Transcript MOND - an alternative to dark matter

Ohio University - Lancaster Campus
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Is Dark Matter the Only
Possible Solution?
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In 1983, Mordehai Milgrom, a
professor at the Weismann
Institute in Israel, proposed a
startling alternative to dark
matter.
It was a revision of Newton’s
2nd Law of Motion.
Milgrom called it MOND:
Modified Newtonian Dynamics
www.weizmann.ac.il
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Newton’s Law of Gravity states that the force between
two objects comes from the product of their masses,
and is proportional to the inverse of the square of the
distance between them…
Force = Gm1m2
r2
G is a proportionality constant, 6.67 x 10-11 m3/kgs2
The fact that G is so small indicates that gravity is a
weak force.
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Newton’s 2nd Law also states that a force on an
object is given by the object’s mass and the
acceleration applied to it…
F = ma
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What Milgrom proposed was that when the distance
between two objects was very large, then the
acceleration would be very small, but not as small
as Newton predicted. Newton’s 2nd law changes to…
F = ma2
a0
where a0 is 1.2 x 10-10 m/s2
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a0 is a constant derived from the speed of light and the
age of the universe. If an object had started at rest and
accelerated with an acceleration a0 since the beginning
of the universe, today it would be moving at c, the speed
of light, 3.00 x 108 m/s.
More importantly…
then F = Gm1m2 = ma2
r2
a0
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Since, over great distances, the gravitational force is
proportional to a2, not just a, less mass is needed to
account for the force.
In other words, Milgrom’s equation eliminates the
need for dark matter.
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How does Milgrom’s equation eliminate the need
for dark matter in our galaxy?
Diagram Credit: Phil Hibbs, Michael Gmirkin
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Gm1m2 = ma2
r2
a0
Let’s substitute in mgalaxy for m1 and msun for m2 and
the m on the right, then we can cancel out the msun
on both sides:
GM = a2
r2
a0
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GMa0 = a2
r2
GMa0 = a
r
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Now take the square
root of both sides:
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Finally, set this equation equal to the equation that
relates velocity to acceleration for a star in a circular
orbit around the galaxy’s center:
a =
GMa0
r
=
v2
r
and cancel out the r’s on both sides:
GMa0
=
v2
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Take the square root of both sides:
4
GMa0
=
v
What we understand from this, is
that the velocity of a star orbiting
the center of the galaxy has no
dependence on its distance, r,
from the center of the galaxy.
And NO dark matter was needed.
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Does this mean that the idea of dark matter is worthless?
Many astrophysicists agree that Milgrom’s equation
predicts and describes the rotational behavior of the
galaxy (and many other low acceleration situations also!)
But most astrophysicists don’t agree that the equation
explains the cause of the behavior. Most astrophysicists
remain convinced that the equation just coincidentally
coincides with the behavior of dark matter.
What do you think?