🔥 Orbital Maneuver Δv Calculator

Hohmann transfer · combined plane change · pure inclination change · phasing

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Hohmann Transfer

Burn 1 Δv
– m/s
Burn 2 Δv
– m/s
Total Δv
– m/s
Transfer time
– min

Pure Plane Change

Circular velocity
– km/s
Plane-change Δv
– m/s

Phasing Maneuver

Phasing orbit period
– min
Phasing perigee/apogee
– km
Total Δv (2 burns)
– m/s
Time to complete
– h
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📖 How to use

  1. Hohmann: enter start/target circular altitudes; add a Δi to combine the plane change with the second (slowest) burn — far cheaper than a separate change.霍曼转移：输入起始/目标圆轨道高度；填 Δi 可把倾角改变合并到第二次（速度最低处）点火——远比单独改倾角省。
  2. Pure plane change: Δv = 2·v·sin(Δi/2). At LEO speeds 1° costs ≈ 130 m/s — avoid plane changes whenever the launch can do them.纯改平面：Δv = 2·v·sin(Δi/2)。LEO 速度下每 1° 约需 130 m/s——能靠发射入轨解决就不要在轨改。
  3. Phasing: to shift along-track by Δφ, lower (to advance) or raise (to fall back) the orbit for N revs, then restore. More revs = less Δv but more time.相位机动：沿迹移动 Δφ 时，先降轨（超前）或升轨（滞后）飞 N 圈再恢复。圈数越多 Δv 越省，但耗时越长。
  4. Add the drag make-up Δv from the Orbit Lifetime tool and margins (typ. 5–10%) to build the full mission Δv budget.再加上轨道寿命工具给出的阻力补偿 Δv 与余量（通常 5–10%），即得完整任务 Δv 预算。

Maneuver equations

Hohmann: transfer ellipse a_t = (r₁+r₂)/2; Δv₁ = √(μ(2/r₁−1/a_t)) − √(μ/r₁), Δv₂ = √(μ/r₂) − √(μ(2/r₂−1/a_t)); time = half the transfer period.

Combined 2nd burn: Δv₂ = √(v_ta² + v₂² − 2·v_ta·v₂·cos Δi) — doing the plane change where velocity is lowest.

Pure plane change: Δv = 2·v·sin(Δi/2)

Phasing: the phasing period is T_p = T·(1 − Δφ/(360·N)); the burn pair enters and exits an ellipse with the same radius at the burn point. The tool warns if the phasing perigee dips into the atmosphere.

All computation runs locally in your browser.

机动公式

霍曼转移：转移椭圆 a_t = (r₁+r₂)/2；Δv₁ = √(μ(2/r₁−1/a_t)) − √(μ/r₁)，Δv₂ = √(μ/r₂) − √(μ(2/r₂−1/a_t))；转移时间为转移轨道周期之半。

合并第二次点火：Δv₂ = √(v_ta² + v₂² − 2·v_ta·v₂·cos Δi) —— 在速度最低处改平面。

纯改平面：Δv = 2·v·sin(Δi/2)

相位机动：相位轨道周期 T_p = T·(1 − Δφ/(360·N))；两次点火进出一条在点火点等半径的椭圆。若相位轨道近地点过低，工具会给出告警。

全部计算在你的浏览器本地完成。