17. Here are possible answers. Yours may vary.

Newton's First Law: If there are no net outside forces acting on an object, then that object's velocity (speed and direction) will remain constant.

• A cow at rest will remain at rest until someone tips it over.
• A cow that is pushed on to a frozen pond will continue to slide on the ice in a straight line at constant speed (neglecting friction), until it encounters an outside force.

Newton's Second Law: If a net outside force acts on an object, that object will accelerate (i.e.: its velocity will change), in accordance with the formula force = (mass) (acceleration).

• When a cow is fired vertically out of a cannon, there is a net outside force acting on it during its flight: the Earth's gravitational pull. This force will cause the cow to first slow down (as it rises), then speed up (as it falls).

Newton's Third Law: When one body applies a force to a second body, the second applies an equal but opposite force on the first.

• A cow on roller skates fires a bazooka. The bazooka propels a projectile forward, accelerating it out of the bazooka with a certain amount of force. Simultaneously, the projectile will exert an equal but opposite force on the bazooka-weilding cow. This recoil will cause the cow to roll backwards on its roller skates.

20. An object's mass is the amount of material it contains. Its weight is the gravitational force with which the Earth (or whatever body it happens to reside on) pulls the object downwards.

21. Since the Earth would be 4 times closer to the Sun, the Sun's gravitational pull on the Earth would be 4² = 16 times stronger. This is because the strength of the gravitational force between two objects is inversely proportional to the square of the distance between them.

23. No matter how far you travel from the Earth, you will never be "completely beyond the pull of its gravity." When you are extremely far from the Earth, its gravitational pull on you will be very small, but it can never be zero. Mathematically, this can be seen by using the formula for the strength of the Earth's gravitational force on you: F = G m_Earth m_you / r². No matter how large a value for r you insert into this equation, you cannot make F equal to zero.

33. a) By examining the following picture, you can see that the length of the major axis is 2 + 6 = 8 AU. Therefore the length of the semimajor axis is half of this, or 4 AU.

b) The period can be found using Kepler's Third Law:

The period of this asteroid is therefore 8 years.

36. There are two effects going on here. The fact that the planet has 3 times the Earth's mass makes you weigh 3 times more than you would on Earth, while the fact that the planet has 3 times the Earth's diameter makes you weigh only 1/9 of what you would weigh on Earth. Combining the two effects means that, on this planet, you would weigh 3 x 1/9 = 1/3 of what you would weigh on Earth. In other words, you would weigh less, by a factor of 3.

Last edited 03 Feb 04 M. A. Weinstein.