World Science Scholars
2.4 The Hubble Constant
demonstration

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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