Kerbal space.program is a great and easy way to learn about the mechanics of space flight.
Think of a quarter back being earth, the ball the shuttle and the wide receiver the moon or mars.
When the shuttle is launched it is aimed to be where we think the wide receiver will be when we throw it. The ball travels and is then caught by the wide receiver which in this case is the moon’s gravity field. Orbiting then allows a declaration period before landing
You got it in one – fuel management.
To fly a straight path would require large amounts of fuel to reach the appropriate speeds. The problem is that the more fuel your carry, the larger and heavier your rocket needs to be, and the harder it is to launch. So instead we look to find every way possible to reduce fuel expenditure.
One of these is to utilise the gravity of things like moons and planets. The gravity will attract the craft and boost its speed as it gets closer, and then we can use relatively short bursts of the engines to escape from that gravity will, now travelling at a much faster speed (but having spent much less fuel).
For longer journeys like the deep space probes, it can even be possible to plan a route to do this multiple times with different bodies in a row.
On top of the answers about fuel and gravity, there are other great reasons for going into orbits.
Go / no-go decisions: getting into a stable orbit gives you time to assess the condition of the spacecraft and its crew coming out of the previous phase of flight. Remediate anything that needs remediation, and if there’s a need to abort the mission and turn 180° then it’s better to do that using gravity than fuel.
Positioning accuracy: if you have a particular landing spot in mind then there’s a certain point back from that where you want to start your descent. If you *don’t* go into orbit first, then you have to end your previous phase of flight at *exactly* the right place, velocity and time. But if you get into a stable orbit first then you can determine where in the orbit you need to start that descent, and wait until you reach it. This way you only have to adjust your flight enough to make orbit.
>Is it to reduce the amount of fuel?
Yes, straight path would be incredibly energy efficient to the point that modern rockets just can’t do it. As for why this is so, easiest way to get a grasp on orbital mechanics is to play [Kerbal Space Program](https://store.steampowered.com/app/220200/Kerbal_Space_Program/), it’s a gamified physics sim. A fair bit of fun and a for a game fairly realistic learning experience on just how orbital mechanics works, how to maneuver a spacecraft etc.
The answer is complex.
If we look at a program like apollo, the saturn V first went into orbit and then spent an orbit checking to make sure it was okay before sending the apollo spacecraft towards the moon. That sort of pause is not common with current designs, which generally send payloads directly to their destinations.
The original Apollo approach involved sending a spacecraft directly to the surface of moon and then back to earth. But that would have required a much larger rocket than the Saturn V, so NASA chose an approach called lunar orbit rendezvous. They send the command and service module to lunar orbit along with the lunar module. They leave the command and service module in lunar orbit (to save fuel), leave half the lunar module on the surface (save fuel), and leave the rest of the lunar module in lunar orbit (save fuel).
Even with all of that, Apollo was just barely able to send two astronauts to the moon and bring them home.
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