Contextualization

Orbiting bodies are a phenomenon that occurs when a body, whether a satellite, a planet, or even a star, moves around another body, attracted by the force of gravity. In order to understand these processes, it is essential to know some laws and principles of physics, such as Kepler's Third Law, Newton's Law of Universal Gravitation, and the universal gravitational constant (G).

Kepler's Third Law, also known as the Law of Periods, states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of the ellipse described in its orbit. At the same time, Newton's Law of Universal Gravitation states that two bodies attract each other with forces directly proportional to their masses and inversely proportional to the square of the distance between them.

The constant G, called the universal gravitational constant, is a fundamental physical constant that appears in Isaac Newton's law of universal gravitation. It is a proportionality constant in the equation that describes the force of attraction between two masses.

The study of orbiting bodies has direct application in our daily lives. It is through this study that we can understand the functioning of the communication satellites that allow, among other things, the transmission of television signals, the functioning of GPS, and even weather forecasting. Furthermore, the analysis of orbits is also fundamental to space exploration, from sending probes to other planets to maintaining the International Space Station in its orbit.

Knowing how bodies behave in orbit also allows us to understand tides, seasons, and eclipses. These phenomena, so present in our lives, can only be fully understood when we master the physical concepts that govern orbiting bodies.

We recommend as resources for deepening the subject the following materials:

• Book "Physics for Scientists and Engineers" by Douglas C. Giancoli, which has a chapter dedicated to gravitation and planetary motion.
• Documentary "The History of the Universe" available on Netflix, which in certain episodes deals with celestial mechanics and orbiting bodies.
• Website Só Física, which has a section on Universal Gravitation with several examples and solved exercises.
• YouTube channel Ciência Todo Dia, which has several videos on the subject, explaining in a clear and didactic way.

Practical Activity

Activity Title: Simulating Orbits: Notable Celestial Bodies

Project Objective:

To allow students to gain practical knowledge about the movement of celestial bodies in orbit. Students will create simulated models of orbits of notable celestial bodies and compare the characteristics of these bodies and their orbits. In addition, students should estimate what could happen in hypothetical scenarios such as changes in mass, distance, and speed.

Detailed Project Description:

Students, divided into groups of 3 to 5 people, should choose a celestial body (or more, depending on the size of the group) and, based on the theory studied about orbiting bodies, model and simulate their orbits.

Celestial bodies can be planets in our solar system, a natural satellite (such as the moon), an artificial satellite, or even a space station, such as the ISS.

After carrying out the simulation, students must prepare a detailed report explaining the concepts and laws involved in the movement of the chosen celestial body, the configuration of the orbit, the calculations and methods used, and a study on what would happen if some variables were to change - such as the mass of the celestial body, the distance from Earth, or its initial velocity.

This interdisciplinary project involves concepts from physics, mathematics, and to a lesser extent, geography and technology.

The execution time of the project is estimated to be more than 12 hours per student, considering the research, the study, the carrying out of the simulations, and the preparation of the reports of each group.

Materials needed:

• Textbooks or online support material for research.
• Computer or notebook with internet access.
• Orbit simulation software, which can be free, such as "Orbit Simulator" (available online).

Detailed step by step:

1. Divide the class into groups of 3 to 5 students.
2. Each group should select a celestial body to study, it can be a planet or a satellite.
3. Students should research this celestial body: its physical characteristics, mean distance from Earth, orbital period, mean orbital velocity, and other relevant data.
4. Using simulation software, students should set up the simulation with the data from the chosen celestial body and observe the result.
5. Students should then describe and analyze the characteristics of the celestial body's orbit, based on the simulation and also on theoretical concepts.
6. After designing and analyzing the original orbit, students should perform simulations with changes in variables, such as the mass of the celestial body, the distance from Earth, or the initial velocity, and analyze the results.
7. Finally, students should present their findings and analysis in the form of a written report, which should include an introduction (with a description of the chosen celestial body and the relevance of the study), a development section (with the details of the simulation process and the results obtained), a conclusion (with the interpretation of the results and the implications of the changes made in each scenario), and a bibliography with the sources consulted.

Project Deliverables:

The final project report should be composed of four main parts: Introduction, Development, Conclusions and Bibliography. Students should describe the entire project execution process, the results obtained and their interpretations.

In the Introduction, they should include a contextualization of the topic, as well as their motivations and objectives. In the Development, they should detail the preparation and simulation process, the changes made, and the results obtained. In the Conclusions section, they should evaluate the results, relate them to the theory studied, and reflect on the learning obtained. Finally, in the Bibliography, the students should list the sources of information consulted during the project.

Students should be encouraged to explore different formats for presenting their results, such as graphs, tables, images, videos, and interactive presentations. The preparation of the report should demand reflection and cooperation, developing communication, argumentation and synthesis skills, as well as the ability to deal with abstract concepts and critical thinking.