Contextualization

The study of Physics is an incredible journey through knowledge. It allows us to understand, through its laws and concepts, the reality that surrounds us, from the smallest elements to the vastness of the Universe. One of these concepts is spatial dilation, which is part of the Special Theory of Relativity, developed by Albert Einstein.

The effects of spatial dilation may seem distant from our daily reality, after all, we live at much lower speeds than the speed of light. However, this phenomenon has a direct influence on technologies we use every day.

To aid in the understanding of this concept, we recommend the following resources:

1. "Fundamentals of Physics: Gravitation, Waves, and Thermodynamics". Volume 2, Halliday & Resnick.
2. Brazil School Portal: Spatial Dilation
3. YouTube Channel: Temporal and Spatial Dilation

Introduction

The concept of spatial dilation stems from the idea that space and time are intertwined and form a single entity called space-time. Spatial dilation is influenced by the relative velocity between two observers and is not perceived in our daily lives due to the small speeds we are accustomed to dealing with.

When an object moves at speeds close to the speed of light, the space around it dilates, making the object appear longer to an observer at rest. It is important to note that for the moving object, everything will seem normal, as this phenomenon occurs due to the observers' point of view.

Lastly, it is important to note that spatial dilation and temporal dilation are connected concepts. As space dilates, time also stretches, becoming longer.

Real World Application

Have you ever wondered how GPS satellites work? They orbit the Earth at approximately 20,000 km above sea level and at speeds around 14,000 km/h. At this speed and altitude, the effects of time and space dilation due to Special and General Relativity become significant and need to be taken into account in the satellite's programming.

Time dilation causes a GPS satellite's clock to advance faster than a clock on Earth, an effect that would be fatal to the system's accuracy if not corrected. Understanding and correcting this difference is crucial for the GPS to function. This shows how spatial dilation, an abstract and seemingly distant concept, has very concrete and everyday applications.

Practical Activity: "Space Travel: The Dilation of Space-Time"

Project Objective

This project aims to assist in the understanding of spatial dilation and its practical effects in everyday life, specifically in GPS systems.

Detailed Project Description

The student groups, with 3 to 5 members each, should initially research and understand how GPS works and how space-time dilation is considered in this system. They will then develop an educational presentation explaining this concept and its application.

Required Materials

• Internet access for research
• Presentation software (PowerPoint, Google Slides, Prezi, etc.)
• Books or theoretical references on spatial dilation and GPS

Step by Step

1. Research and understand the concept of spatial dilation and how it is considered in GPS systems. Use the references provided in the introduction and seek other sources to complement your research.
2. Divide the group into research tasks: some members can focus on spatial dilation, while others can research more about the GPS system.
3. Gather and share your research, then discuss how to connect the concept of spatial dilation with GPS systems.
4. Develop a presentation outline, defining which topics each group member will present.
5. Create the presentation, using explanatory texts, graphics, images, and animations if necessary.
6. Review the presentation as a group, ensuring that all points are well explained and that the connections between spatial dilation and GPS are clear.
7. Schedule a day to present the work to the class and be prepared to answer questions from your classmates and teacher.

Project Deliverables

Students must deliver the presentation in digital format, along with a written report. This report should follow the proposed documentation model, containing:

1. Introduction: Provide context for the theme and explain its relevance and real-world application.
2. Development: Describe the theory behind spatial dilation, explain in detail the activity carried out, the methodology used, and present the results obtained.
3. Conclusions: Summarize the main points of the work, highlighting what was learned and the conclusions about the project.
4. Bibliography: Indicate the reference sources used in the project.

The technical skills required for the execution and completion of the project are: understanding the concept of spatial dilation, its relationship with the speed of light, and its practical application in GPS systems.

The necessary socio-emotional skills include: time management for project planning and execution within a month, communication skills to present the work clearly and concisely, problem-solving skills to search for necessary information, and creative thinking to develop an engaging and didactic presentation.