09 Feb '15 13:031 edit

So I was imagining a magic acceleration platform that would accelerate at a constant rate of 1.2 G's, 11.76 M/sec^2 or 38.4 M/sec^2, take your pick.

So this device is hooked to a space-worthy vehicle and can accelerate straight up, no curved flight to make it easier. So the thing that obviously pops up when trying to figure out at what altitude does it achieve escape velocity or how much time it takes to get to that point and how fast would it be going when it passes the moon, for instance.

Clearly, when it takes off, you subtract Earth's gravity, 32 F/S^2 or 9.8 M/S^2 so it is only going up at a rate of 0.2 G. But higher up, Earth's gravity is going down, so at 2 R (about 4000 miles up or 6400 Km) Earth's gravity is 1/4th of the surface.

So how do you combine those two to get a formula that can calculate the altitude it achieves escape velocity or the velocity after X amount of seconds, at infinity, the craft will achieve its full accel, 1.2 G's So it starts at 0.2 G's and ends at 1.2.

What would the formula be for velocity at a certain altitude, velocity after a certain time?

I assume this kind of problem was solved by Isaac himself but I would like to learn how to handle this situation.

So this device is hooked to a space-worthy vehicle and can accelerate straight up, no curved flight to make it easier. So the thing that obviously pops up when trying to figure out at what altitude does it achieve escape velocity or how much time it takes to get to that point and how fast would it be going when it passes the moon, for instance.

Clearly, when it takes off, you subtract Earth's gravity, 32 F/S^2 or 9.8 M/S^2 so it is only going up at a rate of 0.2 G. But higher up, Earth's gravity is going down, so at 2 R (about 4000 miles up or 6400 Km) Earth's gravity is 1/4th of the surface.

So how do you combine those two to get a formula that can calculate the altitude it achieves escape velocity or the velocity after X amount of seconds, at infinity, the craft will achieve its full accel, 1.2 G's So it starts at 0.2 G's and ends at 1.2.

What would the formula be for velocity at a certain altitude, velocity after a certain time?

I assume this kind of problem was solved by Isaac himself but I would like to learn how to handle this situation.