  We propose a quantum ranging protocol to determine the distance between an
observer and a target at the line of sight in the near-Earth curved spacetime.
Unlike the quantum illumination scheme, here we employ multiple quantum
hypothesis testing to decide the presence and location of the target at the
same time. In the present protocol, the gravity of the Earth influences the
propagation of photons and the performance of quantum ranging. We find that the
maximum potential advantages of the quantum ranging strategy in the curved
spacetime outperform its flat spacetime counterpart. This is because the effect
of gravitational red-shift and blue-shift on the entangled signal photons can
be canceled out, while the thermal photons only suffers from the gravitational
blue-shift effect. We also show that the number of transmitted modes can
promote the maximum potential advantage of the quantum ranging tasks. The
maximum potential advantage of quantum ranging in the curved spacetime can not
be raised sharply by dividing the range into multiple slices.
