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Comment by kobeya | Hacker News Reader

> The orbit becomes less circular and more elliptical. While the higher point (apogee) is further away than before, the lowest point (perigee) is closer.

Orbital dynamics is complicated and I admit I could be wrong here, but I'm pretty sure this is incorrect. If you push radially outward from a circular orbit, it should raise the apogee but keep the perigee the same.

I could see this working if you exert a radially outward force on an object in an elliptical orbit that is already coming in from apogee to perigee, because relative to the object's radial velocity that would actually be a braking maneuver. Is that what you meant?

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When the laser force acts for a short enough time and is strong enough, after the impact the orbiting body will acquire non-negligible positive radial velocity while changing its distance from the Earth only negligibly.

In the limit of an instantaneous impact, the body will change its velocity in a jump while not moving from the point of impact at all. Then it will continue to orbit the Earth on a new, elliptic orbit that shares with the old circular orbit the point of impact.

Since at this point the new radial velocity is positive, the body at this point is getting further away from the Earth. This means that before it will approach the point of impact again, it will have to be nearer the Earth. Hence the perigee is nearer the Earth than the point of impact.

No if you raise the apogee without giving the object any additional speed, the perigee will be lower.

You did give the object additional speed.

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.

If x is the direction of travel at the moment of impact, Vx remains the same but it gains Vy. Total V increases.

It depends on the angle at which you hit the debris with the laser, as well as the shape of the debris.

The idea is, generally, to hit the debris at an angle as it approaches you (bottom front of you may)[1]. Depending on the shape of the object as well as the material of the surface, you'll be able to transfer enough momentum to actually slow it down as well as nudge it further (loss of mass?) out into a new orbit with a low enough perigee.

It's obviously not easy to predict the new orbit because debris comes in very different shapes, and of many different materials.

Also, because there's a transfer of energy, the part of its original Vx is lost in the process (the laser is deflected at an angle). There's no loss of total Vx (sum of laser Vx and debris Vx) however.

1: See figure 3 in page 6 of this pdf (the laser at an angle). https://arxiv.org/pdf/1004.0390

I understand, but this subthread was about what happens when you hit it when it is directly overhead, pushing it outward.

That seems unlikely, but even in that case you'll achieve a lower perigee. It's also extremely unlikely that it would happen - hitting debris when it's directly overhead, yes, but hitting it on a surface that's perpendicular to the laser, like a letter T, probably not.

But assuming we do hit it like a T, the two things happen: loss of mass (laser ablation) and transfer of momentum. Vy will increase but Vx remains constant. The debris is moving in a straight line - that speed doesn't increase, but now it's moving at a different orbit so, relative to its previous orbit, Vx will appear to have reduced (but it hasn't).

But I'm definitely not an expert in orbital mechanics so don't quote me on that.

Okay, you're right, it does speed up very very slightly, but by an amount that is not anywhere near sufficient to keep the perigee from falling, as you originally claimed. The increase in eccentricity of the orbit is the larger effect.

Before intervention, it's velocity points perpendicular to the direction of the laser fire.

Maybe you can grok it by thinking of the laser as excerting torque on its current path, twisting it so that it soars higher initially but afterwards comes closer to the center of gravity of earth?

Spend some time in Kerbal Space Program to get a sense of how little energy it takes to change a low orbit to one that grazes the atmosphere.

I got better things to do than play games :)

> If you push radially outward from a circular orbit, it should raise the apogee but keep the perigee the same.

I believe that effect requires thrust to "speed up" the object along its current heading. (Prograde)

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