Galileo's Data

 

Description

Shown is an adaptation of Galileo’s data of the angle between Jupiter and its moon Callisto.

Question a

Given what you know about the orbit of planets and satellites, why does Galileo’s data look like it does?

 


Start

Question b

Given your finding above, explain the possible relationships depicted in the above animation. 

 


Instructor Resources

Reference: See Giancoli-PA: 11-1, Giancoli-SE: 14-2.
Answer a: Answer: The data suggest a negative cosine curve, yet planets and satellites move in mostly circular orbits. Therefore, Galileo was seeing circular motion edge on.
Answer b: As suggested in Galileo’s data, circular motion viewed edge on, looks like a sine or a cosine curve. Here there is a direct relationship between the position, velocity, and acceleration in the y- direction for the coin on the turntable and the position, velocity, and acceleration in the y-direction for the mass on the spring. Since the magnitude of the velocity for the coin on the turntable is constant, we can determine that when y=+/- ymax, vy=0 and when y=0, vy=+/- vmax. These relationships are also true for the mass on the spring..
Script Author: Mario Belloni