Introduction: Mechanics of Time Travel
Time travel only works if you plot the movement of planets, stars and galaxies. For a time machine to stay in one spot on Earth as it travels through time, it must also follow the Earth's trajectory through space.
This instructable lists a few, but not all of the mathematical projections you will need to take into account before you set off on your trip across time.
Step 1: First, You Need to Know Where You Are Going.
For instance, it's May 9th 2008, you want to go back to Nov 4 2007.
If you just pop back in time, without moving in space, you'll wind up on the other side of the sun from where you want to be. Due to the Earth being in a different place on Nov 14th
The Earth spins counterclockwise at approximately 1675km per hour, looking down from the north pole.
The distance from the Earth to the Sun changes due to it being in an Elliptical orbit. The Average distance is 149.6 million km with the Perihelion (shortest distance) being on January 3rd 147,300,000 Km, and the Aphelion (longest distance) being 152,100,000 km on July 4th.
You'll need to find a way to move through the Suns gravity well to the point where the Earth was before.
Step 2: Then You Need to Know Where Our Solar System Has Moved.
Then the difficulty increases when you look into how the solar system moves in our galaxy.
As our solar system orbits the galaxy at a speed of almost 220km per second, it moves in a sine wave that has a 64 million year cycle.
So the entire solar system on November 14th 2007 would be over 3,364,416,000 Kilometers from where it was on May 9, 2008.
Step 3: Where Has the Galaxy Gone?
To further complicate things, The Milky Way Galaxy is even moving.
Many astronomers believe the Milky Way is moving at approximately 600 km per second relative to the observed locations of other nearby galaxies. Most recent estimates range from 130 km/s to 1,000 km/s. If the Galaxy is moving at 600 km/s, Earth travels 51.84 million km per day, or more than 18.9 billion km per year, about 4.5 times its closest distance from Pluto. The Galaxy is thought to be moving towards the constellation Hydra, and may someday become a close-knit member of the Virgo cluster of galaxies.
Another reference frame is provided by the Cosmic microwave background (CMB). The Milky Way is moving at around 552 km/s with respect to the photons of the CMB. This can be observed by satellites such as COBE and WMAP as a dipole contribution to the CMB, as photons in equilibrium at the CMB frame get blue-shifted in the direction of the motion and red-shifted in the opposite direction.
Step 4: So Before You Set the Date in Your De Loren and Take Off.
So in order to land on the same spot on Earth at any time in the future or past you would have to be able to map the movements of the Earth while taking into account all this spatial movement from the rest of the universe. Otherwise you will pop up in the right time, but in empty space, the sun, or in solid rock.
These calculations would show you where you need to move to, but you'd still have to find a way to move through the time barrier so that you and the Earth would meet up.
If you think of how this would actually work, you would actually be able to move anywhere in the Universe, in time. Only if you can do the calculations.
To all your budding time travelers, good luck!
Update: I changed the title to Mechanics of Time Travel from your suggestions. Thanks!