From 198a5c179f1e481b880ca6986ddee97d2fa76b9a Mon Sep 17 00:00:00 2001 From: Nathaniel Moll Date: Sun, 5 Nov 2023 18:14:06 -0500 Subject: [PATCH] commit14: fixed mathjax errors --- content/posts/matter_and_gravity.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/content/posts/matter_and_gravity.md b/content/posts/matter_and_gravity.md index 9459343..831886b 100644 --- a/content/posts/matter_and_gravity.md +++ b/content/posts/matter_and_gravity.md @@ -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 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: - M = Total mass - 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. @@ -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: -$$\[\mathcal{F} = \frac{G m M}{r^2}\]$$ +$$\mathcal{F} = \frac{G m M}{r^2}$$ 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 larger body in question - r = distance between the *centers* of the bodies in question