What delta-v is necessary for a spacecraft to raise its orbit altitude by 1km?

GPT-5.4

Answer: There is no single fixed delta-v for raising an orbit by 1 km, but for a typical circular low Earth orbit around 400 km altitude the total required delta-v is about 0.57 m/s using a two-burn Hohmann transfer.

I maintain my position, but the other responses sharpened the numerical example rather than changing the underlying conclusion. The key point remains that the question, as stated, is under-specified: the required delta-v depends on the central body, the initial orbit radius, and whether the orbit raise means changing apoapsis only or performing a full circular-to-circular transfer. The strongest support came from the answers that explicitly quantified the common Earth case. Both Claude Opus 4.7 and Gemini 3.1 Pro gave a consistent value of about 0.57 m/s total for raising a roughly 400 km circular Earth orbit by 1 km via a standard two-burn Hohmann transfer, with each burn about 0.28 to 0.29 m/s. That is fully consistent with my earlier statement that the answer is not universal and that a low Earth orbit example is well under 1 m/s. I would refine my previous wording slightly: instead of saying only “about 0.5 m/s total delta-v,” the better representative figure for a ~400 km Earth orbit is about 0.57 m/s total. That is a refinement of precision, not a change in position. I do not adopt Mistral Large’s stronger claim that it is “approximately 1 m/s in low Earth orbit,” because its own derivation produces about 0.57 m/s and then it jumps to “~1 m/s” for the two-burn case, which overstates the total by roughly a factor of two for the stated example. So the best final answer is still conditional rather than universal: there is no single fixed delta-v for “1 km,” but if the intended case is a typical circular LEO around Earth, the needed total is about 0.57 m/s.

Claude Opus 4.7

Answer: For a spacecraft in low Earth orbit near 400 km altitude, raising the circular orbit by 1 km requires a total delta-v of approximately 0.57 m/s via a two-burn Hohmann transfer, though the exact value depends on the central body and starting altitude.

I'm maintaining my original position because the physics are unambiguous and my calculation agrees closely with both GPT-5.4 (~0.5 m/s) and Gemini 3.1 Pro (~0.57 m/s). The derivation from the vis-viva equation for a small Hohmann transfer gives Δv_total ≈ (Δh/2r)·v, which yields ~0.566 m/s at 400 km altitude — this is a well-established result. I respectfully disagree with Mistral Large's claim that a 'more accurate' Hohmann calculation yields ~1 m/s per km in LEO. That appears to be an error. The Hohmann two-burn total is what my 0.57 m/s figure already represents; the approximation Δv ≈ (v/2(R+h))·Δh IS the small-Δh limit of the full Hohmann transfer, not a single-burn simplification. You can verify this directly: the first burn raises apogee by 1 km (Δv₁ ≈ 0.283 m/s), and the second circularizes at the new altitude (Δv₂ ≈ 0.283 m/s), summing to ~0.57 m/s. Doubling this to 1 m/s would double-count. An intuitive sanity check: the ISS performs reboosts of a few m/s to gain several kilometers of altitude, consistent with ~0.5–0.6 m/s per km, not 1 m/s per km. So my answer stands: ~0.57 m/s total for a 1 km raise in LEO near 400 km, scaling as 1/r^(3/2) so that GEO requires only ~0.036 m/s for the same 1 km altitude change.

Mistral Large (changed mind)

Answer: For a spacecraft in a circular low Earth orbit (LEO) around 400 km altitude, raising its orbit by 1 km requires a total delta-v of approximately 0.57 m/s, split between two burns in a Hohmann transfer.

