Sun – Earth – Moon

Update: I didn’t thought about the possibility that Moon’s core and crust may have significantly different spinning frequencies. This post needs some future attention, so don’t take those calculated numbers too seriously.

In this post I’ll do some calculations involving our Sun, Earth and Moon. Let’s start with Sun and Earth. How much mass Sun has? Based on Newton, the mass of Sun is \(1.9891*10^{30}\) kg. Based on ToEbi, the mass of Sun is \[\frac{M_{earth}v^2}{R}=(G_{earth}+G_{sun})\frac{M_{earth}M_{sun}}{R^2}\] where \(G_{sun} = 0.5*f_{sun}^2 \approx 0.5*800*10^{-9^2} \) which gives us \(M_{sun} \approx 1.98*10^{30} \) kg. Total rotation frequency of Sun is an estimation [1] combining the rotation frequency of the core and outer layer.

Ok then, how about our Moon? Current estimation is \( 7.34767309 * 10^{22}\) kg. Based on ToEbi, the mass of Moon can be calculated from \[1.62 = G_{moon} \frac{M_{moon}}{1737100^2}\] where \(G_{moon} \approx 8.97*10^{-14}\), hence \(M_{moon}\approx 5.449695*10^{25} \) kg! That’s right, Moon has a bigger mass than Earth! But Moon orbits Earth, not the other way round! That’s right, the big difference comes from Moon’s much smaller rotation frequency.

How about forces between Sun, Moon and Earth (based on ToEbi)?

  • Sun – Earth: \(\approx 3.53*10^{22}\) N
  • Earth – Moon: \(\approx 1.47*10^{23}\) N
  • Sun – Moon: \(\approx 1.965*10^{21}\) N

So, there is no chance that Sun takes Moon from us 🙂 At least not in the near future.

[1] http://articles.adsabs.harvard.edu//full/1994ApJ…435..874J/0000878.000.html

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