From d98b54f59e745972cdab0388825c54232ac12650 Mon Sep 17 00:00:00 2001 From: Nathaniel Moll Date: Tue, 7 Nov 2023 10:17:16 -0500 Subject: [PATCH] commit15: fixed typos --- content/posts/getting_started_astrophysics.md | 2 ++ content/posts/matter_and_gravity.md | 13 ++++++------- .../astronomy-and-astrophysics/index.xml | 4 ++-- public/index.xml | 4 ++-- .../getting_started_astrophysics/index.html | 1 + public/posts/index.xml | 4 ++-- public/posts/matter_and_gravity/index.html | 16 ++++++++-------- 7 files changed, 23 insertions(+), 21 deletions(-) diff --git a/content/posts/getting_started_astrophysics.md b/content/posts/getting_started_astrophysics.md index 46c713f..6654231 100644 --- a/content/posts/getting_started_astrophysics.md +++ b/content/posts/getting_started_astrophysics.md @@ -6,6 +6,8 @@ date: 2023-11-01 Hello everyone and welcome to the starting point of my astronomy and astrophysics series! Space is something I am very passionate about and I'm very excited to giude you through some basic steps of learning about our universe in a scientific way. This post will simply outline some of the material I will cover in this series. +Adiditionally, this series roughly follows my notes on the Astrophysics course from [Brilliant.org](https://brilliant.org/home/). + ### What to Expect from this Series: I will start out discussing basic things like computing the force of gravity and finding the distances to the closest stars using a trivial trigonometric method called Parallax. As the series goes on, more advanced topics will be discussed such as exoplanet discovery methods and cosmology. Keep in mind that as the topics will become more advanced, in the grand scheme of cosmology and advanced astrophysics, they are still quite rudimentary. Some topics will include: diff --git a/content/posts/matter_and_gravity.md b/content/posts/matter_and_gravity.md index 831886b..d964c23 100644 --- a/content/posts/matter_and_gravity.md +++ b/content/posts/matter_and_gravity.md @@ -10,22 +10,21 @@ 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, is a very expansive place that stretches far into space until it reaches the Interstellar Medium. 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 mass of 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 $10^{-9}$ kilograms per cubic meter. -As you can see, the density is quite low. +As you can see, the density is quite low, five billionths of a kilogram in fact. > #### Note: -> >It's important to realize that a material's density changes with temperature. This is intuitive if you think of a liquid's density versus that of a gas. ### Calculating the Gravitational Force @@ -40,7 +39,7 @@ Where: - M = mass of larger body in question - r = distance between the *centers* of the bodies in question -As you can see from this equation, the force due to gravity is inversely proportional to the square of the distance separating the bodies. As a result, the farther away to bodies are, say a planet and a star, the weaker the gravitational force experienced between them. It's also very important to note that both bodies in a system experience the *same* force. Gravity is mutual. The reason that the Earth rotates around the Sun instead of the other way around is due to the fact that the Sun has a mass that ia about 1 million times larger than the Earth's. Thus, it requires a huge magnitude of force to get it to move in some visible way because of Newton's second law: Force = Mass X Acceleration. +As you can see from this equation, the force due to gravity is inversely proportional to the square of the distance separating the bodies. As a result, the farther away two bodies are, say a planet and a star, the weaker the gravitational force experienced between them. It's also very important to note that both bodies in a system experience the *same* force. Gravity is mutual. The reason that the Earth rotates around the Sun instead of the other way around is due to the fact that the Sun has a mass that is about 1 million times larger than the Earth's. Thus, it requires a huge magnitude of force to get it to move in some visible way because of Newton's second law: Force = Mass X Acceleration. ### Conclusion diff --git a/public/categories/astronomy-and-astrophysics/index.xml b/public/categories/astronomy-and-astrophysics/index.xml index 9b59885..789a22f 100644 --- a/public/categories/astronomy-and-astrophysics/index.xml +++ b/public/categories/astronomy-and-astrophysics/index.xml @@ -14,7 +14,7 @@ https://nathan.freedomland.xyz/posts/matter_and_gravity/ The Basics of Calculating Density of Matter 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. +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, is a very expansive place that stretches far into space until it reaches the Interstellar Medium. @@ -24,7 +24,7 @@ The above statement puts into perspective the unique nature of space and the uni https://nathan.freedomland.xyz/posts/getting_started_astrophysics/ Hello everyone and welcome to the starting point of my astronomy and astrophysics series! Space is something I am very passionate about and I’m very excited to giude you through some basic steps of learning about our universe in a scientific way. This post will simply outline some of the material I will cover in this series. -What to Expect from this Series: I will start out discussing basic things like computing the force of gravity and finding the distances to the closest stars using a trivial trigonometric method called Parallax. +Adiditionally, this series roughly follows my notes on the Astrophysics course from Brilliant.org. diff --git a/public/index.xml b/public/index.xml index 0255e3d..1388661 100644 --- a/public/index.xml +++ b/public/index.xml @@ -14,7 +14,7 @@ https://nathan.freedomland.xyz/posts/matter_and_gravity/ The Basics of Calculating Density of Matter 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. +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, is a very expansive place that stretches far into space until it reaches the Interstellar Medium. @@ -24,7 +24,7 @@ The above statement puts into perspective the unique nature of space and the uni https://nathan.freedomland.xyz/posts/getting_started_astrophysics/ Hello everyone and welcome to the starting point of my astronomy and astrophysics series! Space is something I am very passionate about and I’m very excited to giude you through some basic steps of learning about our universe in a scientific way. This post will simply outline some of the material I will cover in this series. -What to Expect from this Series: I will start out discussing basic things like computing the force of gravity and finding the distances to the closest stars using a trivial trigonometric method called Parallax. +Adiditionally, this series roughly follows my notes on the Astrophysics course from Brilliant.org. diff --git a/public/posts/getting_started_astrophysics/index.html b/public/posts/getting_started_astrophysics/index.html index ef746b9..fa8eb36 100644 --- a/public/posts/getting_started_astrophysics/index.html +++ b/public/posts/getting_started_astrophysics/index.html @@ -37,6 +37,7 @@

