SOLUTIONS TO EXERCISE 14

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Remember that there are 3.09 * 10^19 kilometers in a Megaparsec,
and 3.16 * 10^7 seconds in a year.

(a) Hubble and Humason's measurement implies a Hubble time of

1          3.09 * 10^19 km/Mpc
H^(-1) = ------------- =  ------------------- = 5.4 *10^16 s = 1.7 billion yrs
570 km/s/Mpc       570 km/s/Mpc

(b) The modern measurement implies a Hubble time of

1          3.09 * 10^19 km/Mpc
H^(-1) = ------------- =  ------------------- = 4.4 *10^17 s = 14 billion yrs
70.5 km/s/Mpc      70.5 km/s/Mpc

(c) For this answer, I quote and paraphrase students at Barnard and Columbia
Colleges who worked out Exercises 11-13.

"Hubble and his collaborators are credited with the discovery of the
expansion of the universe because they hit on the concept.  Their measurements
of expansion seem far off today because modern technology allows for much
better measurement.  In the year 2070, the measurements of today will probably
look just as crude.  However, the measurement itself is not the important
part; it is the concept that matters, and that was formulated by Hubble et al."

"We credit Hubble and Humason because they REALIZED the universe is expanding.
Before then, no one noticed.  After them, everyone paid attention.  So even
though they were numerically wrong, they were conceptually right; and

"The process of scientific discovery often proceeds by leaps and bounds, and
is not a one-time affair.  Hubble and his collaborators may not have arrived
at the exact numerical value of the Hubble constant, but they still introduced
the notion that the universe is expanding and that there is a Hubble constant
we can use to describe it... it was through their work and the synthesis that
they achieved that they brought about a revolution in how we think about the
universe, and that is why we credit them."

"While the Hubble constant that Hubble and Humason calculated are far off,
they were still the first to prove that the universe was, in fact, expanding.
Today, we still use their formulae and calculations - modified - and still
we find that the universe is expanding.  Their discovery changed the way we
look at the universe and it continues to affect us today.  Their numbers
may have been far off, but the ideas behind it were correct."

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