During one of the intro to flying, there was a ship sneak mission. You had to turn off all your ships systems except 1 pip of power to the engines, and just slowly putter up to the target. That's what I did when I encountered this satellite surrounded by asteroids.

I'd recommend backing off and trying to approach the satellite from a different angle. The mines are laid out in a pattern, and depending on your approach angle, it'll either be really easy to get through, or basically impossible.

I tried from various different angles, going really slow with just one energy bar in engine. But it would explode every time. So I gave up.

I got through without any problems by approaching it from the side. Did it first try, but I recommend going slowly and quicksaving often