Planetary & Circular Motion Flashcards
What is Law One: The Law of Equal Areas?
The path of the planets about the sun is elliptical in shape, with the center of the sun located at one focus. An ellipse is an oval, but what is a focus? An ellipse has two focus points, called foci. The foci always lie on the major (longest) axis, spaced equally each side of the center. In our solar system, the planets’ orbits are shaped like ellipses, with the sun at one of the focus points.
What is Law Two: The Law of Equal Areas?
An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. Kepler discovered an inverse relationship between how far a planet is from the sun and how fast a planet is traveling. Planets move faster when closer to the sun and slower when farther away from the sun. If the planet went in a circular orbit, it would always be the same distance from the sun and would always travel at the same speed. In an ellipse, the planet’s distance from the sun varies, and Kepler determined mathematically how that affects speed.
What is Law Three: The Law of Equal Areas?
The ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. A period is the amount of time, in earth years, it takes for a planet to orbit the sun once.
This law basically says that the ratio of a planet’s period (T) squared to its average distance from the sun (orbital radius, R) cubed (T2/R3) is the same for every one of the planets. For example, consider the orbital period and average distance from sun (orbital radius) for Earth and Mars, as given below:
Planet Period Average Distance T2/R3
Earth: 3.156 × 107 s 1.4957 × 1011 m 2.977 × 10−19 s2/m3
Mars 5.93 × 107 s 2.278 × 1011 m 2.975 × 10−19 s2/m3
Observe that the T2/R3 ratio is the same for Earth as it is for Mars. In fact, every planet in this solar system has the same T2/R3 ratio.
How is this useful? If you know a planet’s distance from the sun, you can figure out the period of orbit. Or if you know the period of orbit, you can figure out its distance away from the sun.
All objects that move in a circular motion experience a unique force called the_____.
centripetal force
If planet is moving in uniform circular motion it has cons____ or uniform speed. Notice, the length of the velo____ vector does not change, only its direction. The magnit____ of the velocity vector is the instantane_____ speed of the object. The direction of the vector is always directed tange____ to the circle.
Because the planet is changing velocities, it must have acceler_____. Gravity force is constant in magni_____ but always pointing toward the center of the circular path. The gravity force is the centripetal _____.
Centripetal force is the force that causes this acceler_____, and the acceleration vector points in the same direction. If the centripetal force is removed from an object moving in uniform circular motion, then that object will continue to move along a straight-li_____ path according to the velocity vector. You can see this by selecting “off” for Gravity at any time the planet is moving in a circular path.
If planet is moving in uniform circular motion it has constant or uniform speed. Notice, the length of the velocity vector does not change, only its direction. The magnitude of the velocity vector is the instantaneous speed of the object. The direction of the vector is always directed tangent to the circle.
Because the planet is changing velocities, it must have acceleration. Gravity force is constant in magnitude but always pointing toward the center of the circular path. The gravity force is the centripetal force.
Centripetal force is the force that causes this acceleration, and the acceleration vector points in the same direction. If the centripetal force is removed from an object moving in uniform circular motion, then that object will continue to move along a straight-line path according to the velocity vector. You can see this by selecting “off” for Gravity at any time the planet is moving in a circular path.
If a ball is spun in a circle on the a string in a circular path what are the forces on the ball?
Gravitational force and the tension force on the ball.
If a ball is spun in a circle on the a string in a circular path what are the forces along the string?
The force along the string, which could be called the tension force.
If a ball is spun in a circle on the a string in a circular path what is the direction necessay to keep the ball moving in the circular path?
The forces need to be “toward the center” or “inward.”
Get a small, clear plastic container and fill it about half full of water. Take the container of water to an open area. You could go outside or just go to a large room in your home. Hold the container in your outstretched arm. The container will be positioned straight out in front of you. Keeping the container in front of you, slowly spin in a circle. The pattern is similar to a figure skater executing a slow “spin” maneuver. As you are slowly spinning, observe the level of the water in the container. Stop the motion.
What did you observe about the level of the water in the container as you were slowly spinning?
It was raised on one side.
Get a small, clear plastic container and fill it about half full of water. Take the container of water to an open area. You could go outside or just go to a large room in your home. Hold the container in your outstretched arm. The container will be positioned straight out in front of you. Keeping the container in front of you, slowly spin in a circle. The pattern is similar to a figure skater executing a slow “spin” maneuver. As you are slowly spinning, observe the level of the water in the container. Stop the motion.
Was the level of the water higher on the side of the container away from you or the side of the container nearest you?
The side away from you.
Since the path of an object undergoing uniform circular motion is a circle, the distan______ that the object travels one time around the circle is the circumfere_____ of the circle.
Remember that we can calculate the spe___ of a moving object if we know the distance trave____ and the time for the travel. The time required for the object to travel one time around the circle is called the period. The symbol for the period is T. Study the following comparison and example problem:
Since the path of an object undergoing uniform circular motion is a circle, the distance that the object travels one time around the circle is the circumference of the circle.
Remember that we can calculate the speed of a moving object if we know the distance traveled and the time for the travel. The time required for the object to travel one time around the circle is called the period. The symbol for the period is T. Study the following comparison and example problem:
Simple Speed Calculation:
d = distance
t = time
v = d/t
Uniform Circular Motion Speed Calculation
d = distance = circumference = (2)(π)(r)
t = time = period = T
v = [(2)(π)(r)]/T
Yvonne and Eddy are riding a ferris wheel at the Dade County Fair. If the radius of the ferris wheel is 10.0 m, and it rotates once every 35.0 seconds, what is the linear speed of Yvonne and Eddy?
d = (2)(π)(r) T = 35.0 s v = [(2)(π)(r)]/T v = [(2)(3.14)(10.0 m)]/35.0 s v = 1.79 m/s
An object travels in uniform circular motion because a force acts to pull the object out of a straight path and into a circular path. This force is called the centripe _________. The term “centripetal” means “center-seeking” or “toward the center
An object travels in uniform circular motion because a force acts to pull the object out of a straight path and into a circular path. This force is called the centripetal force. The term “centripetal” means “center-seeking” or “toward the center
At this point, some students may confuse “centripetal” which means toward the center with “centrifugal,” which means _____ from the center.
At this point, some students may confuse “centripetal” which means toward the center with “centrifugal,” which means away from the center.
