In this scenario, the asteroid is drawn towards the larger planetary body due to the gravitational attraction between the two objects. As it approaches the planet, the pathway of the asteroid will depend on its initial trajectory and velocity.
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Ellipse pathway: This would generally apply if the asteroid was in a bound orbit around the planet before being captured. This is unlikely unless the asteroid was already in a stable orbit around the planetary body.
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Spiral pathway: A spiral pathway might imply that the asteroid spirals into the planet, which could happen if it were losing energy (for instance, due to atmospheric drag if it were entering an atmosphere) or if there are other forces acting on it. However, in the case of a straightforward collision in space without atmospheric effects, this is less commonly referred to.
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Did not have a pathway: This is not accurate because even before collision, the asteroid would have had a trajectory dictated by gravitational dynamics.
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Hyperbola pathway: If the asteroid is not gravitationally bound to the planet and is merely passing by, it would typically follow a hyperbolic trajectory as a result of its velocity and direction relative to the planet. This is common for objects that are on an intercept course and are not captured by the planet.
Based on these considerations, if the asteroid is simply approaching and eventually impacts the planet, the most accurate statement would be that the asteroid had a hyperbola pathway, provided it was not gravitationally captured prior to impact. If it was captured and eventually collided, then it may have transitioned from a hyperbolic or parabolic pathway to a more complex trajectory. However, during the approach phase before any impact, it would generally be described as having a hyperbolic pathway.
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