Technology has been progressing, but humans have not discovered any new law of physics. So by 2085, all new technologies are still based on today's science.
Many nations and corporates are involved in the competition for space, and none can monopolize space yet. No country can assert absolute hegemony on the Earth either. That said, you can't simply eliminate all who oppose you.
The economy in space relies on mining asteroids and collecting solar power. Many powers, primarily chartered companies, focus on scrambling for the asteroid belt. There are some permanent settlements on the moon too, and the moon is mostly under the control of nation-states on the Earth. The development and exploitation of Mercury have just become cost-effective due to the advancements in rocketry, and the competition for Mercury has just started.
The laser-pushed propulsion system will locate in the orbit of Mercury and operate on the abundant solar power there. It also needs a giant Fresnel zone plate located a few astronomical units away from the sun to focus its laser beam. Advanced AIs can mine Mercury and execute the construction project mostly automatically, with little human labour cost.
A thousand-terawatt laser system around mercury will threaten the settlements on the surface of the Moon and cities on the earth (if it can aim and focus its beam on them at all). It can also easily scorch the mining asteroids in the asteroid belt and destroy the surface outposts and the space stations all over the solar system. Therefore, no party will feel comfortable if they know such or suspect such a system is built with any military capability, unless it is under their control, or so they think.