You can measure c if you define m and E first, as someone before said c is defined first.
However, you may use fission to deal with that.
consider 1g of u235, you bombard a neutron into it to trigger the alpha decay. You Put the whole setup inside a water bath with temperature T,and you weight...
I think you can divide the learning process into three levels.
1. SR: You need the transformation of coordinates and basic physical minds.
2. GR, Introductory level: Some deviation from differential geometry textbook has already naturally make Riemann tensor and revalent tools falling out...
The meaning of "The laws of physics are the same in both coordinate systems." actually means, you won't get F=ma^2 in a rotating system. If you measure things in a rotating frame, and calculate it inside the frame, then all the things follows what you have learnt. However, if you need to...
To be exact, we can't find any "force" in GR, instead we would say the spacetime itself is distorted by some kind of fields.
that means, it is equivalent to say gravity and force is the same thing, under SR's eqv.
There are theories proving photon mass are bounded by some extremely small numbers, however, the mass here means rest mass, not effective mass.
For reference, you may follow classical EM's deviation of what would happen if photon has mass, with fields as the tool.
Photon must follow by geodesic...