direction as the motion, which will do positive work, increasing
the asteroid’s energy and boosting it into an orbit with a greater
radius. On the other hand, if the asteroid’s spin and orbital motion
are in opposite directions, the Yarkovsky push brings the asteroid
spiraling in closer to the sun.
Calculations show that it takes on the order of 10^7 to 10^8 years for
the Yarkovsky effect to move an asteroid out of the asteroid belt
and into the vicinity of earth’s orbit, and this is about the same as
the typical age of a meteorite as estimated by its exposure to cos-
mic rays. The Yarkovsky effect doesn’t remove all the asteroids
from the asteroid belt, because many of them have orbits that
are stabilized by gravitational interactions with Jupiter. However,
when collisions occur, the fragments can end up in orbits which
are not stabilized in this way, and they may then end up reaching
the earth due to the Yarkovsky effect. The cosmic-ray technique
is really telling us how long it has been since the fragment was
broken out of its parent.
Discussion Questions
A The following is an incorrect explanation of a fact about target shoot-
ing:
“Shooting a high-powered rifle with a high muzzle velocity is different from
shooting a less powerful gun. With a less powerful gun, you have to aim
quite a bit above your target, but with a more powerful one you don’t have
to aim so high because the bullet doesn’t drop as fast.”
What is the correct explanation?f/Discussion question A.B You have thrown a rock, and it is flying through the air in an arc. If
the earth’s gravitational force on it is always straight down, why doesn’t it
just go straight down once it leaves your hand?
C Consider the example of the bullet that is dropped at the same
moment another bullet is fired from a gun. What would the motion of the
two bullets look like to a jet pilot flying alongside in the same direction as
the shot bullet and at the same horizontal speed?194 Chapter 3 Conservation of Momentum