7.2 Orbits of Planets and Satellites
2 min read•november 6, 2020
Daniella Garcia-Loos
Daniella Garcia-Loos
7.2 Orbits of Planets and Satellites
One of the most common applications of gravitation that AP enjoys is the orbits of planets and satellites!
Fast Facts of Planets and Satellites in Orbit:
Angular momentum is conserved
Mechanical energy is conserved
GPE is at 0 at an infinite distance away
“Escape speed” 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.
Unit 7.2 Practice Problems
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
Key Terms to Review (7)
Centripetal Force
: Centripetal force is a force that acts towards the center of a circular path and keeps an object moving in a curved trajectory.Conservation of Energy
: Conservation of energy states that the total amount of energy in a closed system remains constant over time. Energy can be transferred or transformed from one form to another, but it cannot be created or destroyed.Gravitational Force
: The gravitational force is the attractive force between two objects with mass. It is responsible for keeping planets in orbit around the sun and objects on Earth's surface.Gravitational Potential Energy (GPE)
: Gravitational potential energy refers to the energy possessed by an object due to its position in a gravitational field. It is the amount of work that would be done on the object if it were moved from its current position to a reference point.Kepler's Third Law
: Kepler's Third Law states that for any two objects orbiting each other, the square of their orbital periods (the time it takes for one complete orbit) is directly proportional to the cube of their average distance from each other.Mechanical Energy
: Mechanical energy refers to the sum of potential energy and kinetic energy in a system. It represents the ability of an object or system to do work.Tangential Velocity
: Tangential velocity refers to the instantaneous linear speed of an object moving along a curved path. It represents how fast an object is moving in the direction tangent to its circular path.7.2 Orbits of Planets and Satellites
2 min read•november 6, 2020
Daniella Garcia-Loos
Daniella Garcia-Loos
7.2 Orbits of Planets and Satellites
One of the most common applications of gravitation that AP enjoys is the orbits of planets and satellites!
Fast Facts of Planets and Satellites in Orbit:
Angular momentum is conserved
Mechanical energy is conserved
GPE is at 0 at an infinite distance away
“Escape speed” 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.
Unit 7.2 Practice Problems
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
Key Terms to Review (7)
Centripetal Force
: Centripetal force is a force that acts towards the center of a circular path and keeps an object moving in a curved trajectory.Conservation of Energy
: Conservation of energy states that the total amount of energy in a closed system remains constant over time. Energy can be transferred or transformed from one form to another, but it cannot be created or destroyed.Gravitational Force
: The gravitational force is the attractive force between two objects with mass. It is responsible for keeping planets in orbit around the sun and objects on Earth's surface.Gravitational Potential Energy (GPE)
: Gravitational potential energy refers to the energy possessed by an object due to its position in a gravitational field. It is the amount of work that would be done on the object if it were moved from its current position to a reference point.Kepler's Third Law
: Kepler's Third Law states that for any two objects orbiting each other, the square of their orbital periods (the time it takes for one complete orbit) is directly proportional to the cube of their average distance from each other.Mechanical Energy
: Mechanical energy refers to the sum of potential energy and kinetic energy in a system. It represents the ability of an object or system to do work.Tangential Velocity
: Tangential velocity refers to the instantaneous linear speed of an object moving along a curved path. It represents how fast an object is moving in the direction tangent to its circular path.
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