While passing between Earth and the Moon, a spacecraft is momentarily located on

Question

While passing between Earth and the Moon, a spacecraft is momentarily located on the line connecting the centers of the two bodies and is at a distance of d=135 km from a radio antenna on the surface of Earth. The distance from the antenna to the moon is denoted by d m.
Part A: recall that the speed of light is 3.0x10^8 m/s. How long, in seconds, does it take for a signal from the spacecraft to arrive at the antenna on Earth?
Part B: scientists on Earth send a command to the Spacecraft, which immediately sends back a receipt confirmation signal. How long, in seconds, after the scientists send the command does it take before they learn it was received?
Part C: Scientists bounce a laser beam off the moon and measure the two-way travel time to be 2.42 s. How far away is the Moon in meters?
Thank you for your help! While passing between Earth and the Moon, a spacecraft is momentarily located on the line connecting the centers of the two bodies and is at a distance of d=135 km from a radio antenna on the surface of Earth. The distance from the antenna to the moon is denoted by d m.
Part A: recall that the speed of light is 3.0x10^8 m/s. How long, in seconds, does it take for a signal from the spacecraft to arrive at the antenna on Earth?
Part B: scientists on Earth send a command to the Spacecraft, which immediately sends back a receipt confirmation signal. How long, in seconds, after the scientists send the command does it take before they learn it was received?
Part C: Scientists bounce a laser beam off the moon and measure the two-way travel time to be 2.42 s. How far away is the Moon in meters?
Thank you for your help!
Part A: recall that the speed of light is 3.0x10^8 m/s. How long, in seconds, does it take for a signal from the spacecraft to arrive at the antenna on Earth?
Part B: scientists on Earth send a command to the Spacecraft, which immediately sends back a receipt confirmation signal. How long, in seconds, after the scientists send the command does it take before they learn it was received?
Part C: Scientists bounce a laser beam off the moon and measure the two-way travel time to be 2.42 s. How far away is the Moon in meters?
Thank you for your help!

Explanation / Answer

given that

d = 135 km

part A:

time taken t = distance /speed

t = 135*1000 / 3*10^8

t = 45*10^(-5) s

part B:

time taken by signal to reach spacecraft = 45*10^(-5) s

time taken by confirmation signal to each earth =   45*10^(-5) s

total time taken = 90*10^(-5) = 9*10^(-4) s

part C:

time taken by signal to reach moon = 2.42/2 = 1.21 s

distance of moon = 1.21*3*10^8 = 3.63*10^8 m

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