Gravitational force works even the object are not in contact. so, this is a field force.
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Gravity as well as electrostatic and magnetic attraction and repulsion provide real life examples of forces being exerted by one object on another without them being in contact with each other. ... However, they are unlikely to think about these experiences as involving forces, i.e. pushes and pulls
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gravitational force is non contact force. This force mean all object in the universe attract each other but we can not feel this force. because gravity force depend on size of the object and our earth and all planet are very huge in size since earth gravity can be obserb. earth attract all object like moon,sattelite,living,non living, attract toward its core. So moon have gravity but very less than earth depend on their size compared to earth