Apart from being a great advertisement for asteroid impact mitigation strategies, this rendering of PHA orbits demonstrates the high degree of precision that goes into tracking and predicting future orbits. For example, we know that none of these particular space rocks will hit Earth for the next 100 years or more. Beyond that, the orbital positions of asteroids become uncertain due to gravitational interactions with the planets and other forces such as the Yarkovsky effect.
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Of course, the orbital path lines of the asteroids are many thousands of times thicker than the width of the asteroids they represent - otherwise no lines would be visible. This adds to the impression that interplanetary space is more crowded than Grand Central Terminal at rush hour. Fortunately for us, space is a very big place and, for the most part, the majority of PHAs will be nothing more than a blip on our radar.
But it's all down to statistics - whether we're safe for the next hundred or 10,000 years, we live in a cosmic shooting gallery where, eventually, our planet will get hit by something big.