After reviewing the responses from GPT-5.4, Claude Opus 4.7, and Gemini 3.1 Pro, it is clear that my initial estimate of ~1 m/s for a 1 km altitude increase in LEO was overly conservative. The other models consistently provided a more precise calculation, demonstrating that the correct delta-v is closer to 0.57 m/s for a typical LEO scenario (e.g., ~400 km altitude). Here’s why I am revising my position: 1. **Orbital Mechanics Clarification**: The delta-v required for a small circular orbit raise is derived from the Hohmann transfer, which involves two impulsive burns. The first burn raises the apogee, and the second circularizes the orbit at the new altitude. The total delta-v is not simply a linear function of altitude change but depends on the orbital velocity and radius, as shown by the approximation: [ Δv_total ≈ (Δh / (2r)) · v ] where ( r ) is the orbital radius and ( v ) is the orbital velocity. 2. **Consensus on LEO Values**: All three models converged on a value of ~0.57 m/s for a 1 km altitude increase at ~400 km altitude. For example: - Claude Opus 4.7 calculated 0.566 m/s using the formula above. - Gemini 3.1 Pro arrived at 0.57 m/s for the same scenario. - GPT-5.4 noted that the delta-v is "about 0.5 m/s" for a 1 km circular orbit increase in LEO, which aligns closely with the others. This consistency across independent calculations strengthens the credibility of the 0.57 m/s estimate. 3. **Missteps in My Initial Argument**: My earlier estimate of ~1 m/s was based on a simplified approximation that did not fully account for the two-burn nature of the Hohmann transfer. While the formula I used was directionally correct, it overestimated the delta-v by failing to split the maneuver into two smaller burns. The other models correctly emphasized that each burn contributes roughly half of the total delta-v, leading to a more accurate result. 4. **Dependence on Altitude**: The other models also highlighted how the delta-v requirement decreases with altitude, which I acknowledged but did not quantify precisely. For instance, at GEO (~35,786 km), the delta-v for a 1 km increase drops to ~0.036 m/s, illustrating the inverse relationship between delta-v and orbital radius. This nuance reinforces the importance of specifying the initial orbit when answering such questions. 5. **Practical Implications**: The revised estimate of ~0.57 m/s aligns with real-world observations, such as the International Space Station's reboost maneuvers, which typically require small delta-v values to raise the orbit by several kilometers. This practical validation further supports the accuracy of the lower delta-v figure. In summary, the detailed calculations and consensus from the other models have convinced me that the correct delta-v for raising a circular LEO orbit by 1 km is approximately 0.57 m/s, not 1 m/s. This adjustment reflects a more precise application of orbital mechanics principles and the two-burn Hohmann transfer method.

Gemini 3.1 Pro

Answer: The necessary delta-v to raise a circular orbit by 1 km depends on the central body and initial altitude, but for a typical spacecraft in a 400 km Low Earth Orbit (LEO), it requires a total of approximately 0.57 m/s.

I am maintaining my initial position because the mathematical principles of orbital mechanics consistently yield approximately 0.57 m/s for a 1 km altitude increase in a standard 400 km Low Earth Orbit (LEO). As Claude Opus 4.7 correctly pointed out, the approximation formula for a small altitude change (Δv_total ≈ (Δh / (2r)) · v) yields roughly 0.57 m/s total. This total already accounts for both burns of a Hohmann transfer (roughly 0.28 m/s each). Mistral Large accurately calculates the 0.57 m/s figure using the approximation formula but then erroneously claims that a two-burn Hohmann transfer yields a different, higher value of '~1 m/s'. The 0.57 m/s calculation is, in fact, the total combined delta-v for the complete two-burn circular-to-circular Hohmann transfer maneuver (approximately 0.28 m/s to raise the apogee, and 0.28 m/s to circularize). Therefore, my initial stance remains mathematically sound: the exact requirement scales inversely with the initial orbital radius (dropping to about 0.036 m/s in GEO, as both Claude and I noted), but 0.57 m/s is the definitive and precise answer for the standard LEO case.

Final Summary

The AI Roundtable reached a unanimous final consensus that raising a typical 400 km Earth orbit by 1 km requires approximately 0.57 m/s. Mistral Large initially suggested a higher value but corrected its position after Claude Opus 4.7 and Gemini 3.1 Pro demonstrated that 0.57 m/s already accounts for both stages of a Hohmann transfer. GPT-5.4 emphasized that these requirements scale with altitude, dropping significantly for spacecraft further from Earth.

All 4 models agreed