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βοΈΒAP Physics C: Mech

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πͺUnit 7

2 min readβ’november 7, 2020

Daniella Garcia-Loos

One of the most common applications of gravitation that AP enjoys is the orbits of planets and satellites!

- Angular momentum is conserved
- Mechanical energy is conserved
- GPE is at 0 at an infinite distance away
- βEscape speedβ is the minimum speed required to escape the gravitational field

Here is the derivation for **Gravitational Potential Energy**:

This also means that the kinetic energy of a satellite in orbit can be simplified down to only be dependent on the satellite and its distance.

We can connect **centripetal/circular motion** to gravitational force too!

The centripetal force acting on a satellite/planet system is caused by the gravitational force.

This means that we can derive some formulas to describe the orbits of these systems that move in a circular path.

Let's try to find **tangential velocity**:

Additionally, I'll leave the proof of this one as an exercise for you, but we can use a similar method to determine the **period** of the orbit.

There is another version of this formula which is known as **Kepler's Third Law,** which is only applicable for objects in circular orbit:

This is commonly rewritten as below in order to simplify the relationship:

Lastly, in **non-orbiting** situations in relation to satellites, you can use the conservation of energy in order to help you describe its motion.

Taken from College Board

Answer

Answer

Most Physics C: Mechanics classes tend to skip over Kepler's Laws, so note that it is perfectly acceptable to justify your answer with other physics you know.

Answer

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