World Science Scholars
2.4 The Hubble Constant

PLEASE NOTE: For better performance, you may download the demonstration by clicking here. If you have not already downloaded and installed the free CDF player, it is available here.

Edwin Hubble showed that the receding speed and the distance of a cosmic body were related by $v=H_0 d$, where $H_0$ came to be known as the Hubble constant. To calculate the age of the universe, we can measure distances and velocities of nearby supernovae, plot them, and solve for $H_0$. In this demonstration, you are provided with real NASA data of distances and red-shifts for six supernovae: $$\array{ \underline{\text{Supernova}} & \underline{\text{Distance (Mpc)}} & \underline{\text{Red-shift (z)}} \\ \text{1995D} & 36.14 & 0.008 \\ \text{1995E} & 55.72 & 0.012 \\ \text{1996C} & 145.88 & 0.028 \\ \text{1990af} & 215.77 & 0.050 \\ \text{1992bs} & 335.74 & 0.064 \\ \text{1992aq}& 463.45 & 0.101 }$$

In astronomy, scientists use red-shifts to infer the velocity of a cosmic body. Red-shift is an apparent increase in the wavelength of light due to the Doppler effect. However, we wish to plot receding speed — not red-shift — as a function of distance. To calculate receding speed, multiply each red-shift value by $c=3 \times 10^5$ km/s. Then, plot the data using the provided tool, and drag the line to best represent your points. The slope of this line, $\frac{v}{d}$, will be the Hubble constant $H_0$. Then, multiply $\frac{1}{H_0}$ by $3.09 \times 10^{19}$ km (the number of km in a megaparsec) to find the age of the universe in seconds. Keep in mind we aren’t accounting for acceleration here. You can check to see if your answer agrees at the bottom.


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