(3) Using your data from tables 1, 2, and 3, create graphs for the relationships of F versus r, F versus m

1

, and

F versus m

2

using a graphing program such as Excel or Logger Pro. In your graphing program determine

the best-fit line or curve for each of the graphs. For the F versus r graph, try the “inverse square” best-fit

curve. What is the correlation for the fit? _____________. Provide a sketch for each of the relationships

below. Make sure to label the axis including units. Also, include the equation for the best-fit line/curve

for the graph. Do not provide a numbered scale on the x and y-axis.

(4) When a graph is linear and passes through the origin, the relationship between the variables is said to be

proportional. When two quantities are proportional, the quantities differ by the multiplication of a

constant. For example, if F is proportional to m

1

then F = (constant)*m

1

.

(5) Write the two equations that represent the proportional relationships in your sketches from the best-fit

lines in your graphing program. Do not include the y-intercept in the equation. Within experimental

uncertainties, we will assume the intercept is zero.

(1) _____________________________ (2)______________________________

(6) One of the graphs should appear to be an exponential decay curve. Determining the relationship between

the variables is more difficult. One way is to use the equation for the best-fit line given by your graphing

program. Write the equation here for the inverse square curve: ______________________________.

Given the high correlation for the curve fit, F is considered proportional to 1/r

2

.

(7) Combine the proportionalities into one equation for F. Fill in the blanks below using the variables F, m

1

,

m

2

, and r. k is a constant.

(8) The value of the constant k can be determined from one of your proportional graphs. Use F versus m

1

.

Write the value for the slope of the graph? (look at your equation) ___________________________

(9) Using our new relationship from (7), for your F versus m

1

graph. Use the value of the

slope, m

2

= 1000kg, r = 5m, and calculate a value for k. Write the value for k: _____________________.

(10) The actual value for k is known as the Universal Gravitational Constant, G. .

(11) Write the complete formula for Newton’s Universal Law of Gravitation in the box below. Using the

internet check if your formula is correct.

_____ = k

_____ ×_____

_____

(12) Using the equation for Newton’s Universal Law of Gravitation (a) determine the force of attraction

between the Earth, , and the Moon, , if the average

mean distance between the Earth and the Moon is . (b) If a single Saturn V rocket has a

thrust of , how many Saturn V rockets is the force in (a) equivalent to?

F = 1.99E20N

Saturn V rocket = 3.5E7 N

5.7E12 rockets or 5.7 trillion Saturn V rockets!