Read "Space Tug" by Murray Leinster online for free on Textopian. Full text with search, annotations, highlights, and AI-powered reading aids.
But even at ten gravities' drive it takes time to travel 4,000 miles. At three, and coasting a great deal of the way, it takes much longer. The Platform circled Earth in four hours and a little more. Anything intending interception and rising straight up needed to start skyward long before the Platform was overhead. A three-g rocket would start while the Platform was still below the western horizon from its launching-spot. Especially if it planned to coast part of its journey -- and a three-gravity rocket would have to coast most of the way.
So there was time. Coasting, the rising manned rocket would be losing speed. If it planned to go no higher than the Platform's orbit, its upward velocity would be zero there. If it were intercepted 500 miles down, it would be rising at an almost leisurely rate, and Joe and the Chief could check their Earthward plunge and match its rising rate.