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commit14: fixed mathjax errors

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Nathaniel Moll 2023-11-05 18:14:06 -05:00
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content/posts/matter_and_gravity.md
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@ -10,17 +10,17 @@ mathjax: true
The average density of the Solar System is about 1 billion times smaller then the Earth's atmosphere. The average density of the Solar System is about 1 billion times smaller then the Earth's atmosphere.
The above statement puts into perspective the unique nature of space and the universe: It's mostly empty, a vacuum. The Solar System, which includes all the planets, asteroids, and the Sun, which has a mass of roughly 2.0 x $\10^{30}$ kilograms. Yet, since the Solar System is so large, the density is still quite less than even a gas. This is due to what density really is and how it's calculated. Density is important in the field of astrophysics and can be calculated using the following equation: The above statement puts into perspective the unique nature of space and the universe: It's mostly empty, a vacuum. The Solar System, which includes all the planets, asteroids, and the Sun, which has a mass of roughly 2.0 x $10^{30}$ kilograms. Yet, since the Solar System is so large, the density is still quite less than even a gas. This is due to what density really is and how it's calculated. Density is important in the field of astrophysics and can be calculated using the following equation:
$$\(\frac{M}{V})$$ $$\\frac{M}{V}$$
Where: Where:
- M = Total mass - M = Total mass
- V = Volume - V = Volume
The average total mass of the Solar System is about 1.9884 x $\10^{30}$ kilograms. This is mostly due to the Sun, since the additional mass of the planets can be ignored for the sake of this example. In addition, the total volume of the Solar System is about 3.9 x $\10^{38}$ cubic meters...that's a lot. The average total mass of the Solar System is about 1.9884 x $10^{30}$ kilograms. This is mostly due to the Sun, since the additional mass of the planets can be ignored for the sake of this example. In addition, the total volume of the Solar System is about 3.9 x $10^{38}$ cubic meters...that's a lot.
Thus, the average density of the Solar System is $\(\frac{1.9884\times10^{30}}{3.9\times10^{38}})$ = 5.09 x $\10^{-9}$ Thus, the average density of the Solar System is $\\frac{1.9884\times10^{30}}{3.9\times10^{38}}$ = 5.09 x $10^{-9}$
As you can see, the density is quite low. As you can see, the density is quite low.
@ -32,10 +32,10 @@ As you can see, the density is quite low.
The force due to gravity can be calculated in a simple way. The formula is as follows: The force due to gravity can be calculated in a simple way. The formula is as follows:
$$\[\mathcal{F} = \frac{G m M}{r^2}\]$$ $$\mathcal{F} = \frac{G m M}{r^2}$$
Where: Where:
- G = The Gravitational constant with a value of 6.67 x $\10^{-11}$ $\(\frac{m^3}{Kg \times sec^2})$ - G = The Gravitational constant with a value of 6.67 x $10^{-11}$ $\frac{m^3}{Kg \times sec^2}$
- m = mass of smaller body in question - m = mass of smaller body in question
- M = mass of larger body in question - M = mass of larger body in question
- r = distance between the *centers* of the bodies in question - r = distance between the *centers* of the bodies in question