$F=Gm_1m_2/d^2$

$F=ma$

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

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?