31 May '15 12:326 edits

I like to do linear acceleration times, especially for space travel and also for drag racing.

The equation for time is T=(2S/A)^0.5 which gives you the time it takes to go S distance with A acceleration.

That works for the racetrack since you want to be going fast at the end.

Not so good for space travel where you want to be doing zero relative velocity at the end of the journey.

So I worked out to get that time, where you accelerate to the half way point, then decelerate the second have, thus arriving on target with zero relative velocity. All you do is multiply the original answer by the square root of 2, so the journey takes 1.414 times the full acceleration trip.

I worked up the equation to enter miles (easy to convert it to km) and give the answer in days. So 1 day accelerating half way and decel the other half in space at one G says you end up 11.5 million miles away.

But the way you enter this into my trusty rusty TI 86 is all algebraic and it is a bit messy:

T=(((((S*10580)/A)^0.5)*2^0.5)/86400)

A in feet per second, 1 G=32.

S in miles.

T in days.

So one G for one day = 11 odd million miles and you are stopped at the end of that journey fully stopped at the end which is vital if you want to orbit a far away planet or do astrological experiments or observations.

One G for 90 days = 91 BILLION miles. And so forth.

But I would like to enter this into my also trusty rusty HP48.

Can anyone help me get this silly algebraic into RPN?

I think this is a fun exercise because I also think in the future, propulsion systems are going to be able to produce long term 1 or more g's of acceleration so you go in a more or less straight line to your goal and in only a few days or weeks max to get anywhere in the solar system. I think that is just a matter of time before we see that kind of space travel.

The last one I mentioned, 90 days, 90 billion miles is also important in my view because it gets you past the first focal point of the focal line of gravitational lensing the sun produces. But that is another story. The first focal point is about 55 billion miles away from the sun. There is not much solar gravity focusing till you get at least that far.

I can elaborate on that theme if anyone wants but that is not about this op. For instance, forgetting solar gravity focus, just BEING 90 billion miles out, if you have a nice Hubble sized scope aboard or even close to that, now the parallax measurements of the distance to stars can be made to much further distant stars, whereas now our parallax is about 190 million miles wide (the diameter of Earth's orbit) but now with a scope at 90 billion miles out, the parallax width is now 50 times greater and so the direct measure of star distances will be at least that much further out, perhaps all the way to the center of the galaxy for accurate direct distance measurements.

The equation for time is T=(2S/A)^0.5 which gives you the time it takes to go S distance with A acceleration.

That works for the racetrack since you want to be going fast at the end.

Not so good for space travel where you want to be doing zero relative velocity at the end of the journey.

So I worked out to get that time, where you accelerate to the half way point, then decelerate the second have, thus arriving on target with zero relative velocity. All you do is multiply the original answer by the square root of 2, so the journey takes 1.414 times the full acceleration trip.

I worked up the equation to enter miles (easy to convert it to km) and give the answer in days. So 1 day accelerating half way and decel the other half in space at one G says you end up 11.5 million miles away.

But the way you enter this into my trusty rusty TI 86 is all algebraic and it is a bit messy:

T=(((((S*10580)/A)^0.5)*2^0.5)/86400)

A in feet per second, 1 G=32.

S in miles.

T in days.

So one G for one day = 11 odd million miles and you are stopped at the end of that journey fully stopped at the end which is vital if you want to orbit a far away planet or do astrological experiments or observations.

One G for 90 days = 91 BILLION miles. And so forth.

But I would like to enter this into my also trusty rusty HP48.

Can anyone help me get this silly algebraic into RPN?

I think this is a fun exercise because I also think in the future, propulsion systems are going to be able to produce long term 1 or more g's of acceleration so you go in a more or less straight line to your goal and in only a few days or weeks max to get anywhere in the solar system. I think that is just a matter of time before we see that kind of space travel.

The last one I mentioned, 90 days, 90 billion miles is also important in my view because it gets you past the first focal point of the focal line of gravitational lensing the sun produces. But that is another story. The first focal point is about 55 billion miles away from the sun. There is not much solar gravity focusing till you get at least that far.

I can elaborate on that theme if anyone wants but that is not about this op. For instance, forgetting solar gravity focus, just BEING 90 billion miles out, if you have a nice Hubble sized scope aboard or even close to that, now the parallax measurements of the distance to stars can be made to much further distant stars, whereas now our parallax is about 190 million miles wide (the diameter of Earth's orbit) but now with a scope at 90 billion miles out, the parallax width is now 50 times greater and so the direct measure of star distances will be at least that much further out, perhaps all the way to the center of the galaxy for accurate direct distance measurements.