Discussion Questions
A. It would have been difficult for Cavendish to start designing an experiment
without at least some idea of the order of magnitude of G. How could he
estimate it in advance to within a factor of 10.
B. Fill in the details of how one would determine Jupiter’s mass by observing
the acceleration of one of its moons. Why is it only necessary to know the
acceleration of the moon, not the actual force acting on it. Why don’t we need
to know the mass of the moon. What about a planet that has no moons, such
as Venus — how could its mass be found.
C. The gravitational constant G is very difficult to measure accurately, and is
the least accurately known of all the fundamental numbers of physics such as
the speed of light, the mass of the electron, etc. But that’s in the mks system,
based on the meter as the unit of length, the kilogram as the unit of mass, and
the second as the unit of distance. Astronomers sometimes use a different
system of units, in which the unit of distance, called the astronomical unit or
a.u., is the radius of the earth’s orbit, the unit of mass is the mass of the sun,
and the unit of time is the year (i.e. the time required for the earth to orbit the
sun). In this system of units, G has a precise numerical value simply as a
matter of definition. What is it.
10.6*Evidence for Repulsive Gravity
Until recently, physicists thought they understood gravity fairly well.
Einstein had modified Newton’s theory, but certain characteristrics of
gravitational forces were firmly established. For one thing, they were always
attractive. If gravity always attracts, then it is logical to ask why the universe
doesn’t collapse. Newton had answered this question by saying that if the
universe was infinite in all directions, then it would have no geometric
center toward which it would collapse; the forces on any particular star or
planet exerted by distant parts of the universe would tend to cancel out by
symmetry. More careful calculations, however, show that Newton’s universe
would have a tendency to collapse on smaller scales: any part of the universe
that happened to be slightly more dense than average would contract
further, and this contraction would result in stronger gravitational forces,
which would cause even more rapid contraction, and so on.
When Einstein overhauled gravity, the same problem reared its ugly
head. Like Newton, Einstein was predisposed to believe in a universe that
was static, so he added a special repulsive term to his equations, intended to
prevent a collapse. This term was not associated with any attraction of mass
for mass, but represented merely an overall tendency for space itself to
expand unless restrained by the matter that inhabited it. It turns out that
Einstein’s solution, like Newton’s, is unstable. Furthermore, it was soon
discovered observationally that the universe was expanding, and this was
interpreted by creating the Big Bang model, in which the universe’s current
expansion is the aftermath of a fantastically hot explosion. An expanding
universe, unlike a static one, was capable of being explained with Einstein’s
equations, without any repulsion term. The universe’s expansion would
simply slow down over time due to the attractive gravitational forces. After
these developments, Einstein said woefully that adding the repulsive term,
known as the cosmological constant, had been the greatest blunder of his
This was the state of things until 1999, when evidence began to turn up
that the universe’s expansion has been speeding up rather than slowing
down! The first evidence came from using a telescope as a sort of time
Book 3, section 3.5 presents
some of the evidence for the
Big Bang.
Chapter 10Gravity
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