The earth attracts a large flying bug toward its center with a force of 0.10 newtons. with what force does the bug attract the earth itself?

0.10 N.

According to Newton's 3rd law, an action has an equal and opposite reaction. For the situation here, the action is the earth's pull and the reaction is the bug's pull. Since they both must be equal in magnitude, we conclude that the bug attracts earth with 0.10 N, but in the direction opposite to earth's pull.

The force at which the bug attracts the earth itself is 0.10N as per the third law of motion by Newton. The third law of motion states that every action has an equal and opposite reaction. In this case, the magnitude will be the same however the direction will be different of both the forces.