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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?

Camille Goudeseune
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Niranjan
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    Radial burns don't help. The only reasonable option is the retrograde burn. – Erin Anne Aug 13 '22 at 05:31
  • FWIW, I show the maths for a radial burn on a circular orbit here. That answer links to a live Sage / Python plotting script. – PM 2Ring Aug 13 '22 at 07:40
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    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. – GremlinWranger Aug 13 '22 at 09:57
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    https://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. – Organic Marble Aug 13 '22 at 11:19
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    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 https://what-if.xkcd.com/58/ – Solomon Slow Aug 13 '22 at 15:14
  • @Solomon: While I am aware that a spacecraft in orbit is already under gravitational influence, what I meant by "So that it is caught by gravity" is that reduction in speed reduces the centrifugal force (which compensates for the gravitational pull) and thus, gravitational pull is more, thus the spacecraft altitude decreases and eventually it reaches earth (with proper entry angles etc.) B.T.W. the : "What if .." site suggested by you is interesting. Thanks. – Niranjan Aug 14 '22 at 12:15
  • @Niranjan, I am not a rocket scientist by any means, but I don't believe that there is any "centrifugal force" in the equations that describe an orbit. What there is is gravity and the spacecraft's momentum. Firing the engine changes the momentum, and thereby changes the spacecraft's ballistic trajectory from one that does not significantly touch the atmosphere to one that does enter the atmosphere. Once in the atmosphere, the aerodynamic drag will continue changing the spacecraft's momentum and trajectory until it meets the ground (or ocean). – Solomon Slow Aug 14 '22 at 18:26
  • @Solomon: Neither am I a rocket scientist. Any object which revolves around another object / axis, is acted upon by a force which tends to swing it away from the axis. This force is known as centrifugal force. if the object is tethered (tied) to the axis, the reaction in the tether, which prevents the revolving object from flying off is a force, called "Centripetal force". If the centrifugal force exceeds the strength of the tether, it will break and let the object fly away. There is insufficient space in this comment, so I am elaborating this further in my next comment. Pls do read. – Niranjan Aug 15 '22 at 04:20
  • @Solomon: Continued... To give you practical day-to-day example, think of driving a car, around a curve. The car also experiences a centrifugal force, which is countered by the friction between the tyres and the road. When you increase your speed (around the turn) beyond a limit, this frictional force becomes in sufficient, and you tend to skid away. (since the car is not physically tied to any object / axis, this friction acts as a tether). Likewise, when a spacecraft revolves (orbits) around earth, "GRAVITY" is the tether which balances the centrifugal force. Hope things are clear now. – Niranjan Aug 15 '22 at 04:27

2 Answers2

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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

Topcode
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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.

Mark Foskey
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