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Gravitational Pull of Distant Objects

I had a bit of fun today trying to explain to a friend how a star millions of kilometers away could have a gravitational pull on us.

It’s pretty simple, and still relies on Newton’s Law of Universal Gravitation.



Gaia, Mother Earth

Our planet has a mass of 5.97E24 kilograms, and a mean radius of 6.37E6 meters. Let’s assume a human mass of 75 kilograms (165 lbs) for the equations on this page.

The Earth pulls a 75kg person with a force of 736.22 N. One Newton is equal to an acceleration of one meter per second per second, for a weight of one kilogram. If we divide the force by our mass of 75 kg, we get Earth’s gravity, 9.81 m/s^2.


Sirius, the Brightest Star in the Sky

It’s actually two stars, Sirius A and Sirius B. Since Sirius A is twice the mass of the Sun, and Sirius B is about the same mass as the Sun, they have a combined mass of 5.96E30 kilograms. The binary star system is about 8E16 meters away.

All this means that Sirius pulls you with a force of 4.66E-12 N. If all the universe was to disappear, except for Sirius, we would initially fall towards it at a rate of 6.21E-14 m/s^2.


Polaris, the North Star

The north star is six times heavier than our Sun, and is 433 light years away. With values of m = 1.19E31 kg and r = 4.10E18 m, we can calculate that Polaris is pulling you with a 3.54E-15 N force.


Proxima Centauri, our Closest Neighbor

With a mass of 2.45E29 kg and a distance of 4.01E16 meters away, Proxima Centauri pulls you with a force of 7.62E-13 N.


The Andromeda Galaxy

Andromeda is 2.40E22 meters away (it takes light 2.5 million years to reach it), and has an estimated mass of 2E42 kg (one trillion Suns). It pulls you with a force of, wait for it, 1.74E-11 N. It pulls you stronger than Sirius, which is a million times closer.


Last but not Least, the Moon

The moon has a mass of 7.3477E22 kg, and a mean distance of 3.84399E8 meters from the center of the Earth.

If the moon happens to be exactly overhead, it pulls on you from a distance of 3.84399E8 m – 6.371E6 m (the radius of the Earth) = 3.78E8 m, exerting a force of 2.57E-3 N.

If, on the other hand, the moon would be on the opposite side of the Earth, its distance from you would be 3.84399E8 m + 6.371E6 m = 3.91E8 m, exerting a force of 2.40E-3 N. This is actually a big difference of around 7%!

Even at its strongest, we would not consciously feel the moon. After all, Earth’s pull is almost 300,000 times stronger!

And before you ask, even on top of Mount Everest wouldn’t change anything.

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