Sure thing, but before we dive into the numbers let’s pin down a few things. What kind of ion engine are you using—cesium, xenon, or something exotic? Do you have a thrust‑to‑weight ratio and specific impulse ready? And, crucially, what trajectory profile are you assuming—direct transfer, Hohmann swing‑by, or a powered‑entry burn? Once we nail those inputs I can sketch a quick energy‑budget equation and run a sanity check on the 30 % claim. Let me know the details, and we’ll see if the math sticks.

Got it. Let’s break it down step by step. First, the thrust from a 10 kW cesium engine at 2.5 m/s² gives about 250 N. Scaling that to your 200 kW budget you’d have 20 × the thrust, so roughly 5 kN. With a thrust‑to‑weight of 0.08, your spacecraft mass is about 62.5 kN/0.08 ≈ 781 kg. That’s a pretty light ship for the power you’re pulling. For a Hohmann from Earth to Mars, the Δv needed is about 2.9 km/s for the transfer burn and another 2.9 km/s for the Mars insertion, ignoring plane changes. Your ion engine’s specific impulse of 4,500 s means each kilogram of propellant gives you 44.4 km/s of Δv. If you’re burning 200 kW over 30 days, the total impulse is 200 kW × 30 days × 86400 s/day = 5.18×10¹¹ N·s. Dividing that by 44,400 m/s gives roughly 11,700 kg of propellant – that’s impossible for a 780 kg craft. So something’s off: either the power figure per kilogram is too low, or the coast time is too short for that Δv. If you reduce the coast to, say, 10 days, the total impulse drops to 1.73×10¹¹ N·s, giving 3,900 kg of propellant – still more than five times the ship mass. That tells us the 200 kW budget is too generous for a 30‑day coast unless you’re dumping a huge propellant load, which would push the mass way up and lower the thrust‑to‑weight. So the math suggests that a 30‑day coast with 200 kW won’t slash travel time by 30 % without dramatically changing the mass or accepting a much smaller Δv. If you keep the mass at 780 kg, you’d need to spread the burn over a longer coast or cut the power. Alternatively, use a higher‑power engine or accept a larger propellant load, but that eats into the thrust‑to‑weight and might negate the time benefit. Bottom line: the numbers you gave don’t line up for a 30 % faster transfer. Re‑check the power per kilogram, the coast duration, and the propellant mass. Once you have those aligned, we can run a more realistic simulation.

No worries, that typo makes a huge difference. With 50 kW over 30 days you get about 1.3×10¹¹ N·s of impulse. Divide that by the 44.4 km/s per kg you get from a 4,500 s Isp and you’re looking at roughly 3,000 kg of propellant. That’s still way more than a 780 kg craft, so you’re either going to need a bigger ship or cut the coast time. If you keep the 30‑day coast, the Δv you can deliver is far less than the 5.8 km/s total needed for a full Hohmann transfer, so the 30 % faster trip is unlikely unless you drastically reduce the mass or increase the engine’s specific acceleration. Re‑run the mass balance with the new power figure and see how the propellant fraction changes. Good luck, and let me know what you find.

Looks like the math lines up with what you’re seeing. The 30‑day coast really caps you at about 2.5 km/s with a 50 kW budget and a 0.05 thrust‑to‑weight, so you’re only getting half the Δv you need for a full Hohmann. To hit the 5.8 km/s you’d have to crank the power up to roughly 100 kW or cut the coast to about 10 days, but that bumps the launch mass even higher. If you’re set on the 30‑day cruise, the only way to keep the 30 % faster time is to reduce the Δv—maybe by using a more efficient transfer or adding a plane‑change at the same time. Either way, the numbers show you can’t get the 30 % cut without re‑balancing mass or power. Let me know which angle you want to explore next.