So when the Simpsons parodied MacGuyver and he said ‘Don’t thank me, thank the Moon’s gravitational pull’, it was funny because it was true?
I believe that it was Patrick Moore the astronomer and well known debunker of astrology.
I think additionally there is a common misconception about tides that is relevant here.
Most people (including me until recently), thought of the moon as pulling water up towards it and partly acting against the earth’s downward pull. It does, but that’s a poor explanation for the tides, since you compute the total force on an object by summing all contributing forces, and the sum of a weak upward force and a strong downward force is going to point down.
Then I saw a video that I think explained it pretty well. It’s actually more about the water that is not directly under the moon having a vector that is not quite normal to the earth. The net effect of this is water sliding over slightly, and increasing the amount of water facing the moon, rather than the moon making water “bulge up”.
Since it’s more “moving over” than “bulging up”, even the moon will not create anything akin to tides in the liquids in your body, let alone the stars.
(clarifying) I mean increasing the volume of water that is on the side of the earth facing the moon, rather than the water itself turning the face the moon 
It may be easier to realize this if you know that tides occur on both the moon-facing side of the the Earth and the opposite side. And both tides have about the same magnitude.
Personally, I always see tides in terms of orbits. Not all the Earth is at the same distance from the Moon. Those parts closer to the Moon are going to try to orbit in a way that takes them closer to the Moon and those further away will try to orbit in a way that takes them further away. The Earth’s gravity counters this, so the Earth stays in one piece, but it doesn’t completely cancel it out.
Speaking of which, it is well known that Newton himself was into the occult, although antithetical to astrology. Indeed, books on theology, numerology and eschatology were dominant in his library, with alchemy being a close second.
It is also worth mentioning that Tycho Brahe, Johannes Kepler and Galileo Galilei were all practicing astrologers. Moreover, Newton’s theory of gravity was considered by his contemporaries as occult, as it implied action at a distance. Even Newton himself famously wrote:
It is inconceivable that inanimate brute matter should, without the mediation of something else which is not material, operate upon and affect other matter without mutual contact…That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.
Considering that science today cannot account for the large majority of matter and energy in the universe, and considering that quantum mechanics posits weird effects like non-locality, I would go slow in denouncing The Girl. Moreover so, in case she has additional qualities.
Said another way, Newton predicted there must be a “graviton” by any other name. The fact we haven’t sorted out its details yet doesn’t mean it’s not (probably) real.
Did he ? He subscribed to the corpuscular theory of light, indeed.
I think he avoided to theorize on the origins of gravity or its causes:
I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.
And the existence of gravitons or indeed quantum gravity is unclear in the least.
In almost Newton’s own words: “that gravity may act without the mediation of something else through which the force may be conveyed is a great absurdity”.
Sounds to me like he posits that something must be mediating = effectuating the force. He said he had no idea what it was. He was right in that.
In so far as the current Standard Model is accurate, it says something conceptually similar. In my deliberately non-technical words:
There is a thing we label a ‘graviton’ that mediates the gravitational force. Beyond naming it and describing its gross features, we don’t have the details worked out yet. But we’re sure it does this much: transmit gravity across empty space.
Out of curiosity would be the force of the Andromeda galaxy on us compared to a cow 18 miles away.
Except science has measured the matter and energy, and knows that that there is more out there than we can currently explain. Science has “known unknowns” that can be objectively studied.
There are no objective studies that indicate that the time of one’s birth and the arrangement of the planets and stars at that moment have any influence at all.
So no, I wouldn’t cut her any slack on astrology.
Wolfram Alpha says the pull of Andromeda on a 80Kg human is about 1.5E-11 Newtons. In old fashioned US units it’s about 3.4E-12 pounds. 3 trillionths of a pound.
A 500Kg cow pulling on an 80Kg human from 18 miles (I just love mixed units, but WA don’t care) is 3E-15 Newtons or 7E-16 lbs.
So the galaxy is pulling about 5,000X harder than the cow.
Move the cow to about 1/4mile away from the human and now they’re pulling equally hard.
Who said cows aren’t powerful? If you’re standing close enough to readily identify that it’s a cow (vs. some other critter), just one is more potent than a whole galaxy. A galaxy probably just teeming with Space Cows.
It would seem a pity not to mention Henry Cavendish’s experiments 24 years later (in 1798):
http://large.stanford.edu/courses/2007/ph210/chang1/
Let me venture that if she were an attractive girl claiming that you fit her stars according to astrology, you might have cut her some slack.
Or not.