From Infinity to Here: Explaining Objects, Escape Velocity & More

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In summary: It is a scalar quantity, determined by the mass of the earth and the object and the distance between them.In summary, moving an object from "infinity to a point" is a concept used in physics to compare interactions between two systems at different distances. It is often used in the context of escape velocity, which is the velocity at which an object can escape the Earth's gravitational pull and reach infinity.
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A phrase that I heard several times in the 2 years of high school AP physics I've completed (being a computer science major, I haven't taken any physics classes in college) was moving an object from "infinity to a point" and I'm a little confused as to what that means and how it works.

Also, how does it fit with escape velocity? The escape velocity of the Earth is about 11km/s. This is also the velocity that an object would have when moved from infinity to Earth (assuming no other planetary object). I'd love an explanation. Thanks, guys! I appreciate any help!
 
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Goodies said:
A phrase that I heard several times in the 2 years of high school AP physics I've completed (being a computer science major, I haven't taken any physics classes in college) was moving an object from "infinity to a point" and I'm a little confused as to what that means and how it works.
When you have two systems that interact, for instance through gravitational or electrostatic interactions, you often want to compare to a situation where the two systems are present but not interacting. As the interactions do not turn off at a certain distance, but continue for ever, the only way to achieve this is to have them an infinite distance apart. If the potential energy due to the interaction is ##V(r)##, where ##r## is the distance between the systems, then ##\lim_{r \rightarrow \infty} V(r) = 0##. So you start by considering the systems an inifinite distance apart, and then bring them closer to investigate the effect of the interaction.

Goodies said:
Also, how does it fit with escape velocity? The escape velocity of the Earth is about 11km/s. This is also the velocity that an object would have when moved from infinity to Earth (assuming no other planetary object).
I've never heard used in that context, so I can't comment. Maybe someone else can chime in here.
 
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What do you mean by "escape"? Any object, at any distance from the Earth will feels some small gravitational attraction and so eventually return to earth. To truly "escape" it must be able to go to infinity.

The "escape velocity" of an object is the velocity at a given instant such that, with its velocity decreasing as it moves away from Earth (due to gravitational pull back toward the earth), with no additional forces (in particular no rocket engines), it would, none the less, "escape" to infinity.
 

1. What is "From Infinity to Here" about?

"From Infinity to Here" is a book that explores the concept of infinity and how it applies to objects and phenomena in our universe, such as escape velocity and black holes. It delves into the history of the concept and provides explanations and examples for readers to better understand these complex ideas.

2. How is infinity related to objects?

Infinity is related to objects in various ways, depending on the context. In terms of size or quantity, many objects can be infinitely large or infinitely small. For example, the universe is thought to be infinitely large, while the smallest particles can be infinitely divided. Additionally, some objects, such as black holes, have infinite density and gravity.

3. What is escape velocity?

Escape velocity is the minimum speed needed for an object to break free from the gravitational pull of a massive body, such as a planet or star. It is determined by the mass and radius of the body and can vary for different objects. For example, the escape velocity for Earth is about 11.2 km/s, while the escape velocity for the Sun is about 617.5 km/s.

4. How does infinity affect our understanding of the universe?

Infinity plays a significant role in our understanding of the universe. It allows us to comprehend the vastness and complexity of the universe, as well as the possibility of other universes beyond our own. Infinity also challenges our understanding of physical laws and theories, such as the concept of an infinite universe in relation to the Big Bang theory.

5. Who would benefit from reading "From Infinity to Here"?

"From Infinity to Here" is suitable for anyone interested in exploring the concept of infinity and its applications in our universe. It is written in a way that is accessible to both scientists and non-scientists, making it a great read for anyone looking to expand their knowledge and understanding of the universe.

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