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Objective: To identify whether positive, negative, or zero work is being done, to identify the force that is doing the work, and to describe the energy transformation associated with such work.

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Kepler’s Laws of Planetary Motion

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Compare the relative speed of an orbiting planet at various locations in its elliptical orbit.

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Use Kepler’s third law to relate the orbital period to the orbital radius for a planet in orbit about the same star.

Use a model and mathematical thinking to predict the effects of a change in one variable on another for objects that travel in elliptical orbits.

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Complete a paragraph that describes the motion of an orbiting satellite about a central body.

Kepler’s Third Law

Relate the relative speed of an orbiting satellite to the time required to move between two points in its elliptical orbit.

Orbits

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Time to Orbit

Satellites in Orbits

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Yes, Return

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Stopping Distance One aspect of safe driving involves the ability to stop a car readily. This ability depends upon the driver's alertness and readiness to stop, the conditions of the road, the speed of the car, and the braking characteristics of the car. The actual distance it takes to stop a car consists of two parts - the reaction distance and braking distance. When a driver sees an event in his/her field of view that might warrant braking (for example, a dog running into the street), a collection of actions must be taken before the braking actually begins. First the driver must identify the event and decide if braking is necessary. Then the driver must lift his/her foot off the gas pedal and move it to the brake pedal. And finally, the driver must press the brake down its full distance in order to obtain maximum braking acceleration. The time to do all this is known as the reaction time. The distance traveled during this time is known as the reaction distance. Once the brakes are applied, the car begins to slow to a stop. The distance traveled by the car during this time is known as the braking distance. The braking distance is dependent upon the original speed of the car, the road conditions, and characteristics of the car such as its profile area, mass and tire conditions. Figure 1 shows the stopping distance for a Toyota Prius on dry pavement resulting from a 0.75-second reaction time. The reaction time of the driver is highly dependent upon the alertness of the driver. Small changes in reaction time can have a large effect upon the total stopping distance. Table 1 shows the reaction distance, braking distance, and total stopping distance for a Toyota Prius with an original speed of 50.0 mi/hr and varying reaction times.

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Four moons orbit a planet in nearly circular orbits as shown. Use Kepler’s third law to complete the table and determine the missing quantities.

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A satellite orbits the earth in a highly elliptical orbit. Time 1 is time to travel from A to B; Time 2 is the time to travel from B to A. Use this information to complete the paragraph.

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