# Commencing atmospheric re-entry

Once a decision is taken to get back home (earth), a spacecraft, I think has two options: 1 - To reduce its speed (by firing the thrusters located in the forward or something similar), so that it is caught by earth gravity, and gradually pulled towards the earth in every subsequent orbit, and 2 - for a faster descent, "pitch" the craft towards earth, and fire the thrusters at the rear, so that the craft is "propelled" towards earth (radially) quickly. Which of the two methods is generally followed? Or is a combination of the two which is followed? Is there any other way to get back home?

• Radial burns don't help. The only reasonable option is the retrograde burn. Commented Aug 13, 2022 at 5:31
• FWIW, I show the maths for a radial burn on a circular orbit here. That answer links to a live Sage / Python plotting script. Commented Aug 13, 2022 at 7:40
• If this area is of interest to you suggest looking at Kerbal space program since while only vaguely accurate science wise it is a great way to get an intuitive feel for this sort of question. Commented Aug 13, 2022 at 9:57
• space.stackexchange.com/a/12014/6944 A small retrograde burn is done which lowers the perigee into the sensible atmosphere. The bulk of the velocity reduction is done by drag. Commented Aug 13, 2022 at 11:19
• Re, "...so that it is caught by Earth gravity..." That's not how it works at all. A spacecraft in any orbit already is "caught" by the central body. FYI The Earth's gravity field at the altitude where the ISS orbits is almost as strong as at ground level. If you could build a tower that tall, you could stand on top of it and feel something like 90% of your surface weight, while the astronauts in the ISS whizzed past you at almost five miles per second in "weightlessness." For a whimsical introduction to what "orbit" means, see what-if.xkcd.com/58 Commented Aug 13, 2022 at 15:14

Burning retrograde is your best choice, but it doesn’t work like how you think.

To reduce its speed (by firing the thrusters located in the forward or something similar), so that it is caught by earth gravity, and gradually pulled towards the earth in every subsequent orbit

All spacecraft are impacted by all gravity, and typical spacecraft perform a burn to reenter earth from inside its Sphere Of Influence. Orbit is continually being pulled by something’s gravity. If you weren’t being pulled by anything’s gravity then you are just aimlessly floating.

Second, all spacecraft (at least those around bodies with atmospheres, are slowly slowing down and spiraling into deorbiting. They periodically have to boost their orbit if they want to stay in orbit.

for a faster descent, "pitch" the craft towards earth, and fire the thrusters at the rear, so that the craft is "propelled" towards earth (radially) quickly.

Don’t forget, you have a lot of velocity “forwards” still, so it takes a lot more delta V to burn radially and manage to deorbit than to cancel some of your velocity and deorbit.

Now, technically a combination of the both is fastest, but afaik no spacecraft uses that method because A) a straight down and fast reentry is far more dangerous because you are going faster, and have less time and air to slow down. B) it’s more delta V expensive and therefore not ideal

• Asteroid return missions have left Earth's Hill sphere and then reentered. This includes Hayabusa, Hayabusa2, and the upcoming Osiris-Rex. Commented Aug 14, 2022 at 14:19
• @Cadence ah, that’s my bad. I’ll edit the statement to be more accurate. Commented Aug 14, 2022 at 17:18

Option 1 is always followed, but I think there are two misconceptions that should be corrected.

First, as others have said, it's not a matter of getting captured by the earth's gravity. Anything that's in orbit has been captured by the earth's gravity. To reenter, the spacecraft has to change to a different orbit that intersects the thick part of the atmosphere. They point the main engine forward and do a single burn that slows down the rocket. That puts them into an orbit that, if the earth were smaller but had the same mass, would get a lot closer to the planet on the other side, but would then loop back up to where they were at the end of the burn. But, because the earth is not smaller, it descends into the thicker part of the atmosphere and that slows it down more until it lands or splashes down. It doesn't spiral in - it's down in less than one full circuit.

Also, pointing directly away from the earth and firing will not work at all. When you give something a significant kick perpendicular to its direction of motion, it ends up going off at an angle but faster. If you keep the engine pointed away from earth and keep thrusting, it is as if earth's gravity were that much larger at that distance, and the effective orbital speed will be faster. The effect is to make the rocket go faster around the earth, and when you turn the engine off, you will be in an elliptical orbit that is the same height at the point where you stopped thrusting, but higher at the other side. Not what you want.

In principle, with a lot of fuel you could keep thrusting and speeding up till you got deep enough into the atmosphere so that it would slow you down and you would reenter, but that would require much more fuel and a much thicker heat shield. In fact, the longer you do this, the more thrust needed to keep the rocket in a tight circle around the earth, so "much more fuel" may translate to "you would need a science fictional fusion rocket to do this."

If you had such a hypothetical fusion engine that could run as long as necessary, you could do a retrograde burn until you come to a full stop over the earth, and then point the rocket away and accelerate faster than free fall straight down before turning around and decelerating just in time to avoid getting burned up. But we don't have the technology to do that, and you would only save about 45 minutes or so.