Boeing unveiled its fix for its troublesome 787 battery on Friday and is aiming to wrap up testing within two weeks. The company hopes to get quick approval from the Federal Aviation Administration, and bring an end to the grounding of the plane that began on Jan. 16. Company executives said the plane could be flying again within weeks, although aviation authorities in the U.S., Japan, and elsewhere will ultimately decide the timing. Boeing still doesn’t know the root cause of the fire on a parked 787 Dreamliner in Boston on Jan. 7, or of the smoldering battery that forced an emergency landing on another 787 nine days later. Boeing executives said they may never know. Instead, they’re building a battery they hope cannot burn. The battery’s eight cells will each be wrapped in an orange tape that won’t conduct electricity. A glass laminate sheet protects the cells from the aluminum case. The wires on top are getting extra heat-resisting insulation. And the whole works now goes inside a new sealed steel tub that looks like a kitchen trash can tipped on its side. If a cell overheats, a titanium hose will carry the gases to the outside of the plane through a new inch-and-a-half hole in the fuselage. The changes make it “very unlikely” that another battery event will happen, said Ron Hinderberger, Boeing’s vice president for 787-8 engineering. Boeing hopes the new steel box won’t just contain a battery fire, but will prevent one from starting at all by choking off the flow of oxygen and venting the battery gases and air inside the box outside of the plane. The new design was tested before Boeing proposed it to the FAA. It will be retested so it can be certified for use on the plane, Hinderberger said. That should be done within a week or two. After that, approval will be up to the FAA. He said it would be inappropriate to speculate on how long that would take. Boeing shares rose $1.81, or 2.1 percent, to close at $86.43. They’ve been rising in recent weeks as investors have been anticipating a fix for the battery problems.