 Gravity assist

A gravity assist is a spacecraft flyby that uses the gravity of a moving planet or other massive body to change the spacecraft's trajectory and its orbital energy relative to another body, such as the Sun. In the ideal unpowered two-body encounter, the incoming and outgoing speeds far from the planet are equal in the planet's reference frame. Their directions differ. Adding the planet's motion converts that directional change into a possible speed change in the Sun's reference frame.^[ref]

Write the planet's nearly constant velocity during the encounter as $\mathbf{V}$, and the incoming and outgoing planet-relative velocities as ${\mathbf{u}}_i$ and ${\mathbf{u}}_o$. Then ${\mathbf{v}}_i=\mathbf{V}+{\mathbf{u}}_i$, ${\mathbf{v}}_o=\mathbf{V}+{\mathbf{u}}_o$, and $|{\mathbf{u}}_i|=|{\mathbf{u}}_o|$. Subtracting the squared speeds gives the local change in specific orbital energy:For a hypothetical $90^{\circ }$ turn, choose $\mathbf{V}=(10,0)$, ${\mathbf{u}}_i=(-5,0)$ and ${\mathbf{u}}_o=(0,5)$, all in $\mathrm{km}{\mathrm{s}}^{-1}$. Planet-relative speed stays $5$, while Sun-relative speed changes from $5$ to $\sqrt{125}\approx 11.18\mathrm{km}{\mathrm{s}}^{-1}$. The specific-energy gain is $50\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}$. Whether a given turn is physically available depends on the planet's mass, the incoming speed and the permitted closest approach.

Conservation of energy is maintained because the planet and spacecraft exchange momentum and energy. The planet's change is extremely small because of its much greater mass. A different encounter geometry can remove orbital energy or mainly change orbital inclination; Ulysses spacecraft used the latter possibility to reach high solar latitudes.^[ref]

Gravity assist, also known as a gravitational slingshot, is a maneuver used in spaceflight to increase or decrease the velocity of a spacecraft by utilizing the gravitational pull of a planet or moon. This technique allows spacecraft to gain energy and change their trajectory without using additional fuel, making it an efficient means of traveling through the solar system. Here's how it works: 1. **Approach the Body**: The spacecraft approaches the target celestial body (like a planet) at a specific angle and speed.