(a) How long does it take a radio signal to travel 150 km from a transmitter to a receiving ant

step 1 In this question, there are four parts. So the four parts are about calculation involving electr

(a) How long does it take a radio signal to travel 150 km...

(a) How long does it take a radio signal to travel $150 \mathrm{~km}$ from a transmitter to a receiving antenna? (b) We see a full Moon by reflected sunlight. How much earlier did the light that enters our eye leave the Sun? The Earth-Moon and Earth-Sun distances are $3.8 \times 10^{5} \mathrm{~km}$ and $1.5 \times 10^{8} \mathrm{~km},$ respectively. (c) What is the round-trip travel time for light between Earth and a spaceship orbiting Saturn, $1.3 \times 10^{9} \mathrm{~km}$ distant? (d) The Crab nebula, which is about 6500 light-years (ly) distant, is thought to be the result of a supernova explosion recorded by Chinese astronomers in A.D. $1054 .$ In approximately what year did the explosion actually occur? (When we look into the night sky, we are effectively looking back in time.)

(a) How long does it take a radio signal to travel $150 \mathrm{~km}$ from a transmitter to a receiving antenna? (b) We see a full Moon by reflected sunlight. How much earlier did the light that enters our eye leave the Sun? The Earth-Moon and Earth-Sun distances are $3.8 \times 10^{5} \mathrm{~km}$ and $1.5 \times 10^{8} \mathrm{~km},$ respectively. (c) What is the round-trip travel time for light between Earth and a spaceship orbiting Saturn, $1.3 \times 10^{9} \mathrm{~km}$ distant?
(d) The Crab nebula, which is about 6500 light-years (ly) distant, is thought to be the result of a supernova explosion recorded by Chinese astronomers in A.D. $1054 .$ In approximately what year did the explosion actually occur? (When we look into the night sky, we are effectively looking back in time.)

Key Concepts

Speed of Light

The speed of light in a vacuum is approximately 3.0 × 10^8 meters per second. This constant is fundamental to modern physics and underpins calculations involving electromagnetic radiation, from radio waves to visible light, across all scales.

Time-of-Flight Calculation

This concept involves using the relationship time = distance ÷ speed to determine how long it takes for light or any electromagnetic signal to travel a particular distance. It is critical in fields ranging from telecommunications to astronomy, where it helps determine communication delays and the age of astronomical observations.

Astronomical Distance Units and Look-Back Time

In astronomy, distances are often so vast that units like kilometers become impractical; thus, units such as light-years are used, where one light-year is the distance light travels in one year. This concept also leads to the idea of look-back time, where observing distant objects means seeing them as they were in the past, since light takes time to travel across space.

Round-Trip Time Calculation

For situations where light must travel to a destination and then return (as in radar or communication systems), the round-trip time is calculated by doubling the one-way travel time. This calculation is essential for determining delay times in systems where signals are bounced off or reflected from distant objects.

Retrospective Timing in Astronomy

Due to the finite speed of light, the events we observe in the universe happened in the past. By knowing the distance to an astronomical object or event, scientists can calculate how long the light took to travel to Earth, and thereby estimate the time period during which the event actually occurred.

Transcript

00:01 In this question, there are four parts.

00:03 So the four parts are about calculation involving electromagnetic wave and they are not related.

00:11 So we'll just do part by part.

00:15 In part a, you want to find the time taken to for radio signal to travel 150 km.

00:23 So using d equals to c times t.

00:29 Then we have delta t equals to d over c which is 150 km divided by the speed of light and the answer is 5 .00 times 10 to the power of negative 4 seconds okay so this is the answer for part a then in part b we need to calculate the time taken for light to travel from the side sun through the earth, through the reflection from the moon, okay, during full moon.

01:16 So how much earlier did the light enters our eye leave the sun? so we have the situation, okay, sun, then earth and moon, okay? of course they are not really on the same plane but this is this is what happens at full moon so at full moon the moon and sun are on opposite sides of earth so the distance travel by light okay is okay so d is the distance between the sun and earth, k, plus two times of the distance between earth and moon.

03:03 Okay, these are in kilometers.

03:05 So we have 1 .51 times 10 to the power 8, km, and is equal to 1 .51 times 10 to the power 11 meters.

03:17 So the time taken by light, k is equal to d over c, so which is 1 .51 times 10 to the 11 5 .3 times 10 to part 8.

03:38 Okay and we get 8 .4 minutes.

03:42 Okay, so this is the answer for part b and then part c...

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