The Force of Gravity on Sirius


Sirius Gravity

This infographic recently showed up on my Facebook feed, posted by the Astronomical League. This just didn’t sound right to me, so I checked it out. It’s true that the force of gravity on Sirius B is way, way stronger than on Earth- it’s a white dwarf, a star containing the mass of the sun squished into a sphere smaller than Earth! That lends itself to TREMENDOUS surface gravity. But Sirius A has nothing to do with it.


The calculation used to determine the force of gravity between two objects is as follows: N = G*((m1*m2)/d^2) where N is force in Newtons, G is the gravitational constant (6.674*(10^-11)N*m^2/kg^2), m1 and m2 are the masses of the two bodies in kilograms, and d is the distance between them in meters.

So if we wanted to calculate the force exerted on a 3g sugar cube on the surface of Sirius B *by Sirius A*, we’d first need to gather the information on masses and distances:

  1. Closest distance between Sirius A and Sirius B: ~6.9 AU or 1.03E+12 meters
  2. Mass of Sirius A: 2.02x mass of Sun or 4.02E+30kg
  3. Mass of sugar cube on Sirius B: 0.003kg

Now we just plug in the values as follows:

(6.674*(10^-11))*((4.02E+30*0.003)/1.03E+12^2) = 7.65E-07 = 0.000000765 newtons


That’s a very tiny amount of force, nowhere near the amount that this quote claims (“Due to Sirius A”). It’s actually less force than the Sun itself exerts on a three-gram sugar cube, sitting on the table! We don’t see those up and floating away.

The tremendous surface gravity of Sirius B comes from its own incredible density. I actually calculate the surface gravity from Sirius B itself to be 437,000x stronger than on Earth, even higher than this quote claims, but one or both of the calculations could be off. The point is, Sirius B would squash you flat in a heartbeat!


Here’s a link to a spreadsheet with many different calculations of gravity for the Sirius and Solar Systems; feel free to check it out, or make a copy and mess around!

https://docs.google.com/spreadsheets/d/127CJPuj0lD5CNVoum1-fQS-7mTFHxwrF1vNNKLuuRK4/edit?usp=sharing

 

Clear Skies!
Lauren Herrington
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