iqbalgomar
I used to see this as a flaw too, but as I've become more familiar with physics I've also become more effectively intuitive in my speculations about same.
Intuitively, it seems to me that such calculation of the Earth's position would be unnecessary. Why? Because we're within the Earth's inertial frame. We share the planet's momentum. Gravity is a four-dimensional waveform, not three...
If you're standing on the roof of a moving train and you jump into the air (disregarding wind-resistance) you land in the same spot when you come down. I picture Earth as the train, in four dimensions. I think the analogy is apt. Physics experts? Correct me if I'm wrong.
You're on the right track (pun intended
).
If we're going to travel in time then we have to face some consequences. Turning a knob to "2359 hrs, 31-DEC-1999" so we can go back and celebrate Y2K New Year's Eve isn't going to work. Hours, minutes, seconds and Gregorian Calendar dates are arbitrary time measurements. We humans made them up.
But if we look at the situation from the POV of Special Relativity it becomes a lot simpler. Space and time become space-time. We can express any "event" as a 4D Cartesian coordinate. We rotate our system of coordinates and we travel along the "x" axis, rotate 90 degrees and we travel along the "y" axis, another 90 degree rotation and we travel along the "z" axis and another "rotation" of 90 degrees and we travel along the "t" (time) axis. That last (hypercubic) rotation isn't something that we can easily picture in our mind but we sure can do it with a computer.
If we rotate less than 90 degrees in any direction we can use trig "sine" (or cosine) funtions to travel in both space and time (something that Boomer, writing as Titor, didn't realize).
So, traveling to an earlier (or later) Earth is a "simple" rotation of the system of coordinates to go from point "A" (hear and now") to point "B" (there and then).
NOTE: Scare quotes on "simple" because it's only simple in the sense of Cartesian coordinates and geometry. It's obviously hugely complex to actually pull it off in the real world.
However, it's a simple process to determine where the Earth is (or was) at some point in time. If we can dial in the 4D coordinate we can get there. The problem then become one of accuracy. We can dial it in, but can we dial in, say, "1975" from "2036" with a degree of accuracy sufficient to avoid a catastrophic "landing". Those two spacetime events can be said to be seperated by 61 years.
They can also be said to be (more accurately) seperated by 61 light years (that's a valid 4D coordinate seperation of the two events).
A light year is ~9.5 * 10^12 km. So 61 light years is ~580 * 10^12 km.
If our instruments are 99.9999999% accurate we'll miss the alternate Earth by only...hold your hat...580 million kilometers, or we could arrive at the right location but miss the time by 122 days, 15 hours, 21 minutes, or a sine function of the combination of the two, i.e, somwehere in between 580 million km and 122 days (assuming that the world you left and the world you arrive at are at rest WRT each other...which may not be a good assumption).
So, in your analogy, you jump up in the train and land at about the same spot. But the jump (event "A") and the landing (event "B") are seperated by a very small period WRT a light year. In that case "almost the same spot" is a very accurate approximation.
If, however, you jumped up and hung in the air for 61 years in some form of Hilbert space you will not land in the same spot by any estimation. Your intuition has to be supplemented by some very complex forms of analytic geometry.
And then you have to hope to God that the linear and angular velocity that you had when you left point "A" is the same as when you arrive at point "B" (in the alternate universe).
There's no guarantee that the angular and linear velocity of point "B" is the same as point "A". You could have a soft landing or you could scream in at Mach 10 and an odd angle for a rather "difficult" landing. I think that Rainman would agree...pilots call this "augering in".