Challenge 12 – Shadow Ground Speed
Use a physics-based model of the earth-moon system to determine the ground speed of the lunar shadow, and the distance to the moon from Earth.
Although we can measure the speed of the lunar shadow on the ground and use this to create a function that predicts the speed from the observer’s longitude (see Problem Set 11) from V(L) = 1.06L2 +179 L +9900, this is an empirical model that dies not explain why the coefficients are as shown. We merely ‘fit’ a quadratic function to the data points and then use this function to interpolate to other longitudes. What we would really like to do is to understand the motion of the moon, Earth and sun, and use this to create a new function that explains the form of the equation in relation to physical parameters like distance, speed and time. The common thing to do is to take a step-by-step approach and each time add an improvement to the previous understanding by considering additional physical factors.