Newton’s Law of Universal Gravitation

An exploration of gravity and its inner workings

One of the most cited stories about Isaac Newton is his ‘discovery’ of gravity.  Even though we’ve learned a bit about Newton’s three basic laws of motion, we haven’t found out anything about his theories on gravity.  This exercise will lead you through his theory’s logic, step by step.

Model 1.  A sheet of paper.

1.       Have one of your group members hold up a sheet of paper by its edges.

2.       Find a light object (paper clip or staple) and a medium-weight object (eraser or pencil) to place on the paper.  Make sure that whatever you choose does not break the paper.

3.       Place the two objects far away from each other on the suspended paper.  Record your observations.

4.       Move the objects closer to each other on the sheet of paper.  Note any similarities or differences in movement between the two objects.

Critical Thinking Questions

1.       What happened when the objects were placed on the paper?

2.       Did the heavier or lighter object have more of an effect on the paper?

3.       Did either object exert no force at all on the paper?

4.       Did the objects exert more ‘influence’ on each other when they were close together or far away from each other?

5.       When the objects were placed close together, which object ‘pulled’ the other object in?

6.       If a third object were placed on the paper, which object would it ‘gravitate’ more toward?

7.       Does any object, in this scenario, not have any influence at all on another object?  Explain your reasoning.

Model 2.  Gravitational Data.

Below is a table of the gravitational forces felt by various masses at various distances from each other.

 Mass 1 (m1) Mass 2 (m2) Distance (d) Your fraction Gravitational Force (Fgravity) 5 kg 1 kg 2 m 8.33 x 10-11 N 5 kg 1 kg 4 m 2.08 x 10-11 N 5 kg 1 kg 6 m 9.26 x 10-12 N 5 kg 2 kg 2 m 1.66 x 10-10 N 5 kg 2 kg 4 m 4.16 x 10-11 N 1 kg 5 kg 2 m 8.33 x 10-11 N 1 kg 5 kg 4 m 2.08 x 10-11 N

Critical Thinking Questions

8.       Find two scenarios (rows) to compare, such that m1 and d stay the same, but m2 changes.

a.       By what factor does m2 change from one scenario to the other?

b.      By what factor does Fgravity change from one scenario to the other?

c.       How are m2 and Fgravity proportionally related?

9.       Find two scenarios (rows) to compare, such that m2 and d stay the same, but m1 changes.

a.       By what factor does m1 change from one scenario to the other?

b.      By what factor does Fgravity change from one scenario to the other?

c.       How are m1 and Fgravity proportionally related?

10.   Find two scenarios (rows) to compare, such that m1 and m2 stay the same, but the distance between them changes.

a.       By what factor does d change from one scenario to the other?

b.      By what factor does Fgravity change from one scenario to the other? (Hint—have your calculator change this value to a fraction.)

c.       Repeat steps a and b, using two different rows where m1 and m2 stay the same.  This time, the distance should change by a different factor from the first to the second scenario.

i.       By what factor does d change from one scenario to the other?

ii.       By what factor does Fgravity change from one scenario to the other? (Hint—have your calculator change this value to a fraction.)

d.      How are d and Fgravity proportionally related?

11.   If you were to express gravity as a fraction involving m1, m2, and d:

a.       Which value(s) would be on top of the fraction?

b.      Which value(s) would be on bottom of the fraction?

c.       Would any of these values have an exponent?

12.   Write the fraction you described in #4.

13.   If you use the fraction from #5 for the first scenario in the table, does it produce the Fgravity shown?

14.   What number do you need to multiply your fraction by to get the Fgravity shown?

15.   The number you wrote for #7 (check with the teacher!!) is called the gravitational constant.  Write it down.

16.   If d is measured in meters, and mass is measured in kg, what unit does the gravitational constant have to be in so that Fgravity is in Newtons (kg∙m/s2)?

17.   Fill out the ‘your fraction’ column for each scenario by plugging your values into your formula and writing the answer in the blank.

18.   For each of the rows in the chart, use the ‘your fraction’ values as x values, and the ‘Fgravity’ values as y values for plotted points in a graphing calculator.

19.   Using the points entered in #11, find the slope of the line with your calculator.  How does it compare with your answer to #8?