Concept Items

A circle is a special case of an ellipse. Explain how a circle is different from other ellipses.

1. The foci of a circle are at the same point and are located at the center of the circle.
2. The foci of a circle are at the same point and are located at the circumference of the circle.
3. The foci of a circle are at the same point and are located outside of the circle.
4. The foci of a circle are at the same point and are located anywhere on the diameter, except on its midpoint.

Comets have very elongated elliptical orbits with the sun at one focus. Using Kepler's Law, explain why a comet travels much faster near the sun than it does at the other end of the orbit.

1. Because the satellite sweeps out equal areas in equal times
2. Because the satellite sweeps out unequal areas in equal times
3. Because the satellite is at the other focus of the ellipse
4. Because the square of the period of the satellite is proportional to the cube of its average distance from the sun

True or False—A planet-satellite system must be isolated from other massive objects to follow Kepler’s laws of planetary motion.

1. True
2. False

1. The string, pins, and pencil method works because the length of the two sides of the triangle remains constant as you are drawing the ellipse.
2. The string, pins, and pencil method works because the area of the triangle remains constant as you are drawing the ellipse.
3. The string, pins, and pencil method works because the perimeter of the triangle remains constant as you are drawing the ellipse.
4. The string, pins, and pencil method works because the volume of the triangle remains constant as you are drawing the ellipse.

1. Gravity and velocity have the same effect and cannot be distinguished from each other. An acceptable illustration of this is any description of the feeling of constant velocity in a situation where no outside frame of reference is considered.
2. Gravity and velocity have different effects and can be distinguished from each other. An acceptable illustration of this is any description of the feeling of constant velocity in a situation where no outside frame of reference is considered.
3. Gravity and acceleration have the same effect and cannot be distinguished from each other. An acceptable illustration of this is any description of the feeling of acceleration in a situation where no outside frame of reference is considered.
4. Gravity and acceleration have different effects and can be distinguished from each other. An acceptable illustration of this is any description of the feeling of acceleration in a situation where no outside frame of reference is considered.

1. $1.35{\text{m/s}}^2$
2. $3.49{\text{m/s}}^2$
3. $3.49\times <!--\; \times \; -->{10}^6{\text{m/s}}^2$
4. $1.35\times <!--\; \times \; -->{10}^6{\text{m/s}}^2$

Saturn’s moon Titan has an orbital period of 15.9 days. If Saturn has a mass of 5.68×10²³ kg, what is the average distance from Titan to the center of Saturn?

1. 1.22×10⁶ m
2. 4.26×10⁷ m
3. 5.25×10⁴ km
4. 4.26×10¹⁰ km

1. The weight is two times the gravitational force between the object and Earth.
2. The weight is half the gravitational force between the object and Earth.
3. The weight is equal to the gravitational force between the object and Earth, and the gravitational force is inversely proportional to the distance squared between the object and Earth.
4. The weight is directly proportional to the square of the gravitational force between the object and Earth.

1. It can be explained by using the concept of atmospheric refraction.
2. It can be explained by using the concept of the special theory of relativity.
3. It can be explained by using the concept of the general theory of relativity.
4. It can be explained by using the concept of light scattering in the atmosphere.

The Cavendish experiment marked a milestone in the study of gravity.
Part A. What important value did the experiment determine?
Part B. Why was this so difficult in terms of the masses used in the apparatus and the strength of the gravitational force?

1. Part A. The experiment measured the acceleration due to gravity, g. Part B. Gravity is a very weak force but despite this limitation, Cavendish was able to measure the attraction between very massive objects.
2. Part A. The experiment measured the gravitational constant, G. Part B. Gravity is a very weak force but, despite this limitation, Cavendish was able to measure the attraction between very massive objects.
3. Part A. The experiment measured the acceleration due to gravity, g. Part B. Gravity is a very weak force but despite this limitation, Cavendish was able to measure the attraction between less massive objects.
4. Part A. The experiment measured the gravitational constant, G. Part B. Gravity is a very weak force but despite this limitation, Cavendish was able to measure the attraction between less massive objects.