When we walk on earth why do moon covers distance with us?
Your perspective of the moon is completely relative. Compared to the earth, the moon is moving very fast in a circular orbit, about 18000 mph. However, when a person walks on the earth, they can see the moon for an extended period of time because of the large distance the moon must traverse to cover the distance across the night sky. If you were to walk with the passage of night, the moon would move slower with respect to you, but infinitesimally so. Therefore, the reason the moon appears to move with you is because in the time it takes you to travel 1 meter, it must travel a million times that.