I highly recommend you play Kerbal Space Program if you want to get an intuitive understanding for how it works. But in short, yes, and also if you accelerate towards another orbiting object your own orbit becomes more elliptical such that over sufficient distance you will actually move away from it rather than toward it.
I thought it might be that, except Kerbal certainly does elliptical orbits, and you'd actually have to work rather hard not to, because a basic integrator hooked up to the 1/r^2 law of gravitational attraction gives you elliptical orbits for free.
Go play a bit of KSP. NASA employees have stated that Kerbal Space Program has given them an intuition of orbital mechanics that a degree didn't.
And working with things that make you go _slower_ when turning on your engine to push you in the direction of travel needs intuition to even begin. Yes, once you get to the other side of the planet you are orbiting, you are going slower than if you didn't use your engine at all.
If you're accelerating towards an orbital object you are by definition not in the same orbit as the target object. If you were you would be moving at the exact same speed. This effect makes getting yourself close enough for docking all sorts of tricky if you don't know what you're doing. Once you get close enough (like in the linked simulator) you can mostly ignore the problem since the effects are small given the relative speeds involved.
I can heartily recommend messing around with orbital maneuvers in KSP to get a feel for the problem. It's not exactly intuitive.
No. Thrusting the "intuitive" way will indeed bring you closer to your target in the short term. Over time (specifically, enough time to be an appreciable fraction of the orbital period) the difference in speed will cause you to drift into a higher or lower orbit, but at low speeds and low distances this effect is tiny, and you can easily compensate for it by thrusting radially.
Funnily enough orbital mechanics don’t work that way. To accelerate towards an object ahead of you in your orbital plane you need to lose velocity, drop into a slightly lower orbit, then gain velocity to slow down and intercept.
Velocity is tightly coupled to altitude when orbiting.
No, you've deflected it in a direction perpendicular to the one it's moving in; turning it slightly away from the Earth, initially, but not speeding it up. This will increase the eccentricity of the orbit.
> The closer the eccentricity is to 1 without being equal or less, the more "curved" the trajectory is and the nearer its closes approach to the sun will be.
Is this true? I thought it depends on the object’s speed. You can have an object with e=3 have a closer approach to the sun than an object with e=2 if the first object is traveling sufficiently faster.
In other words, at a given perihelion, you can change an object’s e by accelerating or decelerating. Not a orbital mechanics major, just played too much KSP.
Orbits are very non-intuitive until you've had a chance to play around with them, KSP did wonders for my understanding of orbits. Lots of people make the mistake that once you're in orbit you can just freely move in 3D to wherever you want a perception not helped by the number of times movies show it working that way.
The orbit you are in is directly dependent on your velocity. So if your orbit is similar to another objects, you'll be going at a similar velocity as well.
Put another way, if you are in the same orbit as another object, your velocity must be the same.
This illustrates itself in space docking procedures. If two objects are in the same orbit, one thrusting towards another in the direction of the orbit puts the first at a higher orbit and it'll rise with respect to second object. The converse holds true; thrust against the orbit and you'll fall with respect to the other object.
Thus, to dock, you have both crafts at slightly different orbits and the lower orbit will slowly gain on the higher orbit. In this way, one can control how fast the approach is. This will be how the satellite approaches debris most likely.
This is only true for circular orbits. It’s pretty transparently obvious that elliptical orbits move closer to and farther from the center of mass (and lose and gain momentum accordingly).
On the blue orbit, you can see Ap and Pe. Ap is the apogee; the place in the orbit where the spacecraft is closest to the earth. Pe is the perigee, the place where the spacecraft is farthest from the earth. Since the blue orbit is mostly circular, they are at about the same altitude.
If you look at the large white orbit, the apogee would be the leftmost point, close to the apogee of the blue orbit. The perigee would be all the way at the right of the image.
When your spacecraft is at position X, thrusting your engines will not meaningfully change your current position - the acceleration they generate is negligible to the speed at which you are moving. However, the maneuver will change your speed, which affects your orbit.
