Unit 3 Breakdown
You are on Lesson 1 of 4
- Unit 3.1 | Understanding circular motion and centripetal forces
- Unit 3.2 | Solving circular motion problems using FBDs
- Unit 3.3 | The gravitational force
- 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.
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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
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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.
Which of the following best explains why astronauts experience weightlessness while orbiting the earth?
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.
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.
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.
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?
Unit 3 Recap
Take a second to read the Unit 3 Speed Recap. This goes over everything you learned (in 5 minutes). Moreover, be sure to get in tons of practice in using 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!
