1. 1) When the Earth was believed to be flat, objects fell because they were seeking their natural places. Down had an absolute direction – toward Earth. When the Earth was realized to be spherical, down meant toward the center of the Earth. Kepler postulated that planets were magnetically driven along their paths by the Sun. Newton developed our modern view of gravity.

2. 2) The Moon accelerates as it orbits the Earth. Newton attributed this acceleration to a gravitational force exerted by the Earth. The Moon’s acceleration is 1/3600 of a falling apple’s acceleration. The distance from the center of the Earth to the center of the Moon is about 60 Earth radii. What happens to gravitational force if distance is doubled? Tripled?

3. 3) Newton’s law of gravity is called a universal law because the force of gravity (according to Newton) exists among all objects in the universe. We use the letters m for mass and r for distance whence: F = GMm/r 2. When the Earth attracts an apple, all the cubic meters of the Earth act as if they were concentrated at the Earth’s center. Do you exert a gravitational force on the person next to you?

4. 4) G does not equal g!!! G is a universal constant (like  ). Cavendish determined the value of G. G = 6.67 x 10 -11 The units of G are Nm 2 /kg 2. Why do you not feel a gravitational attraction between you and the person next to you?

5. 5) We assume the gravitational force on an object is constant near the Earth’s surface. We are able to make this assumption because the force changes so little over the distances in question. The force does vary, though. You weigh about one ounce less in Denver than you do in New York. Is your mass different in Denver? Why do you weigh less?

6. 6) As altitude increases, orbital period increases. A geosynchronous orbit is an orbit around Earth that takes exactly one day. Geosynchronous satellites are useful in establishing worldwide communications networks. When positioned above the equator, where does a geosynchronous satellite appear to be?

7. 7) Newton attributed Earth’s tidal bulges to the Moon’s gravity. The force on different parts of the Earth is different since gravity weakens with increasing distance. The difference between low and high tides is about 1 m in the middle of the ocean. The Sun’s tidal effect is about half the Moon’s. When do the highest high tides occur?

8. 8) Binary stars revolve around each other in exactly the way predicted by Newton’s laws. Using Newton’s laws, we have been able to estimate the total mass of the Milky Way Galaxy as well as the number of stars in it. When, if ever, have we discovered exceptions to the Newtonian world view?

9. 9) A gravitational field is a modification in the space surrounding a mass produced by virtue of the object having mass. The gravity interaction between two masses now has two steps – Mass #1 produces a field around itself. This field then exerts a force on Mass #2. The value of the field at a point in space is the acceleration experienced by a 1 kg mass placed there. What is the value of the gravitational field near the Earth’s surface?

10. Exercise 54

11. Exercise 56

12. Exercise 58

13. Exercise 60

14. Exercise 62

15. Exercise 64

16. Exercise 66

17. Exercise 68