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, we multiply each red-shift value by the speed of light, $c=3 \times 10^5$ km/s.

Drag the slider below to set the slope of the line to best represent the data points. The slope of this line, $\frac{v}{d}$, will be the Hubble constant $H_0$. Then, to convert from kilometers to parsecs, we 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. Keep in mind we aren’t accounting for acceleration here.

The accepted value of the Hubble constant is roughly 70 (km/s)/Mpc and the accepted value of the age of the universe is approximately 13.8 billion (\(1.38\times 10^{10}\)) years. How do the numbers we calculate from these six supernovae compare?

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