Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

(a) How much time does it take light to travel from the moon to the earth, a distance of 384,000 km? (b) Light from the star Sirius takes 8.61 years to reach the earth. What is the distance from earth to Sirius in kilometers?

Short Answer

Expert verified
(a) Approximately 1.28 seconds. (b) Approximately \(8.161 \times 10^{13}\) kilometers.

Step by step solution

01

Understand the Speed of Light

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s). For convenience, this can be approximated to 300,000 kilometers per second (km/s) to simplify calculations.
02

Convert Distance from Kilometers to Kilometers per Second (Part a)

You are given a distance of 384,000 km from the Moon to the Earth. To find the time, use the formula:\[\text{Time} = \frac{\text{Distance}}{\text{Speed of Light}}\]Substitute the values into the formula:\[\text{Time} = \frac{384,000 \text{ km}}{300,000 \text{ km/sec}}\]
03

Compute the Time for Light to Travel from the Moon to the Earth (Part a)

Calculate the time required for light to travel from the Moon to the Earth:\[\text{Time} \approx 1.28 \text{ seconds}\]
04

Convert Time from Years to Seconds (Part b)

Light from Sirius takes 8.61 years to reach Earth. First, convert this time from years to seconds, knowing there are about 31,536,000 seconds in a year.\[\text{Time in seconds} = 8.61 \text{ years} \times 31,536,000 \text{ sec/year}\]
05

Calculate Distance Using Time and Speed of Light (Part b)

Using the time in seconds and the speed of light to find the distance:\[\text{Distance} = \text{Time in seconds} \times \text{Speed of Light} = (8.61 \times 31,536,000 \text{ sec}) \times 300,000 \text{ km/sec}\]
06

Compute the Distance from Earth to Sirius (Part b)

Perform the multiplication to get the distance:\[\text{Distance} \approx 8.161 \times 10^{13} \text{ km}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distance Calculation
Understanding how to calculate distances using the speed of light is an essential skill in physics and astronomy. When light travels from one point to another, such as from the Moon to Earth, the distance can be calculated using a simple formula:
  • First, we know that the speed of light is approximately 300,000 kilometers per second.
  • The formula we'll use is: \( \text{Time} = \frac{\text{Distance}}{\text{Speed of Light}} \).
  • By applying the distance from the Moon to Earth, which is 384,000 km, and dividing by the speed of light, we get the time light takes to travel that distance.
This method is a straightforward approach that helps us visualize how incredibly fast light is, allowing us to calculate time based on vast yet reachable astronomical distances.
Light Travel Time
Light travel time is a fascinating concept that demonstrates just how fast light travels over enormous distances. When we talk about light traveling, we're discussing how long it takes for light to go from one celestial body to another.
  • This concept can be seen in practice when calculating how long it takes light to travel from the Moon to Earth, which takes only about 1.28 seconds.
  • For stars much farther away, like Sirius, light can take years to reach us, showing the vastness of space.
  • For example, from Sirius, light takes 8.61 years to reach the planet Earth.
This shows us the immense distance light covers, stretching over trillions of kilometers, a testament to the vastness and wonder of the universe. When making such calculations, convert all units appropriately to avoid errors.
Astronomical Distances
Astronomical distances often involve incomprehensibly large numbers. These distances are frequently measured in light years, which is the distance light travels in one year. By knowing the time light takes to travel from Sirius to Earth, we can calculate this massive distance.
  • First, convert the years into seconds, using the known conversion of 31,536,000 seconds per year, to comprehend just how large a single light year is.
  • Next, multiply this time in seconds by the speed of light to find the total distance covered by light in kilometers.
  • In the exercise example, light from Sirius covers roughly \( 8.161 \times 10^{13} \) kilometers.
These distances reveal just how immense the universe is. Tools like the speed of light and conversion of time enhance our understanding and capability to calculate these vast stretches of space. Such insights help deepen our understanding of the cosmos and all it encompasses.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A circular wire loop has a radius of \(7.50 \mathrm{~cm}\). A sinusoidal electromagnetic plane wave traveling in air passes through the loop, with the direction of the magnetic field of the wave perpendicular to the plane of the loop. The intensity of the wave at the location of the loop is \(0.0275 \mathrm{~W} / \mathrm{m}^{2}\), and the wavelength of the wave is \(6.90 \mathrm{~m}\). What is the maximum emf induced in the loop?

In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency 110.0 MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standing-wave pattern to occur. (a) How far apart are the nodal planes of the magnetic field? (b) If the standing- wave pattern is determined to be in its eighth harmonic, how long is the cavity?

A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area 0.500 m\(^2\). At the window, the electric field of the wave has rms value 0.0400 V/m. How much energy does this wave carry through the window during a 30.0-s commercial?

A small helium-neon laser emits red visible light with a power of 5.80 mW in a beam of diameter 2.50 mm. (a) What are the amplitudes of the electric and magnetic fields of this light? (b) What are the average energy densities associated with the electric field and with the magnetic field? (c) What is the total energy contained in a 1.00-m length of the beam?

There are two categories of ultraviolet light. Ultraviolet A (UVA) has a wavelength ranging from 320 nm to 400 nm. It is necessary for the production of vitamin D. UVB, with a wavelength in vacuum between 280 nm and 320 nm, is more dangerous because it is much more likely to cause skin cancer. (a) Find the frequency ranges of UVA and UVB. (b) What are the ranges of the wave numbers for UVA and UVB?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free