astrogate: To navigate or avigate in space.
Copyright ©2017 by Paul Niquette. All rights reserved.
Permission granted by Nick Anthony Fiorenza, The Lunar Planner
There are millions of asteroids in orbits around the sun. They appear to be concentrated in belts. The main asteroid belt is depicted above as a speckled red circle outside the orbit of Mars, far away from Earth. Asteroid orbits are not all that circular, however. Kepler's Laws mandate that in eccentric orbits asteroids must spend more time loitering out there in the asteroid belt near aphelion than falling toward the sun, whipping around at perihelion, and sweeping back out again to await observation by astronomers.
As of this writing (2017), more than 16,000 asteroids have been classified as Near Earth Objects (NEOs), which means their eccentric orbits bring them within 195 Mkm (120 Mmi) of the sun at perihelion. Meanwhile, the Earth's orbit is approximately circular with a radius of 150 Mkm (93 Mmi).
NEOs are less worrisome than others:
An Apollo asteroid struck Earth as the Chelyabinsk meteor in 2013. It was about 18 meters in diameter. The largest Apollo asteroid, Sisyphus, is seven kilometers in diameter -- nearly half the size of the Chicxulub impactor, which brought the end of the dinosaurs 66 million years ago.
It is customary to
at the top of maps and to
use counter-clockwise as the
prograde direction for solar
on the Fiorenza illustration above is
a representation of a particular
Apollo-class asteroid with a semimajor
axis about 1.8 times larger than the
radius of the Earth's orbit.
Let's give it the name "Puzzler." Using Kepler's
Third Law, one can estimate Puzzler's
orbital period as 365×1.83/2
= 881 days.
Here is a scenario for
solvers to consider based on the
information at hand...
Before clicking to the solution page, solvers may want to take into account the fact that Earth presents a rapidly moving target to NEOs.
With an orbital radius of 150 Mkm (93 Mmi), our planet travels through space 942.5 Mkm (585.4 Mmi) every year. That's 2.6 Mkm (1.6 Mmi) each day or 107,600 km/h (66,800 mph). Earth's diameter is about 12,800 km (7,900 mi). Therefore...