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In season two of The Expanse, (episode 5, "Home") when

Eros starts moving towards Earth and becomes invisible to missiles

a suggestion is made to tag the asteroid with a laser beam from Rocinante.

The way I understand it, Rocinante is moving from the Belt; missiles are launched from Earth. They're on opposite sides of Eros.

Since this guidance relied on missiles following the laser beam, how was it supposed to work since the beam was on the opposite side of the asteroid?

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The missiles would not move on a straight line from Earth, but on an elliptical orbit (a consequence of orbital mechanics). Therefore, they wouldn't approach Eros head on but on an angle, thus making it possible to see the laser tag from the side.

I'm guessing they could also extrapolate the trajectory thus limiting the volume of space they look at.

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    The orbit wouldn't be elliptical as the missles are under thrust, but the key idea (path not straight) is correct. Additionally the same considerations apply to the planetoid's path. – dmckee Aug 20 '17 at 19:12
  • I'll try to watch that episode again, but I think what @dmckee said applies - Roci was under very heavy acceleration, and it would be very unlikely for it not to move more or less straight towards Earth. The same must apply to Eros. Point is, it's unlikely for them to move from the side of the asteroid, because then it would easily outrun them. – Gallifreyan Aug 20 '17 at 19:28
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    @Gallifreyan There is at least 15 km/s second difference in the orbital velocity of Earth and objects with near circular orbits in the asteroid belt, so not only will the paths not be exactly straight, but the chase trajectory will put the chases slightly to one side of the chased object. It's not going to be a big angle from the POV of the missles, but it will be enough because the Roci is lighting the asteroid up with a very well collimated laser (it must be because of the ranges over which they can make use of it). There is no gaping plot hole here. – dmckee Aug 20 '17 at 19:42
  • It's probably also simple to launch the missiles at a straight line from Earth, past Eros, and then turn them back towards Eros. Although Eros moves pretty fast. – tobiasvl Aug 21 '17 at 9:15
  • I watched the episode again and took a few screencaps. Roci isn't directly behind Eros, that's true, but it doesn't look like missiles are approaching at a non-negligible angle (cc @dmckee). – Gallifreyan Aug 26 '17 at 9:34

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