How do space probes use gravity tricks to fly to other planets?

"Gravity assist maneuvers alter a spacecraft's velocity vector and potentially allow spacecraft to achieve changes in velocity which would otherwise be unfeasible given our current technological limitations."

"redirecting JUICE toward its next destination: Venus (August 2025) and ultimately Jupiter (2031)."

"However we have also seen that for many planets, in particular Mercury and the outer planets, the energy levels are too high to reach for current launchers."

"Unfortunately, designing MGA trajectories is difficult and in order to find good solutions, deep space maneuvers (DSM) are often required which further increase the complexity of the problem."

"Recent advancements have revolutionized interplanetary spacecraft missions by combining low-thrust propulsion systems with planetary Gravity-Assist (GA) maneuvers."

"increasing the assumed total correction allowance from 0.10 to 0.40kms−1 reduces capacity-compliant configurations from 18 to 15."

"which used the gravity of Venus to slingshot its way to Mercury in 1974."

"use that planet’s massive gravity to bend their trajectories"

"The Titan encounter changed Voyager 1’s trajectory so it could not make any further planetary encounters"

"Such trajectories are commonly employed by planetary science missions to reach Mercury or the Outer Planets."

"In the PGA portion, continuous thrusts are conducted to change the speed and drive the altitude of a vehicle below the atmosphere edge."

"They may also be used at the Outer Planets for the design of science tours with multiple flybys of those planets’ moons."

"which will be fired by ground radio signal eight days after launching when tracking computers have precisely defined"

"future missions to completely or partially unexplored planets, such as Mercury7,8 or Pluto,9,10 will be possible thanks to gravity-assist maneuvers."

"Mariner 2 blasted away from .Cape Canaveral at 1:53 a.m. atop a powerful Atlas-Agena B rocket."

"show advantages in lower launch costs and low-energy capture."

"Dabei überholte die Sonde den Kometen und stoppte etwa 100 km vor ihm."

"it gradually began to slow down as planned for the long haul on the 109-day"

"Multiple gravity-assist trajectories have been extensively investigated over the last forty years, and their preliminary design has been approached mainly relying on the experience of mission analysts"

"Zunächst erkundete die Sonde sechs Wochen lang auf einem dreiecksförmigen Kurs das gravitative Fernfeld des Kometen, um seine genaue Masse und Schwerpunktlage zu bestimmen"

"the midcourse motor on Mariner 2 may be capable of"

"the design of missions to Pluto, Mercury or to the Sun, which require consideration of the real inclination of the orbit of the planet or of the final heliocentric orbit"

"optimal gravity-assist sequences are important in the design of low-thrust gravity-assist trajectories7."

"The reason that gravity assist is important for these missions is that they allow the spacecraft to reach outer planets which otherwise would not be possible because of the large amount of energy required."

"Incorporating gravity assists provides highly efficient interplanetary trajectories, enabling otherwise infeasible spacecraft missions."

"An interesting way to reduce such a requirement is to resort to Gravity Assist (GA) maneuvers as shown by Langevin2 in 1999."

"Gravity assist trajectories allow the spacecraft to gain momentum from the planets."

"Preliminary interplanetary trajectory designs frequently use simplified two-body orbital mechanics and linked conics methodology to model the complex trajectories in multi-body systems."

"The simplest way to model a gravity assist maneuver is to resort to link-conic approximation: the sphere of influence of a planet is assumed to have zero radius and the gravity maneuver is considered instantaneous."

"During a close approach of a gravitational body momentum is exchanged between the spacecraft and the gravitational body."

"Gravity assist (GA) proposed by Michael A. Minovitch is an indispensable technique for present solar system exploration."

"For an ideal hyperbolic orbit, not subject to perturbations or ∆v maneuvers, the modulus of the incoming relative velocity must be equal to the modulus of the outgoing relative velocity:"

"In reality the planet loses momentum but due to the huge mass difference the change in velocity of the gravitational body is negligible compared to the gain in velocity of the spacecraft."

"In solar system exploration, it is important to optimize the maneuver and flight time to the target planet."

"An interesting alternative approach is to resort to direct collocation as demonstrated by Betts6, who efficiently optimized a transfer trajectory to Mars combining low-thrust with two swing-bys of Venus."

"Low-thrust propulsion is then used to shape trajectory arcs between two subsequent encounters and to meet the best incoming conditions for a swing-by."

"Einige Trägerraketen fliegen zuerst eine niedrige Parkbahn an und starten von dort meist einen Hohmann-Transfer , dessen elliptischer Teil die geostationäre Transferbahn ist."

"Normalerweise setzt eine Rakete den Satelliten am (oder in der Nähe des) erdnächsten Punkts (dem Perigäum ) der Ellipsenbahn aus."