Question

It is the year 2235 and you are the lead Flight Engineer of an operations team1 directing the Star Skimmer space mission. Star Skimmer is a satellite that was put into a circular orbit around a neutron star,2 just barely beyond the neutron star’s surface to measure ambient conditions very close to the stellar remnant. The neutron star has a radius ??? = 20.0 km, and mass ??? = 1.42 ?⊙, where ?⊙ = 1.99 × 10^30 kg is the mass of the Earth’s Sun. In this problem we will neglect general relativistic effects, which means that we assume that Newton’s law of gravity can be used to express gravitational interactions. The satellite itself is a sphere, and has a diameter ?_0 = 100.00 m, as measured in the construction yard in which it was made, on a planet very far away from the neutron star. There is also an electronics monitor, which is connected to a blinking laser beam on the surface of the satellite, which blinks at frequency ? = 6.0000 Hz, also as measured in the construction yard. 0 Using a very long-baseline interferometric telescope array located at your headquarters on the distant planet, you and your team obtain extremely high-precision images of Star Skimmer for the times when the satellite passes along the line of sight between your observation point and the neutron star, as shown in Figure 1a. To make sure that the satellite hasn’t been damaged during flight, you use the images to ascertain its operational status.

a) To check the satellite’s structural integrity, you measure its horizontal (?) and vertical (?) dimensions as seen in the images (shown in Figure 1b) and compare them to the predicted values for the known orbital motion of the satellite. What are the predicted values of ? and ??

b) To check the electronics integrity, you measure from the images the blink frequency of the satellite’s external laser, and compare it to the predicted value for the known orbital motion of the satellite. What is the predicted blink frequency for the laser?

Answer 1