I have this Dynamics Prac Assignment that asks \'Using only observations taken b
ID: 1850525 • Letter: I
Question
I have this Dynamics Prac Assignment that asks 'Using only observations taken before 1800 AD and your own experimental measurements, try to estimate the distance to the moon and its mass in comparison to the earth.' The tutors said to us that first we have to find the mass of the moon in order to find the distance. It also says that 'By observing the times of moon rise and/or moon set it is possible to predict the angular rotation rate of the moon and hence the period of its orbit'. Im not sure I understand what to look for in moon rise/set times and how i could use these to find the angular rotation rate and how i could get the period from this. Also it says we can estimate the diameter of the moon by photographing the moon and comparing scaled distances on the photo to known distances much closer to earth'. Any ideas on how I could do this? The link to the assignment is below http://web.aeromech.usyd.edu.au/AMME1550/Course_Documents/prac-assignment-two.pdfExplanation / Answer
Well what you need to do is that you take a stop watch and set it to zero when the moon is at a particular angle ( any angle which you can choose as the reference ) .
Then the next day ( or after x days ) when the moon again hits the same angle you stop the watch and note the time which the watch records .
This is the time taken by the moon to complete 'x' rotations around the Earth . (x = no. of days , as specified earlied )
so, time taken = time recorded by your watch = t secs .
angle rotated = x*2*pi radians .
so time period of moon = = t/x secs/revolution
as you know mass & radius of earth , you can find out r, the distance between moon and earth center.
Now you know R = radius of earth
and r = distance of moon for center of earth.
so , if you take a photograph of moon and it's diameter is d from earth surface . Let the original diameter be D
so we have the following relation ,
D/r = d/R
so, D = d*r/R