= Hohmann transfer compared with a slow spiral
{c}
For $u=\sqrt{r_1/r_0}>1$, the sum of the two <Hohmann transfer> impulse magnitudes minus the integrated thrust per mass in a <quasi-circular spiral transfer> is
$$
v_0\frac{u-1}u\left[\frac{\sqrt2(u+1)}{\sqrt{u^2+1}}-2\right].
$$
It is negative because $(u+1)^2<2(u^2+1)$ is equivalent to $(u-1)^2>0$. Thus the Hohmann transfer uses less ideal total impulse for any strictly outward pair of coplanar circular orbits. This comparison does not optimize over all other transfer families.
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