10:41 o Back Lab 6 Hubble Constant Lab.docx Switch To Light Mode Hubble Constant and the Age of the O) NS Adapted from Astronomy Lab Manual AST-1002C for Distance Learning by Professor M. Werhner Objectives: Graphically determine the Hubble constant and from that determine the age of the Universe. Background: Edwin Hubble made one of the most important discoveries of modern astronomy in 1929 when he determined that the spectra of most galaxies were red- shifted. Since a Doppler red shift occurs when an object is receding from the observer, Hubble concluded that the Universe is expanding. He further discovered that the farther away a galaxy is from us, the greater its red shift and hence it must be moving away at a greater velocity than nearby galaxies. This is known as Hubble's Law and states that galaxies are receding from us at a speed that is proportional to their distance. This relationship between velocity and distance is written mathematically as: v=Hxd v = velocity, d = distance, H = Hubble constant The value of H, the Hubble constant can be used to determine the age of the Universe as follows: an object that travels at a given velocity (v) for a given time (t) will cover a distance (d) equal to its velocity multiplied by time. d=vxt solving for 'v' by dividing both sides by t and cancelling gives: v=d/t since v=H x d (Hubble's Law, from above) then: Hxd=di we can cancel out the 'd's by multiplying both sides by 1/d H=1/t now solve for 't\" by multiplying both sides by t and cancelling, then dividing both sides by H and cancelling (a two step process) to give: t= 1/H or, in other words, the age of the Universe (t) (since it started expanding) is the inverse of the Hubble constant. Procedure: show your working on the worksheet otherwise you will not receive full credit. STEP 1 Plot the data in the table below (Data Table of Distance and Recessional Velocities of Galaxy Clusters) either on your own graph paper or on the graph paper provided or using Excel or similar program. Use dots to indicate each galaxy cluster in % = 2 N N Dashboard Calendar Notifications 10:41 o Back Lab 6 Hubble Constant Lab.docx Switch To Light Mode STEP 1 Plot the data in the table below (Data Table of Distance and Recessional Velocities of Galaxy Clusters) either on your own graph paper or on the graph paper provided or using Excel or similar program. Use dots to indicate each galaxy cluster in terms of distance and velocity (40 pts.). STEP 2 Use a ruler or straight edge to draw a best fit line through the data points. Do not connect the dots. A best fit line is a straight line that keeps an equal number of data points above and below the line an equal distance. I prefer that you do this by hand to get a better 'feel\" for how to do it but, if you used Excel it is okay to let it fit a best fit line. (10 pts.) STEP 3 Determine the slope of the line, this is the Hubble constant. You must do this yourself and show your calculation to get the points. The slope is determined as follows: Slope = run = change in velocity/change in distance To obtain the slope from your plotted line chose two locations on your line that are far apart. Write down the velocity value and the distance value for each location. Subtract the smaller velocity value from the larger velocity value (for example 200 km/s minus 20 km/s = 180 km/s). This is the 'change in velocity'. Put that number at the top of a fraction and subtract the smaller distance value from the larger distance value, (for example 100x10720 minus 10x1020 km = 90x10"20 km) and put that number on the bottom of the fraction. This is the 'change in distance'. Divide the fraction, giving you a value for H (in my example this would be 180 km/s/90x10720 km = 2x107-20, note the negative sign in front of the exponent. The correct values from your graph. Show your work and enter your answer on the answer sheet (below). Note the units for H (the slope) = velocity (km/s)/distance (km) leaving 1/s (\"per second\"). Be careful: the distance scale on the horizontal (x)_axis is in 10* km that is 100 quintillion km! (20 pts.) STEP 4 Remember that the age of the Universe is 1/H so take the inverse of the value for H you calculated in STEP 3 (1 divided by H). Our units are now 1/1/s so the 1/1 part cancels and we have an age of the Universe in seconds. That is a lot of seconds! (10 pts.) % = 2 N N Dashboard Calendar Notifications 10:41 46