 One of these moons is Io. Galileo and others used their telescopes to determine the time that it takes Io to orbit Jupiter, starting from the disappearance of Io behind Jupiter's shadow. These measurements were taken when the Earth was between the Sun and Jupiter, or when Jupiter was in opposition. This way, Jupiter and its moons could be easily seen high in the sky. Remember, Jupiter and its moons are non-luminous, but they reflect the sunlight towards the Earth and into Galilean telescopes. Galileo and others found that Io always, that is year after year, took 42.5 hours to orbit Jupiter. Now the distance between the Earth and Jupiter varies between 365 and 601 million miles. Do you think the speed of light affected their measurement of 42.5 hours per orbit? If so, could Galileo use the measurements to determine the speed of light? Let's reason it out. There is a time lag for the light, a signal, to get to Earth from Io, marking the beginning of the orbit. But there is also a time lag for light to get to Earth from Io when Io disappears the second time, marking the end of a single orbit. If those time lags are the same, then the orbit time measured on Earth should be the same as the time of orbit on Io, and the speed of light should not affect the measurement. Now, let's confirm this with some math. Let's call C the speed of light in space. Remember, we ultimately want to find a numerical value for C. The time that it takes for light to travel from Io to Earth is X on C, or X is a distance in kilometers, and C is the speed of light in units of kilometers per hour. So let's use a timer. When Io first disappears into the shadow of Jupiter, we start the timer on Io. T is equal to zero. But on Earth, you see Io disappear into the shadow a little bit later in time, because it takes time for the light reflected from Io's surface to reach the Earth. Earth sees the start of the orbit at this time, T is equal to X1 on C, where this term is the time that it takes for the light of Io to reach Earth. When Io reappears, orbits once, and disappears a second time behind the shadow, the timer shows 42.5 hours. But again, on Earth, you see Io disappear a little bit later in time because it takes time for the light to reach Earth. That is the time at which Earth sees the end of the orbit is this, 42.5 hours plus X2 on C. So the time of orbit as measured on Io is this, T1 minus T0, it's 42.5 hours. And the time of orbit as measured on Earth is 42.5 hours plus X2 minus X1, all on C. As suggested by this pictorial demonstration, the difference in the path lengths X2 minus X1 turns out to be very small, and C is such a big number that this whole number is small. And so it wasn't in the resolution of timepieces in Galileo's day. So the speed of light did not affect Galileo's measurement on Io's time of orbit. A single orbit of Io could not be used to find the speed of light.