How to decrease your orbital velocity relative to other planet

[UltraMinus1]

I've been trying to return to kerbin from mission to jool but when I enter kerbins SOI I'm going over 4000m/s and I don't have enough deltaV to slow down . What should I do to enter Kerbins SOI at lower speed?

[Vanamonde]

The speed of interplanetary transits is determined by geometry. The only 3 things you can do to affect that are 1) engine burns, 2) use the planet's atmosphere to slow down as you pass through it, or 3) do some complicated passes around the destination's moon(s), but that can be quite difficult. 

[Cpt Kerbalkrunch]

This is assuming you went to land on Kerbin and not reestablish orbit for some reason:

As long as you have a shield, you don't actually need to slow down. Kerbin's atmosphere will do that for you. I've survived as high as 8km/s with an Mk1 Command Pod and shield. Just set your PE on Kerbin at around 35km. Quicksave along the way, cuz you may need to make adjustments. You may land on the first try, or you might pass through and swing around again. As long as you get captured by Kerbin, you're good.

You may need to reload and adjust your PE up or down. You may be coming in too hot and blow up, or too high and not capture. Also, any fuel you have left, burn retrograde just before or just after you hit the atmosphere and stage your engine off. Any speed you can shed will help. Experiment a bit to see what works best.

[Leganeski]

There is one relatively complicated technique that will actually reduce your velocity relative to Kerbin: the gravity assist.

Two gravity assists at Kerbin, followed by one at Eve, can slow down your speed from 4000 m/s to 3100 m/s.

 

However, if you just want to return a few kerbals to Kerbin, @Cpt Kerbalkrunch's suggestion of using a heat shield is much easier and more effective.

Edited March 19, 2023 by Leganeski

[Cpt Kerbalkrunch]

2 minutes ago, Leganeski said:

There is one relatively complicated technique that will actually reduce your velocity relative to Kerbin: the gravity assist.

Two gravity assists at Kerbin, followed by one at Eve, can slow down your speed from 4000 m/s to 3100 m/s.

 

However, if you just want to return a few kerbals to Kerbin, @Cpt Kerbalkrunch's suggestion of using a heat shield is much easier and more effective.

This is correct. I was just guessing that he was on a standard return mission, but if he's looking for extreme efficiency in maneuvers, the multiple pass through method is the way to go. I'm just too impatient for that .

[jimmymcgoochie]

Kerbin’s escape velocity is about 3100m/s so you can’t come back from outside its SOI going slower than that by the time you hit the atmosphere. You could brake into a very loose orbit and use a few gravity assists from the Mun to reduce your velocity a bit, but not by much.

[Empiro]

Try to get your approach PE as close to Kerbin as possible. If you're at 4000 m/s at 100 km, this kind of speed is actually quite reasonable and expected when returning from Jool via a direct transfer. When you left for Jool, you probably were moving just as fast when you finished your burn. This is the reverse of that.

If you can't survive directly driving into the atmosphere, you don't need to slow all the way down. Just slow down so that you're not on an escape trajectory, which means spending about 1000 m/s to be slower than escape velocity, about 3000 m/s. You can then take your time, at AP lower your PE into the atmosphere and slowly aero brake until you're able to land safely.

In either case, it's most efficient to perform this maneuver as close to Kerbin as you can.