- Rotational Period of the sun
- Angular diameter of the sun
- Rotational velocity of the sun
The purpose of this post is to describe the process used to find the sun's rotational period.
Theoretical Background
The sun has sunspots (seen above), which travel along the sun's lines of latitude. They can be used as location markers on the sun and tracked over time to determine the sun's rotational motion. If one knows how far a sunspot moved (in degrees) over a known amount of time, one can figure out the sun's rotational period using this formula:
$\frac{P_\odot}{360^{_o}}=\frac{\Delta t}{\Delta \theta }$
Supplies
- Heliostat - a device that uses mirrors to keep sunlight reflected onto a single target
- Piece of paper and pencil
- Clock
- Latitude and longitude transparency
Process
Use the heliostat to get a reflection of the sun onto a piece of paper by angling the mirrors to aim the light toward the target. Trace the outline of the reflection with a pencil (the reason for this will be evident later). Identify a sunspot and trace and label it. Circle it so that it can be identified as the original sunspot. Turn off the heliostat so that it no longer traces the sun's motion across the sky and the reflection moves across the paper. Trace the sunspots' motion across the paper until a clear line of latitude emerges. Be sure you mark the time and date.
The next time you're in the lab, repeat the procedure described above. You may not track the same sunspot.
Find two sheets on which the same sunspot is tracked on different days (you might end up using other groups' sheets). Overlay one piece of paper on the other--the most recent one on top--against a window. Line up the outlines of the suns (this is why you traced the outline before) and rotate the papers so that the line followed by the sunspot on one page is parallel to the line it followed on the other.
Take the transparency and line it up with the two suns' outlines. Orient it so that the sunspot line is parallel to a line of latitude on the transparency. Find the difference in longitude between the sunspot on the first and second day it was observed. This difference is the $\Delta \theta$ in the formula above. The time elapsed between the two observations is the $\Delta t$
Doing this process with multiple sunspots gave our group, Team Crush*, the following data.
Like I said before, the sun has sunspots that move along the sun's lines of latitude (which is helpful because we don't know the angle of the rotational axis of the sun). Once lines of latitude are established (using the sunspots), differences in longitude can be measured.
Between the first and second observations, the sunspots move a certain distance around the sun. We don't know the actual distance, but the difference in longitude between the spots on the different observation days gives an angular distance. If one knows the amount of time it took the spot to move this angular distance, one can use the formula above by comparing the $\Delta \theta$ to the 360 degrees that the spot would move if it made a full rotation.
Team Crush included Tom Leith, Dylan Munro, Sammy Mehra, Jennifer Shi, and myself.
Doing this process with multiple sunspots gave our group, Team Crush*, the following data.
By averaging the periods in the above table, Team Crush found a solar rotational period of 28.3 days.
Why This Works
Between the first and second observations, the sunspots move a certain distance around the sun. We don't know the actual distance, but the difference in longitude between the spots on the different observation days gives an angular distance. If one knows the amount of time it took the spot to move this angular distance, one can use the formula above by comparing the $\Delta \theta$ to the 360 degrees that the spot would move if it made a full rotation.
Team Crush included Tom Leith, Dylan Munro, Sammy Mehra, Jennifer Shi, and myself.
Good job Moiya! Two things you should watch out for:
ReplyDelete1) you write that the sunspots’ motion across the page once the heliostat is turned off corresponds to a line of latitude. It would be worth clarifying that this is Earth latitude as opposed to solar latitude. The sunspots appear to move due to the Earth rotation, so they are tracing out the East-West direction on Earth.
2) Throughout the post you write things like “sunspots move along the sun’s lines of latitude”, which is confusing because it makes it sound as if the sunspot is traveling on the surface of the sun along a given line of latitude. When, really, each spot remains at a fixed location and their apparent direction of motion is due to solar rotation and traces out a line of latitude.