Chapter 11, Problem 1P

(a)

To determine

To Find:Whether the given statement is true or false.

Answer to Problem 1P

False

Explanation of Solution

Introduction:

Kepler described three laws of planetary motion:

1. A planet goes around sun in an elliptical orbit with the sun located at one focus.

2. The line joining each planet and the Sun covers equal areas in equal interval.

3. The square of orbital period is directly related to the cube of the mean orbital radius.

Kepler’s law of equal areas is a result of the gravitational force that acts along the line joining two bodies but it is independent of the way in which the force changes with distance.

Conclusion:

Thus, the given statement is false.

(b)

To determine

To find:Whether the given statement is true or false.

Answer to Problem 1P

True

Explanation of Solution

Introduction:

Kepler described three laws of planetary motion:

1. A planet goes around sun in an elliptical orbit with the sun located at one focus.

2. The line joining each planet and the Sun covers equal areas in equal interval.

3. The square of orbital period is directly related to the cube of the mean orbital radius.

From the third law, one can understand that more the planet is closer to the sun, lesser would be its orbital period.

Conclusion: The given statement is true.

(c)

To determine

To Find:Whether the given statement is true or false.

Answer to Problem 1P

True

Explanation of Solution

Introduction:

Kepler described three laws of planetary motion:

1. A planet goes around sun in an elliptical orbit with the sun located at one focus.

2. The line joining each planet and the Sun covers equal areas in equal interval.

3. The square of orbital period is directly related to the cube of the mean orbital radius.

Venus is closer to the Sun as compared to the Earth.

From the Kepler’s third law, one can find that

  $v_{Venus}>v_{Earth}$

Conclusion:

Thus, the given statement is true.

(d)

To determine

To Find:Whether the given statement is true or false.

Answer to Problem 1P

False

Explanation of Solution

Introduction:

Kepler described three laws of planetary motion:

1. A planet goes around sun in an elliptical orbit with the sun located at one focus.

2. The line joining each planet and the Sun covers equal areas in equal interval.

3. The square of orbital period is directly related to the cube of the mean orbital radius.

As the period of planets does not depends on planet’s mass according to Kepler’s third law, the given statement is false.