface missions, due to their limited operational capabilities at high temperatures, high/low solar irradiance, and corrosive environments;
3. Long-duration Mars surface solar powered missions, because of dust accumulation on solar arrays;
4. High-power, solar electric propulsion missions to small bodies and outer planets, because such solar arrays would be heavy, bulky, and could not function in LILT environments.
• Thank you for the speedy and conclusive answer! I added a bit of info from the source in case the NASA link breaks, which happens from time to time as they move things around.
– uhoh
Nov 26, 2019 at 15:33
• Both solar arrays and RTGs degrade significantly over time; it would be interesting to see how the break-even distance changes over time. Nov 26, 2019 at 21:27
• – uhoh
Feb 14, 2020 at 5:27