does anybody here know how to measure how far moon travel in one year?

Yes

Relative to the Earth it travels the following distance:

In one lunar month it moves Orbital diameter x pi = 440,000 miles x 3.14= 1,382,000

In one year there are 12.38 lunar months.

So distance travelled in one year = 1,382,000 x 12.38 = 17,104,000

 

Relative to the sun it is also moving, on average, an additional distance equivalent to the earth's orbit.

This is 3.14 * 186,000,000 = 584,040,000

So, the total distance travelled, relative to the sun, is 600,000,000 miles

thanks a lot!

Yes

Relative to the Earth it travels the following distance:

In one lunar month it moves Orbital diameter x pi = 440' date='000 miles x 3.14= 1,382,000

In one year there are 12.38 lunar months.

So distance travelled in one year = 1,382,000 x 12.38 = 17,104,000

 

Relative to the sun it is also moving, on average, an additional distance equivalent to the earth's orbit.

This is 3.14 * 186,000,000 = 584,040,000

So, the total distance travelled, relative to the sun, is 600,000,000 miles[/quote']

 

If you are looking for the distance relative to the Earth you should use the sidereal month rather than the synodic month. There are 13.38 sidereal months in a year. this increases the distance traveled to 18,491,000 miles.

If this happens to be a more advanced calculus class, then for the distance relative to the sun, you may be required to do integration along the moon's trajectory. Given that you know its period and the integration period, this should be trivial.... numerically integrating that is

would you plz explain me a bit about what you mean, i'm soo not math person, maybe with an example