# What gravitational force is stronger, the star Alpha Centuri far away or a skyscraper next to you?

I was having a conversation about the sillyness of astrology, and the (of course a girl) was trying to tell me that the stars have gravity that effect the tides and can affect your personality in the same way. I argued that because the stars are so far away, thier gravity effects are essentially zero and i argued that the gravitational effects of a skyscraper (mass=gravity) that you brush your shoulder with as you walk by on the street probably has a greater gravitational impact on you. I of course have no idea if this is actually true. Is it?

You’re absolutely right - both times. The gravitational effect of Alpha C on you is way smaller than the effect due to the skyscraper - and the tidal effect of Alpha C is even smaller than the tidal effect of the skyscraper (tides decrease with the third power of the distance).

How about a cow in the next county? From https://www.johndcook.com/blog/2018/03/28/cow-astrology/

Alpha Centauri, the closest star to Earth (other than the sun, of course) has about the same pull as a cow 18 miles away.

Moderator Note

jonpluc, let’s refrain from sexist remarks in this forum (or elsewhere on the board). This implies that silly remarks are typical of “girls.” No warning issued, but don’t do this in the future.

Colibri
General Questions Moderator

But the skyscraper is both more massive and much closer than that cow.

It should be pretty easy to get a wild guess about the mass and distance of the skyscraper and of Alpha Centauri, but I don’t remember the formula for gravitational attraction. Anyone else?

I can’t do formulas on my phone, but it’s given in the wiki article:

The ratio of forces would be:

(mass_object1/mass_object2)/(distance_object1/distance_object2)^2

so in this case the mass of Alpha Centuri is about 22 orders of magnitude larger. If we imagine you’re standing 1 m away from the skyscraper them the distance to Alpha Centuri is 16 orders of magnitude larger, so we get:

10^22/(10^16)^2

which is about

10^-10

pretty small.

mass divided by distance squared for gravity (times a constant we don’t need for this comparison)
mass divided by distance cubed for tides (times the same constant).

The distance to Alpha C is 10^17 feet (or so). The mass of Alpha C is 2.510^29 kg. So the force from Alpha C is 2.510^29/10^34 = 2.5/10^5. The skyscraper is (say) 100 feet way, so its force is Mass of Skyscraper/10^4. If the skyscraper weighs more than a quarter of a kilogram (half a pound) - which it does, the skyscraper has a larger force than the star.

On the other hand, if the skyscraper was about 100km away the gravitational force would be about equal to Alpha Centauri.

The bottom line of course is that it doesn’t matter which skyscrapers, cows, cars, whatever are nearby. Whatever random arrangement of terrestrial stuff there is, and wherever on Earth you happen to stand, the effects of all the Earthly stuff totally overwhelms the microscopic gravitational signal from the planets, much less the far more distant stars.

The formula is on the link I posted. The board wouldn’t let me C&P it.

Not to mention the gravitational pull of the Earth. That’s got to swamp out everything else.

Who was it who said that at the time of a baby’s birth, the gravitational effect of the obstetrician is larger than the gravitational effect of any planet. (The arrangement of the planets against the fixed stars is used in calculating natal charts. Most astrology fans cite the gravitational pull of the planets, rather than the stars.)

We did that calculation high school - and you could add up ALL the exterior planets as if it were a full alignment, and it wouldn’t cancel out a decent-sized OB.

Carl Sagan in the original Cosmos series.

Thanks. I was too lazy to google.

in Homeopathic Astrology the weaker the gravitational effect of a planet the more effect it has on a person’s life. It’s the memory of the gravity that makes the difference.

But . . . but . . that means that we’re most strongly affected by stars we can’t see.

I learned about the https://en.wikipedia.org/wiki/Schiehallion_experiment Schiehallion Experiment here on the Dope - the gravitational effect of a mountain is measurable with low-tech tools!

That was what I was thinking- Newton figured out how to calculate this a long time ago.

Is this how gravitational dilation works?