>>8Source: Sir Issac Newton, namely his Law of Universal Gravitation.
Source 2: The physical observations of every physicist since.
http://www.physicsclassroom.com/class/circles/Lesson-3/Newton-s-Law-of-Universal-Gravitation
Since you don't seem to understand:
http://amazing-space.stsci.edu/resources/qa/gravity.php.p=Capture%2Bthe%2Bcosmos@,capture,%3EGravity@,capture,gravity,
There is no theory that an asteroid could affect the gravitational pull of the moon to affect the Earth. That is 100 percent, pants on head stupid. You aren't going to put an asteroid into lunar orbit and have it affect the gravity of the moon. The moon's gravitational pull is an effect caused by its mass and its acceleration. That's like saying putting racing stripe stickers on your 300z makes it faster.
(Sidenote: The burden of proof in a debate is on the person making the claim. The only reason I am even giving you this information is for other people who end up reading this. Also, learn to science, small mass is attracted to larger mass. I.e. You and the earth. That is pretty much the scale you are talking about with an asteroid and the moon. By the time you get an "asteroid" up to the size where it would affect the moon, you basically have another moon or dwarf planet.
Now for some of those maths you couldn't crack a physics textbook, do a google search, or check out anything written on the subject.
The mass of a 4 cubic mile object, lets make it really dense and say its made up of lead, so it has a density of 11.34 grams per cubic centimeter. Lets say there are four cubic miles of it with a constant orbital velocity of 1.023 km/s.
Now, 4 cubic miles into cubic centimeters (4.16818184306E+15 * 4) cubic centimeters to deal with. This comes out to 16672727372240000 cubic centimeters at 11.34 grams per cubic centimeter which comes out to: 189068728401201.6kg (kilograms), not a light object at all. Humans weigh, on average, 62kg for a comparison of mass.
The Moon, having an iron core and various upper strata, comes in at 7.3477×10^22 kg or 73477000000000000000000 kg now, which mass is larger? The moon, by ages. You don't need to believe me. Do the math yourself. The weight in grams per cubic centimeter of lead is known, the mass of the moon is known, the orbital distance for LLO (Low Lunar Orbit) is known (62-69mi), do the physics work yourself.