Question

Hubble's constand and age of the universe question

please show the working out for both parts

Answer 1

basically the Hubble constant is used to determine the diameter of the Universe. In reality its not really a constant but an average value.
That it why its been changing all the time.
The age of the Universe has be based upon this constant.
However if we consider that it took one second to form a star out of atomic structure,and that one trillion trillion stars exist in the Universe than the calculated time would exceed what the standard model

calculated.

According to Stephen Hawking time had a beginning only at the inception of the Universe.

If we agree that Hubble's Law tells us that the universe is expanding, it also implies that in the past the universe was much smaller than it is today. If we assume that the expansion's apparent velocity (that is, how fast the galaxies appear to be moving apart) has been constant over the history of the universe, we can calculate how long ago the galaxies began their separation. This should tell us the time that the expansion began, which should give us an estimate of the age of the universe.

If the expansion of the universe is happening rapidly, then we expect the universe to be relatively young, because it has taken only a short time for the galaxies to expand to large distances. If, on the other hand, the universal expansion is progressing at a slow speed, then the age of the universe should be relatively old, because it has taken a long time for the galaxies to reach large distances from each other. We know how fast the universe is expanding, because we know the value of Hubble's constant (H₀ ). The faster the universe is expanding, the faster the galaxies will appear to be moving away from each other.

You can actually calculate an estimate for the age of the Universe from Hubble's Law. The distance between two galaxies is D. The apparent velocity with which they are separating from each other is v. At some point, the galaxies were touching, and we can consider that time the moment of the Big Bang. If you take the separation between the two galaxies (D) and divide that by the apparent velocity (v), that will leave you with how long it took for the galaxies to reach their current separation. The standard analogy here is to consider that you are now 300 miles from home. You drove 60 mph the entire time, so how long did it take you to get here? Well, 300 miles / 60 mph = 5 hours.

• So the time it has taken for the galaxies to reach their current separations is t = D / v.
• But from Hubble's Law, we know that v = H₀ x D.
• So, t = D / v = D / (H₀ x D) = 1 / H₀. So you can take 1/H₀ as an estimate for the age of the Universe.
• The best estimate for H₀ = 73 km/s/Mpc. To turn this into an age, we'll have to do a unit conversion.
• Since 1 Mpc = 3.08 x 10¹⁹ km, H₀ = (73 km/s/Mpc) x (1 Mpc/3.08 x 10¹⁹ km) = 2.37 x 10^-18 1/s.
• So the age of the Universe is t = 1/H₀ = 1 / 2.37 x 10^-18 1/s = 4.22 x 10¹⁷ s = 13.4 billion years.

From stellar evolution, we have estimated the ages of the oldest globular clusters to be approximately 12-13 billion years old. These are the oldest objects we have identified, and it is a nice check on our estimates for the age of the Universe that they are consistent. It would have been strange if we were unable to find any objects roughly as old as the Universe or if we found anything significantly older than the estimated age of the Universe. For many years, until about 10 years ago, however, there was a controversy over the age of the universe derived from Hubble's Constant. The best theories available at the time were estimating that the stars at the Main Sequence Turn Off in many globular clusters had ages of 15 billion years old or more. This creates a problem. How can the universe contain an object older than itself? Recently, however, advances in our understanding of the stars have led us to refine the ages of the stars in globular clusters, and we now estimate them to be about 13 billion years old. This means, though, that the stars in the globular clusters must have formed within the first several hundred million years of the universe's existence!

Hubble's Law Hubble's law is a statement of a direct correlation between the distance to a galaxy and its recessional velocity as determined by the red shift. It can be stated as The reported value of the Hubble parameter has varied widely over the years, testament to the difficulty of astronomical distance measurement. But with high precision experiments after 1990 the range of the reported values has narrowed greatly to values in the range An often mentioned problem for the Hubble law is Stefan's Quintet. Four of these five stars have similar red shifts but the fifth is quite different, and they appear to be interacting. The Particle Data Group documents quote a "best modern value" of the Hubble parameter as 72 km/s per megaparsec (+/- 10%). This value comes from the use of type Ia supernovae (which give relative distances to about 5%) along with data from Cepheid variables gathered by theHubble Space Telescope. The WMAP mission data leads to a Hubble constant of 71 +/- 5% km/s per megaparsec. Hubble distance calculation Calculation of expansion time

Index Distance measurement Distance units Particle Data Group Section 18

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Hubble Parameter The proportionality between recession velocity and distance in the Hubble Law is called the Hubble constant, or more appropriately the Hubble parameter since it does depend upon time. In recent years the value of the Hubble parameter has been considerably refined, and the current value given by the WMAP mission is 71 km/s per megaparsec. The recession velocities of distant galaxies are known from the red shift, but the distances are much more uncertain. Distance measurement to nearby galaxies uses Cepheid variables as the main standard candle, but more distant galaxies must be examined to determine the Hubble constant since the direct Cepheid distances are all within the range of the gravitational pull of the local cluster. Use of the Hubble Space Telescope has permitted the detection of Cepheid variables in the Virgo cluster which have contributed to refinement of the distance scale. The Particle Data Group documents quote a "best modern value" of the Hubble constant as 72 km/s per megaparsec (+/- 10%). This value comes from the use of type Ia supernovae (which give relative distances to about 5%) along with data from Cepheid variables gathered by the Hubble Space Telescope. The value from the WMAP survey is 71 km/s per megaparsec. Another approach to the Hubble parameter gives emphasis to the fact that space itself is expanding, and at any given time can be described by a dimensionless scale factor R(t). The Hubble parameter is the ratio of the rate of change of the scale factor to the current value of the scale factor R: The scale factor R for a given observed object in the expanding universe relative to R0 = 1 at the present time may be implied from the z parameterexpression of the redshift. The Hubble parameter has the dimensions of inverse time, so a Hubble time tH may be obtained by inverting the present value of the Hubble parameter. One must use caution in interpreting this "Hubble time" since the relationship of the expansion time to the Hubble time is different for the radiation dominated era and the mass dominated era. Projections of the expansion time may be made from the expansion models. Hubble distance calculation

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Hubble Parameter and Red Shifts The Hubble Law states that the distance to a given galaxy is proportional to the recessional velocity as measured by the Doppler red shift. The red shift of the spectral lines is commonly expressed in terms of the z-parameter, which is the fractional shift in the spectral wavelength. The Hubble distance is given by