this leg of the trip, the traveling twin sees his own clock advance 3 years and the clock in the screen advance 1 year, so it seems to advance at the normal rate, just 20 image seconds per ship minute. This combines the effects of time dilation due to motion (by factor ε=0.6, five years on Earth are 3 years on ship) and the effect of increasing light-time-delay (which grows from 0 to 4 years). Of course, the observed frequency of the transmission is also the frequency of the transmitter (a reduction in frequency; "red-shifted"). This is called the relativistic Doppler effect. The frequency of clock-ticks (or of wavefronts) which one sees from a source with rest frequency frest is when the source is moving directly away. This is fobs = frest for v/c = 0.8. As for the stay-at-home twin, he gets a slowed signal from the ship for 9 years, at a frequency the transmitter frequency. During these 9 years, the clock of the traveling twin in the screen seems to advance 3 years, so both twins see the image of their sibling aging at a rate only their own rate. Expressed in other way, they would both see the other's clock run at their own clock speed. If they factor out of the calculation the fact that the light-time delay of the transmission is increasing at a rate of 0.8 seconds per second, both can work out that the other twin is aging slower, at 60% rate. Then the ship turns back toward home. The clock of the staying twin shows "1 year after launch" in the screen of the ship, and during the 3 years of the trip back it increases up to "10 years after launch", so the clock in the screen seems to be advancing 3 times faster than usual. When the source is moving towards the observer, the observed frequency is higher ("blue-shifted") and given by This is fobs = 3frest for v/c = 0.8. As for the screen on Earth, it shows that trip back beginning 9 years after launch, and the traveling clock in the screen shows that 3 years have passed on the ship. One year later, the ship is back home and the clock shows 6 years. So, during the trip back, both twins see their sibling's clock going 3 times faster than their own. Factoring out the fact