Do you know why the same half of the moon always faces Earth?
The moon has been facing Earth like this for more than 4 billion years. Just like Earth rotates on its axis once every day with respect to stars, the moon also rotates on its axis with respect to stars. Since the moon keeps facing Earth this means that the moon needs to travel 360 degrees around Earth with respect to stars in order to rotate 360 degrees on its axis with respect to stars. When the moon first formed it was very close to Earth and it orbited Earth once every few hours, today this period is 27 days, and as the moon continues to recede this period will continue to increase; the greater the distance from Earth the greater this period becomes. When this period becomes 50 days, for example, this also means that it will take the moon 50 days to rotate 360 degrees on its axis with respect to stars. So as the moon recedes from Earth its spin with respect to stars slows down, that is, it loses rotational kinetic energy (this is different from moon's kinetic energy due to moon's motion around Earth). If the distance to the Earth increases to infinity, the moon would stop spinning with respect to stars and hence its rotational kinetic energy decreases to zero. This proves that the moon's rotational kinetic energy is a function of the distance from Earth. Similarly, the total energy of the Earth-moon system is a function of the distance from the sun.
The moon has been facing Earth like this for more than 4 billion years. Just like Earth rotates on its axis once every day with respect to stars, the moon also rotates on its axis with respect to stars. Since the moon keeps facing Earth this means that the moon needs to travel 360 degrees around Earth with respect to stars in order to rotate 360 degrees on its axis with respect to stars. When the moon first formed it was very close to Earth and it orbited Earth once every few hours, today this period is 27 days, and as the moon continues to recede this period will continue to increase; the greater the distance from Earth the greater this period becomes. When this period becomes 50 days, for example, this also means that it will take the moon 50 days to rotate 360 degrees on its axis with respect to stars. So as the moon recedes from Earth its spin with respect to stars slows down, that is, it loses rotational kinetic energy (this is different from moon's kinetic energy due to moon's motion around Earth). If the distance to the Earth increases to infinity, the moon would stop spinning with respect to stars and hence its rotational kinetic energy decreases to zero. This proves that the moon's rotational kinetic energy is a function of the distance from Earth. Similarly, the total energy of the Earth-moon system is a function of the distance from the sun.
