--- title: "Unit 3.4 | Combining circular motion and gravitation (satellites, orbits, & more)" description: "Master circular motion and gravitation. Understand the equations needed to solve problems involving centripetal and gravitational forces." featured_image: "https://nerd-notes.com/wp-content/uploads/2024/06/3.4-gravitation-and-ciruclar-motion-nerdnotes.webp" url: "https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/" date_modified: "2024-06-21T17:46:18+00:00" --- # Unit 3.4 | Combining circular motion and gravitation (satellites, orbits, & more) ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/ ### Unit 3 Breakdown You are on Lesson 1 of 4 1. **[Unit 3.1 | Understanding circular motion and centripetal forces](https://nerd-notes.com/unit-3-1-understanding-circular-motion-centripetal-forces/)** 2. **[Unit 3.2 | Solving circular motion problems using FBDs](https://nerd-notes.com/unit-3-2-solving-circular-motion-problems-using-fbds/)** 3. **[Unit 3.3 | The gravitational force](https://nerd-notes.com/unit-3-3-the-gravitational-force/)** 4. **Unit 3.4 | Combining circular motion and gravitation – satellites, orbits, and more** (Current Lesson) #### In this lesson:  - We will learn how centripetal and gravitational forces are related - Learn how to solve problems that involve both forces ### Making the connection To see the connection between circular motion and gravitation, let’s use a satellite as an example. Locked Video Content ### Common Equations to Know Now that you understand how to use circular motion and gravitational forces together, it’s a good idea to know which equations you need to know. These are **not** equations that will be given to you. Instead, you need to know how to derive them. **Equation 1: General Relationships (you can manipulate these equations as you wish)** [katex] F_c = \frac{mv^2}{r} = G \frac{M m}{r^2} [/katex] **Equation 2: Speed of an orbiting object** [katex] v = \sqrt{G \frac{M}{r}} [/katex] **Equation 3: Period of an orbiting object** [katex] T = 2\pi \sqrt{\frac{r^3}{GM}}[/katex] ### PS – More satellite and gravitational questions Locked Video Content ### Your Turn – Practice Circular Motion and Gravitation Here are six questions to help you really understand how to apply the equations and solve problems. Remember to use the framework: Draw an FBD; Apply Newton’s second law; Solve for the variable in question. [Open in UBQ](https://nerd-notes.com/ubq/22696/) Question 1 Intermediate Conceptual Which of the following best explains why astronauts experience weightlessness while orbiting the earth? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/21012/) Question 2 Intermediate Mathematical A satellite circling Earth completes each orbit in \(132 \, \text{minutes}\). Part (a)3 pts Find the altitude of the satellite. Part (b)4 pts What is the value of \(g\) at the location of this satellite? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/23238/) Question 3 Intermediate Mathematical Consider a neutron star with a mass equal to the sun, a radius of 10 km, and a rotation period of 1.0 s. What is the radius of a geosynchronous orbit about the neutron star? The mass of the sun can be found in the formula sheet above. Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/29539/) Question 4 Intermediate Mathematical A communications satellite orbits the Earth at an altitude of \(35{,}000 \, \text{km}\) above the Earth’s surface. Take the mass of Earth to be \(6 \times 10^{24} \, \text{kg}\) and the radius of Earth to be \(6.4 \times 10^6 \, \text{m}\). What is the satellite’s velocity? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/23210/) Question 5 Intermediate Mathematical In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we can approximate it as a 50 km diameter circular orbit with a period of 11 days. Part (a)3 pts What was the satellite’s orbital speed around the comet? (Both the comet and the satellite are orbiting the sun at a much higher speed.) Part (b)3 pts What is the mass of the comet? Part (c)3 pts The lander was pushed from the satellite, toward the comet, at a speed of 70 cm/s, and it then fell-taking about 7 hours -to the surface. What was its landing speed? The comet’s shape is irregular, but on average it has a diameter of 3.6 km. Assume the lander experienced constant acceleration form the time it left the satellite. Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) [Open in UBQ](https://nerd-notes.com/ubq/35712/) Question 6 Advanced Mathematical A \(2.2 \times 10^{21} \, \text{kg}\) moon orbits a distant planet in a circular orbit of radius \(1.5 \times 10^8 \, \text{m}\). It experiences a \(1.1 \times 10^{19} \, \text{N}\) gravitational pull from the planet. What is the moon's orbital period in Earth days? Powered by[UBQ](https://nerd-notes.com/ubq)·[Find More Questions](https://nerd-notes.com/ubq)·[Quiz Labs](https://nerd-notes.com/quiz) ### Unit 3 Recap Take a second to read the [Unit 3 Speed Recap](https://nerd-notes.com/circular-motion-in-10-minutes/). This goes over **everything** you learned (in 5 minutes). Moreover, be sure to get in tons of practice in using [UBQ](https://nerd-notes.com/ubq/). These questions are hand selected for you to master the concepts you learned! ### Unit 4 Preview Congrats! You finished Unit 3. It’s time to move on to Unit 4 Energy. This unit marks the halfway point and is one of the easier to understand topics! ## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please credit Nerd Notes and link to https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/. **Publication:** Nerd Notes **Original URL:** https://nerd-notes.com/unit-3-4-combining-circular-motion-and-gravitation-satellites-orbits-and-more/