Chapter 9

The intensity of light from a central source varies inversely as the square of the distance. 1) lf you lived on a planet only half as far from the sun as our Earth, how would the light intensity compare with that on Earth? 2) How about a planet ten times farther away than the Earth?

1) 4 times farther 2) 1/100 ((invert and square it))

1) What would be the effect on the Earth's tides if the diameter of the Earth were very much larger than it is? 2) lf the Earth were as it presently is, but the moon very much larger and had the same mass?

1) The tides would be stronger because the outer part of the Earth would be closer to the moon 2) Weaker because it's smaller so it doesn't make that much of a difference. And the center of mass of the moon is the same distance away from the earth because it's mass hasn't changed.

1) lf the Earth somehow expanded to a larger radius, with no change in mass, how would your weight be affected? 2) How would it be affected if the Earth instead shrunk?

1) you would be lighter since you would be farther away from the earth's center 2) You would weigh more --> F=G m1 x m2/d2

The value of g at the Earth's surface is about 9.8 m/s2. What is the value of g at a distance from the Earth's center that is four times the Earth's radius

1/16 x 9.8 = 0.6125 m/s2 ((invert and square))

lf the Earth were of uniform density what would the value of g be inside the Earth at half its radius?

1/2 the force ((not inverted and squared when inside the earth))

The value of g at the Earth's surface is about 9.8 m/s2. What is the value of g at a distance of twice the Earth's radius?

1/4th of 9.8 m/s2 = 2.45 m/s2

Find the change in the force of gravity between two planets when their distance becomes 1/5th the original distance

25 ((invert and square))

Gravitational force acts on all bodies in proportion to their masses. Why, then doesn't a heavy body fall faster than a light body?

Because although it has a greater mass, it requires a bigger force to bring it down faster. M x f = m x F

lf our sun shrank in size to become a black hole, show from the gravitational force equation that the Earth's orbit would not be affected.

Because force is inversely related to distance and the masses remain constant, the orbit of the earth would not be affected. The distance is too great to make a difference. The distance between the centers are the same.

lf the Earth were hollow but still had the same mass and same radius, would your weight in your present location be more, less, or the same as it is now?

The same. The distance to the center is still the same.

lf the moon pulls the Earth as strongly as the Earth pulls the moon, why doesn't the Earth rotate around the moon, or why don't both rotate around a point midway between them?

They rotate around the center of mass of the system which is not the center of the earth but still on part of the earth because it has more mass, therefore more gravity.