Gravitational attraction of stars and cows


One attempt at rationalizing astrology is to say that the gravitational effects of celestial bodies impact our bodies. To get an idea how hard the stars and planets pull on us, let’s compare their gravitational attraction to that of cows at various distances.

Newton’s law of gravity says that the gravitational attraction between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. From this we can solve for how far away a cow would have to be to have the same gravitational attraction.

d_{\text{cow}} = d_{\text{star}} \sqrt{ \frac{m_{\text{cow}}}{m_\text{star}} }

For round numbers, let’s say a cow weighs 1000 kg. (Strictly speaking, that’s a more typical weight for a bull than a cow.) Then Jupiter has as much gravitational tug on a person as does a cow about two feet away.

Regulus, the brightest star in Leo, has the same pull as a cow about 5 miles away. Alpha Centauri, the closest star to Earth (other than the sun, of course) has about the same pull as a cow 18 miles away.

Calculations were based on average distance. The distance to planets changes over time, but so does the distance to a given cow, and the relative change in the latter over time is potentially much larger.

| Body           | Cow distance |
| Jupiter        |     0.57 m   |
| Venus          |     2.45 m   |
| Mars           |    10.06 m   |
| Regulus        |     7.81 km  |
| Alpha Centauri |    28.70 km  |

21 thoughts on “Gravitational attraction of stars and cows

  1. Conclusion: Astrology is bull.

    My predicted response of an astrologer-believer to this analysis is, “But there are so many more stars than cows!” Good luck explaining vector addition to them. :-)

  2. One thing I didn’t get into is the dynamics of cows and stars. The relative distance to a cow wandering around a pasture changes more in an hour than the relative distance to Regulus changes in a lifetime.

  3. What this article overlooks is the indirect effect of this gravitation. Yes, the moon’s effect on only my body is tiny, but the moon’s cumulative effect on every particle on Earth adds up to substantial cycles which we observe as tides. If it affects the whole, then it also affects the parts.

  4. The analogy to dark matter is what comes out of the back end of the cow. It is invisible until you step into it. Cows produce a lot of this but I don’t know if 23% of the mass in the pasture.

  5. Actually we are in free fall relative to the gravitational force of distant objects. The only thing that is locally measurable are tidal forces. Which follow a cube law.
    A back of the envelope calculation says that EVERY cow on Earth exerts a larger tidal pull on us than ANY distant star. Excepting, of course, some calves.

  6. I feel like a cow 0.57m from me all the time would have an effect on my life. Clearly, there is something to a astrology.

  7. I forget the exact numbers, but a while back I worked out that the moon has about 1/300,000 as much gravitational pull on us at the surface of the Earth than the Earth does.
    So even the moon has no effect on us, unless we live in a tide pool.

  8. Well, just plug in the numbers.

    Unless I miscalculated, the cow distance would be about 3.4mm (as the Sun is much closer to us and more massive than Jupiter).

  9. Abhishek Bamotra

    Something really interesting that made my day. It will be good if you can also write about the pull in cow terms as asked by @Harris S. Newman.

  10. If a star is very far away, would it’s pull have a quantum effect? If it’s too small or wouldn’t happen at all?

  11. Rough estimate, the sun pull is the equivalent of 22,000 cows located at 50 centimeters

  12. Thank you for this, I’m going to hang it on the wall.
    More relative-to-cow posts please!

  13. So if I eat more beef, I’m clearly more likely to be affected by the stars. QED – Astrology proved.

  14. Thanks a lot for this, helped me on a Twitter discussion about astrology and gravitational pull just a second ago. ;)

  15. The Sun being equivalent to a cow being 3mm away is not quite right. The equivalence requires 3mm of distance from the center of mass, but also being outside the mass. This could be an issue with being 0.57m from a cow, as part of the cow could be on the other side of you from the cow’s center of mass, which invalidates the similarity.

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