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I need help with an exercise in the book that I can't tackle. I need to calculate how much time we have to intercept and eliminate a NEO. I got the following orbital parameters:

  • a=-2791.44 km (semi-major axis),
  • i=22.3 deg /Hyperbolic),
  • e=2.77
  • v=247.96 deg,
  • r= 2,106,101.331 km (radius from Earth's center of mass)

My problem is that I don't know where to begin, but I did an attempt. I assume that the intercept with the target only can happen when the phase angle between Earth and the NEO are the same. I know that one can calculate the velocity of the S/C with ($m_y$=gravitational param.): $$v=\sqrt{(2m_y/r)-(m_y/a)}$$ If we calculate the escape velocity of the Earth with $V_e=\sqrt{2GM_e/r}$, we will get the difference in velocity. With this information, we can calculate the time needed. Anyone that can help me?

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Assuming that you have a phaser array sufficiently powerful to pulverize the NEO into a harmless meteor storm, I read this as a question of when an object with those geocentric orbital elements arrives at perigee. However, I get a different value for $r$ if I treat that $\nu$ value as a true anomaly; it could be a mean anomaly or hyperbolic anomaly instead.

I suppose your textbook covers this stuff in detail, but for other readers these lecture notes by M. Peet at ASU, using $f$ instead of $\nu$, may help.

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  • $\begingroup$ Thanks for the help. This problem only involves the calculation of how much time we have to reach the asteroid. Then we can do whatever we want there, in this case destroying it (which we can to by reaching it). I was looking at this problem again and came to the conclusion that the NEO is in orbit around the Sun, so we have to do some kind of orbit maneuver (they NEO is probably in the same plane all the time, so it may be easier to calculate this move). I just have no idea how to calculate the time to reach the NEO $\endgroup$
    – Newbie_01
    Sep 10, 2016 at 8:42

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