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 angle of the gravitational maneuver depends on the aiming range, the mass of the planet and the velocity of the rocket relative to the planet.

Notation:

1. \(G\) (G) is gravitational_constant.

angle

angle of rotation during a gravitational maneuver (angle at which the velocity vector of the rocket rotates)

Symbol:

phi

Latex:

\(\varphi\)

Dimension:

angle

planet_mass

The mass of the planet.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

aiming_range

The aiming range is the euclidean_distance between the asymptote of the hyperbolic trajectory of the circumnavigation of the planet and its focus coinciding with the center of the planet.

Symbol:

d

Latex:

\(d\)

Dimension:

length

rocket_speed

Rocket’s speed relative to the planet.

Symbol:

v

Latex:

\(v\)

Dimension:

velocity

law

phi = 2 * atan(G * m / (d * v^2))

Latex:

\[\varphi = 2 \operatorname{atan}{\left(\frac{G m}{d v^{2}} \right)}\]