The angle from the sub-solar point to Cape Laplace must now be determined. Of course, to determine this angle, one must have the coordinates of Cape Laplace itself. Here, the coordinates of Cape Laplace from the center of the Moon will be determined.
First, the
location of Cape Laplace from the original image must first be measured. Here,
we will also find the location of the shadow tip, since we will certainly
require it later.
From the original image, the location of the Cape's top and the shadow's tip are:
x_{top} = 1035 and y_{top}^{
}= -705
x_{tip} = 1026 and y_{tip} = -704
Use the following equations to calculate the top and tip longitude and latitude from the center of the Moon:
l_{top}
= sin^{-1} [ (y_{top} - y_{c}) / r ]
m_{top}
= sin^{-1} [ (x_{top} - x_{c}) / (rcosl_{top})
]
l_{tip}
= sin^{-1} [ (y_{tip} - y_{c}) / r ]
m_{tip}
= sin^{-1} [ (x_{tip} - x_{c}) / (rcosl_{tip})
]
Such that the values should be:
l_{top}
= +39^{o}.923625 and m_{top}
= -26^{o}.260392
l_{tip}
= +40^{o}.010846 and m_{tip}
= -27^{o}.176001
The angle from the sub-solar point to the cape's top can now be calculated using the following equation:
g_{top} = cos^{-1} [ sinl_{top}sinl_{ss} + sinl_{top}sinl_{ss}cos (m_{top} - m_{ss}) ]
The answer for this example should be:
g_{top} = 83^{o}.298948
Using the same equations for finding the angle from the sub-solar point to the shadow tip should give you the following value:
g_{tip} = 84^{o}.002173
5 - Location of Feature was Last Updated on December 07, 2010 |