Understanding the Infinity Sign for Beginners

[vipson231]

Homework Statement

Question is in attachment
Can someone explain to me what the infinity sign is I'm new to this topic.

All I know is that as a satellite goes to a higher orbit that the velocity decreases.

 

[Redbelly98]

It looks like that "infinity" sign is really a greek letter omega, "ω". It is the symbol used for angular velocity when given in terms of radians.

 

[vipson231]

Oh ok. The only knowledge i have of angular velocity is it determines how fast something is turning. So wouldn't the angular velocity be proportional to the velocity and since the satellite is going to a higher orbital, the speed would thus decrease and so if angular velocity is decreasing, wouldn't the velocity be decreasing as well? =}

 

[Redbelly98]

Angular velocity depends on both the radius (of the orbit) and the velocity. I would expect your textbook to have a discussion of how ω, v and r are related. There should be other important information in the book's sections on Newton's Law of Gravitation and also Keppler's Laws. If you're really stuck on understanding this problem, you'll want to go over those parts of your book. Post back with questions if you don't follow it.

 

[Nickie]

The infinity sign, also known as the lemniscate, is a mathematical symbol that represents infinity, or limitless, without end. It is often used in mathematics and physics to represent concepts such as infinite sets, infinite series, and infinite limits. The shape of the infinity sign is similar to a figure eight on its side, with two loops that are connected in the middle.

In terms of satellite orbit, the infinity sign can represent the concept of escape velocity, where a satellite's velocity decreases as it moves to a higher orbit, eventually reaching a point where it can escape the gravitational pull of the planet. This is because the gravitational force decreases with distance, so as the satellite moves further away from the planet, the force decreases and the velocity decreases as a result.

I hope this helps in understanding the concept of the infinity sign. If you have any further questions, please feel free to ask.