For this portion of the lab we are going to calculate the velocity and acceleration of a CME coming off of our Sun based on its position in a series of images taken by the LASCO instrument on the Solar and Heliospheric Observatory. And then we will determine how long it would take to get to Earth. Make sure that you have printed out your SOHO CME images that are linked at the top of this instruction page. Below is an image taken from one of the coronagraphs on LASCO. To the right of the disk, we can see a CME erupting from the Sun. The white circle shows the size and location of the Sun. The black disk is the occulting disk blocking out the disk of the Sun and the inner corona. The tick marks along the bottom of the image mark off units of the Sun’s diameter. First Image of CME. The Sun is shown at the center as a white circle, a CME is coming off the Sun to the right with a loop of material. There is a mark at the top of the loop, and a mark at the outskirts of the bulk of ejecta. Time stamp is 8:05. On your printouts, you are going to select a feature that you can see in all five images, for instance, the outermost extent of the bright structure or the inner edge of the dark loop shape. (Each of these is marked on the above image as an example. You’d measure to the inside of the line – depending on the feature you pick.) Measure its position in each image, and then do some calculations to find the velocity of the solar material. Make sure you have printed out the CME images. Select the single feature you’re going to measure and mark it on each image. Try to keep the same straight line out from the center of the Sun. Using your ruler with centimeter marks, place the zero mark right at the center of the Sun (white circle). And then measure to the inside of your mark. Write your measurement on the image next to your mark and then into Table 1, Column “Position (spage) (cm)”. (Noting with your measurements, you can estimate to the closest 10th of a centimeter, e.g. 3.6, or 4.3, etc.) Write your name and the date next to your images, take photos of your work to insert into your report. Next, you will continue filling out Table 1. Under the “Time Interval (t2−t1)” column you will want to find the difference in time for each of the CME images. Note that row 1 is “N/A” since we don’t have the time before 8:05. Fill in the rest of the rows by figuring out the number of minutes between each image timestamp. For example (timerow2 – timerow1), and so on. Once you have the minutes, then convert that number into seconds to put it into the table. Converting Measurements to Kilometers Measurements on your page can be converted to kilometers using the simple ratio: dpage/dactual= spage/sactual where: dpageis the diameter of the Sun measured on the page. With your ruler measure the diameter of the white circle in centimeters, using the outermost part of the outline. dactualis the actual diameter of the Sun. spageis the position of the mass as measured on the page. sactualis the actual position of the mass. The diameter of the Sun = 1.4×106 (1.4 million) km. To solve for the sactual, we just need to rearrange the equation, noticing that the centimeters cancel out and we are left with units of kilometers: sactual = (spage/dpage)×dactual Calculate thesactual for each of your drawings then into Table 1, Column “Position (sactual) (km)”. Calculate Average Velocity Using the position and time, you can calculate the average velocity. Velocity is defined as the rate of change of position. Using the change in position and the change in time, the average velocity for the time period can be calculated using the following equation: v=(s2−s1)/(t2−t1) where: s2is the position at time, t2. s1is the position at time, t1. Calculate the average velocities Table 1, Column “Average Velocity (km/s)”. Acceleration and Change in Time of Velocity The acceleration is the change in time of the velocity: a=(v2−v1)/(t2−t1) where: v2is the velocity at time, t2. v1is the velocity at time, t1. Calculate the average accelerations Table 1, Column “Average Acceleration (km/s2)”. Table 1 Universal Time Time Interval (t2−t1) (sec) Position (spage)(cm) Position (sactual)(km) Average Velocity (km/s) Average Acceleration (km/S2) 08:05 N/A N/A N/A 08:36 N/A 09:27 10:25 11:23 NOTE: At a minimum, when you fill in Table 1, show all of your detailed calculations for Row 3. Given the average velocity you found for the last CME photo at 11:23, calculate how long it would take to reach Earth in hours and days if it is less than 24 hours. (Use 1AU=1.496x108km, and show your full calculation.) Select another feature of the CME (describe which one), you can eyeball it or make the measurements in centimeters. Does it appear to be moving differently from (faster/slower) last feature you selected? Overall, how does the size of the CME change with time? What kind of forces do you think might be acting on the CME? How would these account for your data? CMEs travel outward from the Sun at speeds ranging from slower than 250 kilometers per second (km/s) to as fast as near 3000 km/s. The fastest Earth-directed CMEs can reach our planet in as little as 15-18 hours. Slower CMEs can take several days to arrive. How does the CME you just examined compare? Optional, but highly suggested to check out: CME’s are indeed beautiful. Here are some videos to enjoy: slow-motion CME (short), many CMEs.