At the apogee, if you thrust in the direction you are moving, your perigee will increase - the orbit will become even more eccentric. Example: at the apogee you are moving at 100 miles per second. Thrusting the engines will not change your current position much; your current position is determined by your 100 miles per second speed and where you came from. But the maneuver will change your speed to 105 miles per second, which will cause your perigee to become much farther away from the earth. However your apogee will stay in the exact same position.
Why? Because in orbit you are basically flying sideways while gravity pulls you down. In a circular orbit this balances out into you flying around in a circle. But if you go faster, you're going more sideways while gravity pulls the same amount. So your orbit becomes more elongated.
You can thrust in the direction of movement at any point in orbit, and it will increase the altitude of the orbit on the opposite side of where you are at - if you thrust at apogee the perigee altitude increases, and in the white elongated orbit if you thrust between the apogee and perigee your orbit will become more circular and bigger. Similarly to make an eccentric orbit circular, you get to the apogee and then use the engines to slow down, which brings down the perigee.
Since thrusting changes your position on the opposite side of the orbit, the most efficient way to increase your perigee is to thrust while at the apogee.
The NASA thing is basically going into an elongated orbit between the Sun and Jupiter, coming back to the apogee near the Sun, and then thrusting. The difference in efficiency between thrusting at the apogee of an orbit and just thrusting in a straight line out into space is really huge. Though I'm not sure why the extra gravity of the Sun makes the maneuver more efficient.
If you're interested in this you should definitely play KSP. It's a great game and gives you a great intuitive sense of how these things work.
The size of your orbit is proportional to the energy of your spacecraft. Use manuever nodes to change the trajectory of your encounter with a planet like Eve, and notice how massively you can change the total size of your orbit (up or down, depending on the direction of the encounter). This implies a significant change in your energy during the encounter. This is from your gentle collision with the planet through its gravity field.
I wrote a small 2D game once, where the Earth is attacked by a swarm of satellites in polar orbits. Your ship is launched from the surface, but after that it's up to you to put yourself in orbit, using thrusters. Thinks Asteroids with gravity. It really taught me a lot about how an orbit's shape changes when thrust is applied in different directions, at different points in an orbit. For example, a good way to circularise an orbit from an elliptical, a small tangential thrust at apogee during each orbit would eventually place the spacecraft in a circular orbit with a radius roughly equal to the apogee distance of the elliptical orbit... or to say it another way, perigee would increase until it equalled apogee...
Anyway, the point being that I never would have understood any of this no matter how many times I read 2010, until I wrote that little game. Some things need to be experienced to really grok.
Sidenote: KSP is the worst way to build intuition in this particular case as it doesn't have any drag model in orbit, or even n-body simulation, so no orbital decay is possible there. Playing around with NASA's GMAT [0] or similar more comprehensive software is much more helpful to understand real-world orbital mechanics.
If you're curious about orbital space mechanics, try Kerbal Space Program. You'll get a much better idea how NASA puts things into orbit after you've done it a few times yourself.
Basically, the rocket doesn't just fire in a straight line away from the Earth all the way into orbit. It starts arcing very soon into the ascent, and the thrust is nearly parallel to the Earth's surface for much of the journey.
Once you're in orbit (say around the sun), you have to cancel the orbital velocity to fall into the object you're orbiting around. If you point at the sun and accelerate 1 km/s directly at it, you're still moving 30 km/s "sideways". All you'd end up doing is making the orbit more elliptical-shaped.
At least that's how I see it, but I am far from being an authority on this topic.
Well, it depends. Over short distances and timescales, relative motion behaves pretty much as you would expect for objects in free-fall. It's only over significant fractions of an orbital period that counterintuitive things start happening, with orbital speed and height influencing each other. (You can think of this as a tidal or Coriolis-esque pseudoforce that appears to increase in magnitude as objects get farther from each other.)
In general, there are many possible paths you can take to achieve an orbital rendezvous, varying widely in how long they take and how much fuel they consume.
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