There are a number of justifications for physics education. Among them is the conviction that by better understanding our world, we can live happier, more productive lives. But an even nobler goal would be to use that understanding to protect life from the perils that threaten. For examples, life would benefit from insuring that nuclear weapons are never again used and a means is found to end warfare between countries and diverse peoples. The author challenges interested readers to ponder such goals and try to make progress. This particular investigation serves as a model for approaching such tasks by outlining another hazard and proposing an open-ended approach that could provide real benefit to life on Earth.
Hollywood had made motion pictures about the extraordinary destruction that a collision of a comet or asteroid with Earth could cause. Examples are Armageddon (1998) and Deep Impact (1998). Based on the destruction caused by past collisions of solar system objects with Earth, there is concern that a similar future collision might doom human civilization. Biologists and other scientists are only beginning to unravel such destruction and extinction to life forms that resulted in such previous collisions. Such an event could easily be the biggest calamity to ever occur to human life.
However if such an object can be detected soon enough, it might be possible to engineer a deflection of the trajectory and avoid the disastrous collision. The challenge is to detect an object on an impact trajectory with sufficient time to change its path to avoid collision. Since such objects are tiny compared to the size of planets and the sky is very big, it is difficult to discover such an object with more than a few months notice. And that may leave too little time to change its trajectory enough.
But it may not be necessary to scan the full sky for possible threats. The earth and other planets are thought to have formed by such collisions adding mass during the early development of the solar system. Any object in an established orbit that crosses the Earth's orbit would have likely collided long ago. So such collisions are now rare since the Earth has been sweeping its orbital path over 4 billion years. The real threat comes from an object that's trajectory is recently deflected by close passage to another planet or moon into a new collision path. So the challenge is to determine where to look for such hazards and how to best monitor those locations.
A possible solution comes from an interest to economically send spacecraft from Earth to the more distant planets. What follows is an abstract of a paper in American Scientist by Shane Ross:Scientists in charge of designing the trajectories for interplanetary space probes traditionally did their calculations as if the only objects of any relevance were the spacecraft itself and one other body, usually the planet located nearby. During the departure phase, for example, only Earth mattered to their calculations of how the probe would move. And upon arrival at its destination, only that distant planet counted. In between, the trajectory was calculated as if the spacecraft was traveling alone in a highly elliptical orbit around the Sun. Although this two-body strategy works, the trajectory it produces is very costly in terms of energy. More sophisticated methods take advantage of the competing gravitational tugs of the different planets and their moons, which create a vast network of passageways by which a spacecraft can travel over large distances while expending very little energy. The author describes this new approach and shows how the same principles explain much about the way comets and asteroids are naturally flung about the solar system.
By choosing a trajectory that passes near a moon or planet, the gravitational attraction can transfer some of the kinetic energy of that body to (or from) the spacecraft, changing its trajectory. The path change can be slight or radical depending on the closeness of the encounter. One of the odd features of our universe is that unless Entropy (as described by the Second Law of Thermodynamics, e.g., friction) plays a role, the reversal in time of events is just as possible as the forward in time sequence. The same sort of trajectories that permit a spacecraft launched on Earth to travel to the outermost parts of the solar system also govern a comet or asteroid's incoming collision path with Earth.
But the effect is more than simple proximity to the planet. For each planet orbiting the Sun there are FIVE locations called Lagrange points where the combination of gravitational pulls would result in an object moving in synchronized orbit with the planet's orbit. Leonhard Euler realized the existence of the first three in the 18th century and his contemporary Joseph-Louis Lagrange proposed the other two. (Note the triangles show an object near Lagrange point L4 or L5 tend to move towards that point.) Low energy trajectories typically pass in the vicinity of such points. The authors listed in the references below are some of the scientists working in this field.
Recall that for early efforts to send space craft to destinations such as the moon and other planets aerospace engineers only computed a single trajectory for the journey. But there exists a launch window in time and an extended tube of possible trajectories that potentially provide a successful journey. For example, to send a spacecraft to an outer planet with a minimum expenditure of energy would require one of a tube containing possible trajectories which pass near an inner planet, providing a course and speed change from that moving inner planet's gravity. Launching at other times or in other directions would miss the intended destination.
Similarly, a spacecraft on a return journey to Earth will need to follow a selected tube of possible trajectories or will miss Earth. For a massive object to be hazardous for life on earth, its path must lay within a specific trajectory tube. So the challenge is to calculate what trajectories involving such close encounters with planets or moons could endanger earth. By knowing the orbits of the solar system planets and moons it should be possible to calculating the locations of such tubes. Once those are know it should be possible to identify small moving windows in space near the planets and their moons which might be monitored to locate potential collision hazards. (artist concept by Cici Koenig for JPL. Click to view larger version.)
Your challenge is to investigate the existence of such trajectory tubes which might identify hazards to life on earth and identify such hazard windows for monitoring to find such collision objects with sufficient advanced notice to allow engineering a timely course deflection.
Communicating technical information such as observations and findings is a skill used by scientists but useful for most others. If you need course credit, use your observations in your journal to construct a formal report.
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