Question

1. What is a "log-log" plot?

a. A plot on which all quantities are related by straight lines.

b. A plot of the log of the log of a quantity.

c. A plot relating the log of one quantity to the log of another quantity.

d. A type of plot that describes the power output of a star.

2. What is the significance of a straight line on a log-log plot?

a. It means that the quantities represented must be related by a "power law".

b. It means that the quantities represented form an ellipse.

c. It means that the quantities represented are described by a "conservation law".

d. It means that the quantities represented must form an "inverse square law".

3. Which of the following are examples of "power laws". (Check all that apply)

a. Kepler's first law

b. The law of conservation of energy.

c. Kepler's third law

d. The inverse square law.

4. You find a star with a some brightness at a distance of 100 pc. You find an identical second star at a distance of 400 pc. How many times brighter is the first star than the second.

5. You find a star with some brightness. You then find a second identical star that is four times brighter than the first one. How many times closer is the second star than the first.

Answer 1

1) c. A plot relating the log of one quantity to the log of another quantity.

2) a. It means that the quantities represented must be related by a "power law".

3) c. Kepler's third law.

d. The inverse square law.

4) By inverse square law:

B2/B1 = (r1/r2)^2

=> B2 = B1* (r1/r2)^2

= B1*(100/400)^2

= 0.0625 B1

Or, B1 = 16B2

So the first start is 16 times brighter than the second star.

5) Given: B2 = 4B1

B1/B2 = (r2/r1)^2

=> r2/r1 =sqrt[ (B1/4B1)] = sqrt(1/4) = 0.5 = 1/2

=> r2 = r1/2

So, the second star is 0.5 times closer than the first one.