Limits on Leading Order Terms in $f(R,T)$ Gravity

We investigate the ideal gas approximation of Earth's atmosphere in the $f(R,T)$ modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the stress-energy tensor. We obtain a generic form for the gravitational field equations and derive the hydrostatic equation for Earth's atmosphere for leading order terms $f(R,T) = \frac{1}{16\pi} \left( R + 2\chi T \right)$. Based on the apparent accuracy of the 1976 U.S. Standard Atmosphere model, which varies no more than $10\%$ from observations, we find limits of $| \chi | \lesssim 1.9 \times 10^{-13}$.