Orbital decay via gravitational emission in a hypothetical, two-body universe Assume we have a universe with nothing in it except for two objects. One of them is a stationary object that is perfectly spherical with the mass of the Moon (without any atmosphere, of course; also, let's call this Body A). The other body is a small satellite similar to the Hubble Space Telescope, orbiting at 100 miles (161 km) above the surface of Body A.
How long would it take for the satellite to crash into Body A via gravitational emission?
Using this equation from Wikipedia for the approximate merger time:
$$\frac{5}{256}\frac{c^5}{G^3}\frac{r^4}{m_1m_2(m_1+m_2)},$$
and Wikipedia's values for the Moon's equatorial radius and mass, and the launch mass of the HST, we can use this query in Google:
((5/256) * (c^5/G^3) * ((100 miles) + (1738.1 km))^4 / ((11110 kg) * (7.347631E22 kg)^2))
to perform the calculation.
The result is $\approx 3.4497 \times 10^{46}$ seconds, or around $1.093 \times 10^{39}$ years, which is about $7.93 \times 10^{28}$ times the current age of the universe.
That equation is for a circular orbit, and it's only a crude estimate based on orbital energy lost via gravitational radiation. It mostly ignores the change in the orbital radius, since that's fairly small until the final stages of the merger.
There's some information about the effect of orbit eccentricity  on changes to orbital angular momentum and energy due to gravitational radiation at Two-body problem in general relativity.