Yes, orbiting black holes would emit gravitational waves even if they are moving at a constant speed in their orbits. The changing direction of their motion, resulting from the gravitational attraction between the black holes, constitutes acceleration, which is a necessary condition for the emission of gravitational waves.
According to Einstein's theory of general relativity, accelerating masses or changing mass distributions generate gravitational waves. In the case of orbiting black holes, their motion involves acceleration because their velocities constantly change direction as they orbit each other.
As the black holes orbit, they undergo periodic changes in their gravitational fields. These changes in the gravitational field propagate outward as gravitational waves, similar to how ripples spread on the surface of a pond when a stone is thrown into it. The emitted gravitational waves carry away energy and momentum from the system of orbiting black holes.
It's worth noting that the emission of gravitational waves is most significant when the orbiting black holes are close to each other or when they approach the final stages of merging. As the black holes get closer, their orbital velocities increase, leading to more significant acceleration and stronger gravitational wave emission.
In 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected gravitational waves for the first time, which were produced by the merger of two black holes. This observation provided direct evidence of the existence of gravitational waves and confirmed one of the predictions of general relativity.