Gravity Assist (Slingshot)
The trajectory path refers to the path of Voyager 2 which is kept in the plane of the ecliptic. The spacecraft could be sent on to Uranus and Neptune by means of utilizing gravity assists during its fly-by of Saturn.
When it travels inside the solar system, we use gravity assist to gain the acceleration without consuming too much fuels. It is the so called slingshot which follows the law of conservative energy. It changes a spacecraft's velocity relative to the Sun. To a first approximation, from a large distance, the spacecraft appears to have bounced off the planet. That is an elastic collision in physics. If the spacecraft travels in a hyperbola orbit, it can leave the planet without firing its engine.
The principle is like that, suppose that you are a "stationary" observer and that you see: a planet moving left at speed U; a spaceship moving right at speed v. If the spaceship is on the right path, it will pass close to the planet, moving at speed U + v relative to the planet's surface because the planet is moving in the opposite direction at speed U. When the spaceship leaves orbit, it is still moving at U + v relative to the planet's surface but in the opposite direction, to the left; and since the planet is moving left at speed U, the total velocity of the spacecraft relative to you will be the velocity of the moving planet plus the velocity of the spacecraft with respect to the planet. So the velocity will be U + ( U + v ), that is 2U + v.
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