Introduction:
In this lab, we measured the angular velocity of the sun (how fast the sun rotates on its axis) to find the time it takes for the sun to make a complete orbit. We did this by printing two images of the sun that are 7 days apart from NASA’s SOHO database to observe and measure one sunspot (the same sunspot in different locations on both images). We looked at sunspots because its dark (due to magnetic activity and heat transfer) and easy to identify since there are few spots from a faraway perspective. were able to solve for the time period it takes for the sun to rotate on its axis using the following formulas:
θ=sin〖x/(R ')〗 where R’ is the radius of the circle the sunspot orbits,
〖θ=sin〗〖x/R_sun 〗 , where R_sun is the radius
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Method:
We first measured for x, R’, and R_sun–for both the initial and final positions of the sunspot. Since both the Earth and the sun orbit, our perspective that we observe the sunspots change. Because the sun and Earth are both spheres on a tilted rotational axis (we must keep in mind that this is from the horizontal and ‘bird’s eye-view’ of the sun), we solved for the longitudinal angles of both the initial and final sun spot positions using the following formulas: θ=sin〖x/(R ')〗
〖θ=sin〗〖x/R_sun 〗
To find ω_S, we must correct for Earth’s orbit because the sun moves at a faster rate than the Earth. To do so, we find ω_E, which is 2.0 x 〖10〗^(-7)rad/s, and ∆ω_OS, using the equation ∆ω_OS=∆θ/∆t . We can substitute the angular velocities of the Earth and the observed angle into the equation ω_S=ω_E+Δω_OS, to find the true angular velocity of the sun. the value obtained is approximately 3.29 x〖10〗^(-7)rad/s. Lastly, we solved for orbital period to fully understand how it takes for the sun to rotate on its axis using the formula T= 2π/ω_s . The answer we concluded is approximately 22.09