What would be the best way to move the earth if possible by human intervention via only using photons from the sun as a means of momentum force to move earth.Even a mile would be considered success so let's start small.This movement would increase its semi-major axis.The sun moves earth 15 cm away each year without our intervention.How could we increase the distance. http://ib-physics-ii-6b-e.aspen.high.schoolfusion.us/modules/locker/files/get_group_file.phtml?gid=4397333&fid=19334358
Earthmoving is impossible by all practical means, because it takes too much energy. This fully unscientific but amusing page lists a number of theoretical methods, none of which would work. The one that is least ridiculous is the method through gravitational fly-bys:
Gravity assistance. This is a method originally proposed as a means of moving Earth to a higher orbit around the Sun in order to save it from the Sun's inevitable Red Giant expansion. It involves asteroids, like the above method, only instead of direct impacts, this time we just steer them past the Earth, allowing rock and planet to exchange a little momentum, with the result of an Earth moving on a slightly different track and an asteroid moving on a significantly different one. You could reuse the same asteroid again and again, looping it around a few gas giants and back to gain lots more kinetic energy from those gas giants in the same way that Earth just gained velocity from the rock. You could repeat this thousands of times over the course of millions of years. Better, you could use many, many asteroids one after the other in a steady stream, and cut down the total time significantly. You could of course use this method to steer the Earth in any direction you wanted, not just away from the Sun... heh heh heh...
So, no. It's not plausible.
You want to move Earth by about 0.5 AU.
First, the easy thing.
If you want to move it in prograde direction, wait a month. If you want to move it in retrograde direction, wait 11 months. Done.
Now radial/antiradial option, somewhat harder.
Earth's orbital velocity is 30km/s. Mass of Earth is 6*10^24kg. From Kinetic Energy equation, that's 2.7e33 Joules. Potential Energy is -5.3e33 Joules (with 0 in infinity) for a total of -2.6e+33.
After moving it to 1.5 AU away, potential energy will be -3.53e33 Joules and kinetic - 1.77e33 J for a total of -1.76e+33
That's 8.4e32 Joules of energy difference in the easier of directions.
2.2e23 Joules is the combined energy of all Uranium, so we still need about four billion times more. Luckily that's not all we have - we're on our way to develop controllable nuclear fusion.
1 Deuterium atom an 1 Tritium atom creates 3.5 MeV (Helium) + 14.1 MeV (Neutron).
Since operating on atomic energies is cumbersome, let's transform that to moles. 1 mole of Deuterium (2 grams) + 1 mole of Tritium (3 grams) binding would produce 1.7e12 Joules. That's promising. We need 5e20 moles of both to produce the energy.
1.5e18 kg of tritium and 1e18 kg of deuterium.
We have 1.35e21 kg of water in all our oceans. 0.0312% deuterium by content is 4.2e17 kg of deuterium.
Ouch, bummer. We have only half the needed amount of deuterium and we still don't even have the tritium which would need to be produced.
And that's even before we begin to consider just how to efficiently utilize the energy for propulsion, with quite certain losses.
Shortly put, we don't have enough resources on Earth for that. Gerrit suggests gravity assists, but the timing would go rather into centuries, locating, encountering and redirecting them by an enormous fleet of extremely powerful starships. And the combined mass of the ones that would be able to be redirected into useful trajectories isn't all that big either...
So, no. It's not plausible. :)
Edit: Using sunlight...
If we took all the Sun energy that hits Earth and converted it to acceleration (somehow?) it would take 150 mln years to grow the orbit by 0.5AU.
Replacing the magical "somehow" with actual light pressure of 9.08 micronewtons/m^2 of solar sail thrust. will give us 0.27 Watt/m^2 at Earth's original orbital speed (and will grow worse with distance=sunlight and orbital speed dropping). (versus 1361 W/m^2 used in the above...) - but let's not limit ourselves to the size of Earth :)
I'll simplify the calculations by assuming constant speed and sunlight - it's a bad cheat but the interals I'd need to use otherwise give me creeps. But I'll happily multiply the requirement by square root of 2 to account for loss due to tacking against the solar wind by turning the sail 45 degrees.
Over 40 years, a square meter of sail perpendicular to the Sun will produce 34e7 Joules of energy, be it kinetic or potential by changing your orbital altitude. So, to reach our 8.4e32J needed for the 1.5AU orbit over that time we need 2.46e24 m^2 of area perpendicular to the Sun. Tilted 45 degrees - 3.48e24 m^2. A square sheet of 1,860,000,000km side. Or just over a billion by billion miles square :) Or 12x12AU which... um, seriously invalidates the "constant sun exposure" assumption. Well, let's just say solar sail is not a good planet propulsion.