Hello everyone and welcome to the starting point of my astronomy and astrophysics series! Space is something I am very passionate about and I’m very excited to giude you through some basic steps of learning about our universe in a scientific way. This post will simply outline some of the material I will cover in this series.

+

Adiditionally, this series roughly follows my notes on the Astrophysics course from Brilliant.org.

What to Expect from this Series:

I will start out discussing basic things like computing the force of gravity and finding the distances to the closest stars using a trivial trigonometric method called Parallax. As the series goes on, more advanced topics will be discussed such as exoplanet discovery methods and cosmology. Keep in mind that as the topics will become more advanced, in the grand scheme of cosmology and advanced astrophysics, they are still quite rudimentary. Some topics will include:

diff --git a/public/posts/index.xml b/public/posts/index.xml index dc2c490..421034c 100644 --- a/public/posts/index.xml +++ b/public/posts/index.xml @@ -14,7 +14,7 @@ https://nathan.freedomland.xyz/posts/matter_and_gravity/ The Basics of Calculating Density of Matter 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. +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, is a very expansive place that stretches far into space until it reaches the Interstellar Medium. @@ -24,7 +24,7 @@ The above statement puts into perspective the unique nature of space and the uni https://nathan.freedomland.xyz/posts/getting_started_astrophysics/ Hello everyone and welcome to the starting point of my astronomy and astrophysics series! Space is something I am very passionate about and I’m very excited to giude you through some basic steps of learning about our universe in a scientific way. This post will simply outline some of the material I will cover in this series. -What to Expect from this Series: I will start out discussing basic things like computing the force of gravity and finding the distances to the closest stars using a trivial trigonometric method called Parallax. +Adiditionally, this series roughly follows my notes on the Astrophysics course from Brilliant.org. diff --git a/public/posts/matter_and_gravity/index.html b/public/posts/matter_and_gravity/index.html index a98c626..717f699 100644 --- a/public/posts/matter_and_gravity/index.html +++ b/public/posts/matter_and_gravity/index.html @@ -60,31 +60,31 @@

The Basics of Calculating Density of Matter

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:

-

$$(\frac{M}{V})$$

+

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, is a very expansive place that stretches far into space until it reaches the Interstellar Medium. 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:

+

$$\frac{M}{V}$$

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.

-

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.

+

The average total mass of the Solar System is about 1.9884 x $10^{30}$ kilograms. This is mostly due to the mass of 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 $10^{-9}$ kilograms per cubic meter.

+

As you can see, the density is quite low, five billionths of a kilogram in fact.

Note:

It’s important to realize that a material’s density changes with temperature. This is intuitive if you think of a liquid’s density versus that of a gas.

Calculating the Gravitational Force

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
-

As you can see from this equation, the force due to gravity is inversely proportional to the square of the distance separating the bodies. As a result, the farther away to bodies are, say a planet and a star, the weaker the gravitational force experienced between them. It’s also very important to note that both bodies in a system experience the same force. Gravity is mutual. The reason that the Earth rotates around the Sun instead of the other way around is due to the fact that the Sun has a mass that ia about 1 million times larger than the Earth’s. Thus, it requires a huge magnitude of force to get it to move in some visible way because of Newton’s second law: Force = Mass X Acceleration.

+

As you can see from this equation, the force due to gravity is inversely proportional to the square of the distance separating the bodies. As a result, the farther away two bodies are, say a planet and a star, the weaker the gravitational force experienced between them. It’s also very important to note that both bodies in a system experience the same force. Gravity is mutual. The reason that the Earth rotates around the Sun instead of the other way around is due to the fact that the Sun has a mass that is about 1 million times larger than the Earth’s. Thus, it requires a huge magnitude of force to get it to move in some visible way because of Newton’s second law: Force = Mass X Acceleration.

Conclusion

In this brief post, we explored density and gravity, tools that will be used in more advanced calculations later down the road. In upcoming posts, I’ll describe to you how to derive gravitational potential energy and how to calculate the mass of the Sun.

For all that and more, I’ll see you in the next post. Thanks for reading!