Hubble’s constant: Astronomers believe that the universe is expanding and that stellar objects are moving away from us at a radial velocity V proportional to the distance D from Earth to the object. ...

Hubble’s constant: Astronomers believe that the universe is expanding and that stellar objects are moving away from us at a radial velocity V proportional to the distance D from Earth to the object.

a. Write V as a function of D using H as the constant of proportionality.

b. The equation in part a was first discovered by Edwin Hubble in 1929 and is known as Hubble’s law. The constant of proportionality H is known as Hubble’s constant. The currently accepted value of Hubble’s constant is 70 kilometers per second per megaparsec. (One mega-parsec is about 3.085 × 1019 kilometers.) With these units for H, the distance D is measured in megaparsecs, and the velocity V is measured in kilometers per second. The galaxy G2237 + 305 is about 122.7 megaparsecs from Earth. How fast is G2237 + 305 receding from Earth?

c. One important feature of Hubble’s constant is that scientists use it to estimate the age of the universe. The approximate relation is

where y is time in years. Hubble’s constant is extremely difficult to measure, and Edwin Hubble’s best estimate in 1929 was about 530 kilometers per second per megaparsec. What is the approximate age of the universe when this value of H is used?

d. The calculation in part c would give scientists some concern since Earth is thought to be about 4.6 billion years old. What estimate of the age of the universe does the more modern value of 70 kilometers per second per megaparsec give?