Example A: The Orbit of Mercury

1. Mercury is the closest planet to the Sun. Its orbit is elliptical and it is observed that the closest point of the ellipse to the Sun (the perihelion) shifts a small amount with each revolution. This orbital shift is known as perihelion precession. The laws of gravity and planetary motion, as discovered by Kepler and Newton, cannot explain the precession in Mercury’s orbit. What causes the precession?

2. One explanation may be that there is an undiscovered planet orbiting the Sun near Mercury that is affecting Mercury’s orbit, much like Neptune perturbs Uranus’ orbit. Another explanation is that Einstein’s theory of gravity, General Relativity, describes Mercury’s orbit more accurately than Newton’s laws.

3. We will hypothesize that the perturbation in the orbit of Mercury is caused by the presence of a previously undiscovered planet that we will call Vulcan. The location of planet Vulcan in its orbit can be calculated based on its supposed interaction with Mercury according to Newton’s and Kepler’s laws of gravity and planetary motion.

4. To test our hypothesis, we calculate the predicted location of planet Vulcan. Then we point telescopes at the predicted location and observe.

5. No planet can be seen. The results of the test do not match the predictions of the hypothesis.

6. It appears that the experiment falsifies the hypothesis. No previously unknown planet was discovered, so it is unlikely that the perturbation in Mercury’s orbit is the result of a nearby planet. We will have to form a new hypothesis and test that instead.

7. Even though we did not confirm our hypothesis, our findings are still of interest to scientists because they rule out a possibility and bring us closer to understanding the phenomenon. We could submit our findings to a journal such as Astronomy & Astrophysics for fellow scientists to read.

8. Astronomers and astrophysicists would be interested in our results because the test rules out an unknown planet as an explanation for Mercury’s orbit. Many astronomers would probably use their own telescopes and observatories to confirm our test as well. The next likely candidate hypothesis to explain this phenomenon is General Relativity. Astronomers can use General Relativity to calculate the predicted orbit of Mercury and then test if the prediction matches the actual orbit.

(In fact, this is what really happened, and it turned out that General Relativity is a successful hypothesis that explains Mercury’s orbit as well as many other phenomena. As such, General Relativity is now referred to as a theory.)

1. When different objects are placed in water, it is observed that some of them sink while others float. For example, a lime sinks in water while a lemon floats. What determines whether an object sinks or floats?

2. One explanation may be that objects with density greater than the density of water sink, while objects with density less than that of water float. Another explanation could be that certain objects are porous or leaky so they fill up with water, causing them to sink. A third possibility could be that the surface material is chemically attracted to water molecules, pulling certain objects under the water.

3. We hypothesize that the density of an object determines whether it sinks or floats. If its density is greater than water’s density, it sinks. If its density is less than water’s density, it floats. Water has a density of 1.000 grams per cubic centimeter (g/cm3).

4. To test our hypothesis, we need to first calculate the density of the objects and then see if they sink or float. Density equals the objects mass divided by its volume. To get the mass of an object, we simply weigh it on a scale. To find the volume of an object, we can submerge it in a full container of water and see how much water overflows.

5. The results of this test are best expressed in a table.

Object Mass (grams) Volume (cm3) Density (g/cm3) Sink or Float

6. The test supports our hypothesis. The objects (Lime and Rubber Band Ball) with densities greater than water’s density (1.000 g/cm3) sank. The objects (Lemon and Coconut) with densities less than water’s density floated. Our results don’t rule out the other hypotheses from part 2 though (leaky objects or chemically attracted objects). To be sure that these other hypotheses don’t explain our results, we would need to check them too.

7. This is a simple experiment, but it has value for teaching. We might submit a paper to the Journal of Science Education and Technology.

8. Other scientists would likely want to check the alternative hypotheses to make sure that there isn’t another explanation for our results. It is simple to check if the objects are porous or leaky, and it is not too hard to test whether any of these objects have an unusually large chemical attraction to water. If further tests rule out these other hypotheses, then we could be pretty confident that our density hypothesis explains why some objects sink while others float.