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Hohmann Transfer Orbit

The minimum-energy transfer ellipse between two coplanar circular orbits. It requires two impulsive burns (trans- and periapsis burns) at the initial and final radii.
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The statement of the theorem

Let r1r_1 and r2r_2 be the radii of two coplanar circular orbits, and μ\mu be the gravitational parameter. The transfer semi-major axis is defined as atrans=r1+r22a_{trans} = \frac{r_1 + r_2}{2}. The required initial velocity burn (ΔV1\Delta V_1) and final velocity burn (ΔV2\Delta V_2) are given by:\n\nΔV1=∣μ(2r1−1atrans)−μr1∣\Delta V_1 = \left| \sqrt{\mu \left( \frac{2}{r_1} - \frac{1}{a_{trans}} \right)} - \sqrt{\frac{\mu}{r_1}} \right|\nΔV2=∣μr2−μ(2r2−1atrans)∣\Delta V_2 = \left| \sqrt{\frac{\mu}{r_2}} - \sqrt{\mu \left( \frac{2}{r_2} - \frac{1}{a_{trans}} \right)} \right|