In a previous paper of mine¹ I discussed Hubble’s Law and the Reciprocal System. I integrated Hubble’s equation to obtain the following equation representing the distance of a galaxy from our galaxy as a function of time:
r = r_{o} + (v_{i}  r_{o})e}^{Ht} 
(1)

where r_{o} is the gravitational limit, H is Hubble’s constant, and r_{i} is the initial distance.
Now if we go back to Hubble’s original equation,
V = Hr 
(2)

we can differentiate this, instead of integrating it as before.
dv/dt = H dr/dt = a = Hv = H²r 
(3)

Hence, the force of the spacetime progression must be
Fp = m_{G²} H²r + F_{G¹G²} 
(4)

where m_{G²} is the mass of the galaxy moving away and F_{G¹G²} is the gravitational attraction.
This equation should have many applications in the Reciprocal System.
References
1. R. W. Satz, “Hubble’s Law and the Reciprocal System,”Reciprocity, Vol. VII, No. 3