If an object is trapped in Earth's orbit, would it because of gravity?

Question

Since gravity pulls you down. So the object in Earth's orbit is trapped there because gravity is pulling it toward the center of the planet. Right???????????????????????????????????

Answer 1

As the object moves with a tangential to its orbit velocity v it generates a centripital acceleration a

a= v^2/R

F= ma = G m M /R^2

so long as
a= G M /R^2

the object will remain in orbit

if a < G M /R^2 it will fall to Earth

and

if a > G M /R^2 it will move away from Earth

so it all depends on velocity v and orbit radius R ;-)

Answer 2

an object orbiting earth would be due to the earth's gravity. so yea your right