Note on scalar–graviton and scalar–photon–graviton amplitudes

In this short note, we propose an algorithm based on the expansions of amplitudes, the dimensional reduction technique and the approach by differential operators, to calculate the tree level scalar–graviton amplitudes with two massive scalars and the tree level scalar–photon–graviton amplitudes with two massive scalars and one photon. While applying the unitarity method, these amplitudes are necessary inputs for the calculation of post-Newtonian and post-Minkowskian expansions in general relativity for two massive charged objects interacting with gravity and the electromagnetic field.