Please answer the question with explanation

2. A signal relay problem. In a future post-apocalyptic world, NASA sends out two spacecraft (named Horizon 1 and 2) into interstellar space. Horizon 1, launched rst, moves at constant velocity v1 in the plane of the ecliptic, formed by the Earth's orbit around the sun. Horizon 2, launched somewhat later, moves at constant velocity v2, at somewhat faster speed, in a straight line perpendicular to the ecliptic plane. To coordinate communications between Earth and the two spacecraft, mis- sion control at Earth sends light signals to both Horizon 1 and 2, timed to arrive at exactly the same time in the observer frame on Earth when the spacecraft are identical distances d from Earth. 0 Assume that d far exceeds the Earth-sun distance, and that the speeds of both spacecraft far exceed the orbital speed of Earth around the sun. Once each spacecraft receives the Earth signal, they each immediately send a light signal to the other spacecraft (i.e. Horizon 1 to Horizon 2, and vice verso). At the instants that each spacecraft receive the signal from the other one, they relay a light signal back to mission control on Earth. (a) Determine the difference in arrival times at Earth of these relayed light signals. Which one arrives rst, the one coming directly from Horizon 1, or the one from Horizon 2? (b) Each spacecraft carries a clock identical to one ticking in mission control on Earth. What is the time dilation factor for the Horizon 2 clock as measured by Horizon 1? What is the time dilation factor of the Horizon 1 clock to someone on Horizon 2? o In practice, such time dilation factors translate to frequency shifts in the light signals that signify the velocity-dependent Doppler effect for light: we will learn about this in due course. (c) What is the angle between the velocity vectors of Horizon 1 and the Earth, as perceived by an astronaut on the Horizon 2 spacecriaft