Documentation / @interstellar-tools/equations / hohmannTransfer

Function: hohmannTransfer()

function hohmannTransfer(
  r1: number,
  r2: number,
  mu: number
): HohmannTransferReturnType;

Defined in: manoeuvres/hohmann-transfer.ts:49

Hohmann transfer (coplanar, circular ($r_1\to r_2$)).

Definitions

$$a_t=\frac{r_1+r_2}{2}$$$$\mathrm{\Delta }{v}_1=\sqrt{\frac{\mu }{r_1}}(\sqrt{\frac{2r_2}{r_1+r_2}}-1),\mathrm{\Delta }{v}_2=\sqrt{\frac{\mu }{r_2}}(1-\sqrt{\frac{2r_1}{r_1+r_2}})$$$$\mathrm{\Delta }{v}_{\text{total}}=\mathrm{\Delta }{v}_1+\mathrm{\Delta }{v}_2,t_t=\pi \sqrt{\frac{a_t^3}{\mu }}$$

Conventions

• Inputs in SI: ($r_1,r_2$) in meters, ($\mu$) in m³/s².
• The returned ($\mathrm{\Delta }{v}_1,\mathrm{\Delta }{v}_2$) are magnitudes (non-negative). Their signs (prograde/retrograde) are provided separately for clarity.
• Works for ($r_2>r_1$) (raise) and ($r_2<r_1$) (lower). If ($r_1=r_2$): ($\mathrm{\Delta }v$)s are 0 and ($t_t$) is half the circular period.

Domain

• ($r_1>0,r_2>0,\mu >0$)

Parameters

Parameter	Type	Description
r1	number	Initial circular-orbit radius (m).
r2	number	Target circular-orbit radius (m).
mu	number	Standard gravitational parameter ($\mu$) (m³/s²).

Returns

HohmannTransferReturnType

Object with transfer semi-major axis at (m), burn magnitudes dv1, dv2, their sum dvTotal (m/s), transfer time tTransfer (s), and burn directions dir1, dir2.

Throws

If an input is not a number.

Throws

If ($r_1\le 0$), ($r_2\le 0$), or ($\mu \le 0$), or a value is non-finite.