explain gravitational field is conservative field

Conservative fields are those fields in which work done in a closed cycle is zero. For example gravitational field is a conservative field let's suppose there are 4 points A,B,C,D. A body is at point A moves to B then to C to D and back to A. Hence work done by this field in this path is zero. Another way we can explain it is that curl of conservative force applied by conservative field is zero hence no work is done by this field.