You math has to be wrong. Nasa says Tycho crater is 53 miles in diameter. We can see the entirety of Tycho with low powered binoculars. This is Not possible if the Moon is 238 thousand miles away. Either the size of Tycho is wrong, the size of the Moon is wrong, the distance to the Moon is wrong, or all 3. My money is on all 3 being wrong.
First I did all my measurements in Kilometers not miles. That aside it's possible to convert the relative size of Tycho crater to an angular size as well as the moon to an angular size using: Angle=2*arctan(actual length/(2*distance to object)) If I use the distance I measured with the listed diameter for Tycho crater in kilometers I get 0.0107 degrees for the visual angle. If I do the same for the moon as a whole I get 0.4423 degrees for the visual angle of the whole moon. If I divide these I get 0.0242 or 2.42% of the moon's width is covered by Tycho crater. So it covers a bit over 2/100 of the moon. Now if I do the calculation of the listed witdh of Tycho divided by the true diameter of the moon again the result is 0.0242 the exact same ratio. When viewing with binoculars say a cheap $10 pair a normal magnification would be about 7x. That means that the apparent size, or visual angle an object takes up is multiplied by 7. Also the field of view in the binoculars is only about 5 to 10 degrees total so again let's say 7 degree field of view. That means Tycho crater through binoculars would be magnified to 0.0714 degrees in the binoculars. Then dividing by 7 for the total field of view you get 0.0107 again, but this time it represents 1% of what is visible in the binoculars. For reference a 12pt character takes up about 1% of the total screen width. So through binoculars it would be easily viewed even at low magnification. Granted all this really proves is the remarkable agreement between NASA, my measurements, and binocular manufactures. However, I find that these parties all happening to agree is sufficiently convincing to accept the stated values for the moon's size and distance as well as Tycho's diameter. But you don't have to take my word for it, go measure it yourself.
You math has to be wrong. Nasa says Tycho crater is 53 miles in diameter. We can see the entirety of Tycho with low powered binoculars. This is Not possible if the Moon is 238 thousand miles away. Either the size of Tycho is wrong, the size of the Moon is wrong, the distance to the Moon is wrong, or all 3. My money is on all 3 being wrong.
First I did all my measurements in Kilometers not miles. That aside it's possible to convert the relative size of Tycho crater to an angular size as well as the moon to an angular size using:
Angle=2*arctan(actual length/(2*distance to object))
If I use the distance I measured with the listed diameter for Tycho crater in kilometers I get 0.0107 degrees for the visual angle. If I do the same for the moon as a whole I get 0.4423 degrees for the visual angle of the whole moon. If I divide these I get 0.0242 or 2.42% of the moon's width is covered by Tycho crater. So it covers a bit over 2/100 of the moon.
Now if I do the calculation of the listed witdh of Tycho divided by the true diameter of the moon again the result is 0.0242 the exact same ratio.
When viewing with binoculars say a cheap $10 pair a normal magnification would be about 7x. That means that the apparent size, or visual angle an object takes up is multiplied by 7. Also the field of view in the binoculars is only about 5 to 10 degrees total so again let's say 7 degree field of view.
That means Tycho crater through binoculars would be magnified to 0.0714 degrees in the binoculars. Then dividing by 7 for the total field of view you get 0.0107 again, but this time it represents 1% of what is visible in the binoculars. For reference a 12pt character takes up about 1% of the total screen width. So through binoculars it would be easily viewed even at low magnification.
Granted all this really proves is the remarkable agreement between NASA, my measurements, and binocular manufactures. However, I find that these parties all happening to agree is sufficiently convincing to accept the stated values for the moon's size and distance as well as Tycho's diameter.
But you don't have to take my word for it, go measure it yourself.