$$F=G m_1 m_2/d^2$$

$$F=ma$$

$$a_g=Gm_{\rm other}/d^2$$

In Newtonian mechanics, the acceleration of object A toward object B is not dependent on the mass of object A but on the mass of object B and the distance between objects A and B.  Because the mass of object A does not affect its acceleration due to the gravitational influence of object B, does Newtonian mechanics predict that a massless particle (e.g. a photon) would be gravitationally affected by an object with mass?

Also, would it predict that an object with mass would not be gravitationally influence by an object without mass.  Would it also predict that two massless particles would have no gravitational influence on each other?