  Near-Earth asteroid (1862) Apollo has strong detections of both orbital
semimajor axis drift and rotational acceleration. We produce a unified model
that can accurately match both observed effects using a single set of
thermophysical properties derived from ground-based observations, and we
determine Apollo's long term evolution. We use light-curve shape inversion
techniques and the ATPM on published light-curve, thermal-infrared, and radar
observations to constrain Apollo's thermophysical properties. The derived
properties are used to make detailed predictions of Apollo's Yarkovsky and YORP
effects, which are then compared with published measurements of orbital drift
and rotational acceleration. The ATPM explicitly incorporates 1D heat
conduction, shadowing, multiple scattering of sunlight, global self-heating,
and rough surface thermal-infrared beaming in the model predictions. We find
that ATPM can accurately reproduce the light-curve, thermal-infrared, and radar
observations of Apollo, and simultaneously match the observed orbital drift and
rotational acceleration using: a shape model with axis ratios of
1.94:1.65:1.00, an effective diameter of 1.55 +/- 0.07 km, a geometric albedo
of 0.20 +/- 0.02, a thermal inertia of 140 +140/-100 J m-2 K-1 s-1/2, a highly
rough surface, and a bulk density of 2850 +480/-680 kg m-3. Using these
properties we predict that Apollo's obliquity is increasing towards the 180
degree YORP asymptotic state at a rate of 1.5 +0.3/-0.5 degrees per 10^5 yr.
The derived thermal inertia suggests that Apollo has loose regolith material
resting on its surface, which is consistent with Apollo undergoing a recent
resurfacing event based on its observed Q-type spectrum. The inferred bulk
density is consistent with those determined for other S-type asteroids, and
suggests that Apollo has a fractured interior.
