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5 years ago, India launched the Mangalyaan spacecraft to Mars, on a budget that raised eyebrows at the time. It was probably the Mars mission launched with the least powerful rocket; a feat only made possible by the lengthy orbit-raising maneuvers that made use of the Oberth effect.

A similar approach was used by the Japanese Nozomi also on its way to Mars, and the Israeli Beresheet on its way to the moon. This can also be used to achieve a trans-Venusian injection.

On the other hand, gravity assists using VEEGA trajectories or similar have been proven by the Galileo and Cassini spacecraft, and soon will be performed by JUICE and Clipper.

Recently, a very exciting proposal called Trident was put forward (see:What is the most fuel efficient way out of the Solar System? and How can Trident be so inexpensive? Will it orbit Triton or just do a (slow) flyby?). This involves VEEGA to achieve a flyby to Jupiter, and then on to Neptune and beyond.

Breakthrough Initiatives announced their intention to privately fund a very austere flyby mission to Enceladus that presumably would then escape the solar system, I recall they said something like less than $100m. The Asian nations mentioned before could consider performing a low-budget mission to the outer solar system.

Is it possible to combine both approaches to perform flybys to the outer planets and escape the solar system?? Launch it first as if it was a Venus mission which heavily relies on oberth trickery, then use Venus and Earth gravity assists to reach Jupiter, and from there beyond

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Is it possible to combine both approaches to perform flybys to the outer planets and escape the solar system?? Launch it first as if it was a Venus mission which heavily relies on oberth trickery, then use Venus and Earth gravity assists to reach Jupiter, and from there beyond

Basically yes. If your main concern is to get to the outer solar system or onto a solar escape trajectory for minimum delta-V (equivalently with the smallest and usually cheapest rocket for the mass of your payload) you use whatever tricks you can find with timing your burns and maybe exploiting lunar and solar tides, to get to Venus at a carefully chosen moment. You use some number of gravity assists from Venus and Earth to eventually get you to Jupiter and one Jupiter assist to get to your target. If you're willing to wait long enough, and have your mission take long enough, you basically only need enough fuel to get into a Venus transfer orbit (around 3.5 km/s once you are in LEO, but maybe a little bit less if you are very patient), plus a tiny but for course corrections.

There are some trade-offs though. These extremely fuel efficient trajectories are only available at specific times, and they take a long time. It costs money to keep a project running and/or support a spacecraft in space, and it might be cheaper to launch sooner, or on a faster trajectory, even if that means the launcher costs more, because the whole project is over sooner. In planning your escape from LEO you also need to factor in the costs of designing a rocket for frequent restarts, the cost savings from being able to use a smaller rocket and the efficiency losses from using storable propellants.

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