They both involve gravity calculations
free from the motion of earth
yes
Continue to follow the motion of the satellite
Projectile motion
In theory, yes. I suggest you research "newton's cannon".
free from the motion of earth
hypothesis on projectile motion
Because a projectile by definition, is in motion.
Projectile motion has two components horizontal motion and vertical motion. Gravity affects only the vertical motion of projectile motion.
hockey and soccer
yes
motion of a projectile
gravity
Gravity
A feather falling in a vacuum is not considered as a projectile motion. Gravity, which is absent in a vacuum, is one of the components of projectile motion.
Gravity
Gravity