Maximum angle of rotation during gravitational maneuver

A gravitational maneuver is a purposeful change in the trajectory and flight speed of a spacecraft under the influence of the gravitational fields of celestial bodies. The maximum angle of rotation of the rocket during a gravitational maneuver depends on the first cosmic velocity of the planet around which the maneuver is performed, and the speed of the rocket relative to this planet. The law describes the closest possible maneuver, when aiming range is at planet radius.

Conditions:

1. Aiming range equals the planet radius.

maximum_angle

Maximum angle of rotation during the gravitational maneuver.

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

first_cosmic_speed

First cosmic speed of the planet.

Symbol:

v_1

Latex:

\(v_{1}\)

Dimension:

velocity

rocket_speed

speed relative to the planet.

Symbol:

v

Latex:

\(v\)

Dimension:

velocity

law

phi = atan((v_1 / v)^2)

Latex:

\[\varphi = \operatorname{atan}{\left(\left(\frac{v_{1}}{v}\right)^{2} \right)}\]