Question

When the NASA Rover Spirit successfully landed on Mars in January of $2004,$ Mars was $170.2 \times 10^{6} \mathrm{km}$ from Earth. Twenty-one days later, when the Rover Opportunity landed on Mars, Mars was $198.7 \times 10^{6} \mathrm{km}$ from Earth. (a) How long did it take for a one-way transmission to the scientists on Earth from Spirit on its landing day? (b) How long did it take for scientists to communicate with Opportunity on its landing day?

Name: Problem 19, Chapter 22: Physics
Uploaded: 2021-04-06T14:20:37-08:00
Duration: 1 min 23 s
Channel: Narayan Hari

   When the NASA Rover Spirit successfully landed on Mars in January of $2004,$ Mars was $170.2 \times 10^{6} \mathrm{km}$ from Earth. Twenty-one days later, when the Rover Opportunity landed on Mars, Mars was $198.7 \times 10^{6} \mathrm{km}$ from Earth. (a) How long did it take for a one-way transmission to the scientists on Earth from Spirit on its landing day?
(b) How long did it take for scientists to communicate with Opportunity on its landing day?

Physics

Robert Coleman… 5th Edition

Chapter 22, Problem 19

Instant Answer

Solved by Expert Narayan Hari

04/06/2021

Step 1

We can use the formula for time, which is distance divided by speed. In this case, the distance is the distance between Mars and Earth, and the speed is the speed of light. The formula is: \[ t_1 = \frac{d_1}{c} \] where $ t_1 $ is the time taken, $ d_1 $ Show more…

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When the NASA Rover Spirit successfully landed on Mars in January of $2004,$ Mars was $170.2 \times 10^{6} \mathrm{km}$ from Earth. Twenty-one days later, when the Rover Opportunity landed on Mars, Mars was $198.7 \times 10^{6} \mathrm{km}$ from Earth. (a) How long did it take for a one-way transmission to the scientists on Earth from Spirit on its landing day? (b) How long did it take for scientists to communicate with Opportunity on its landing day?

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Key Concepts

Speed of Light

The speed of light is a fundamental physical constant that describes how fast electromagnetic waves, including radio signals, travel in a vacuum. It is approximately 3 x 10^5 kilometers per second, and it is used to calculate the time delay for signals to traverse vast distances in space.

Propagation Delay

Propagation delay refers to the time it takes for a signal to travel from the sender to the receiver. This delay is computed by dividing the distance between the two points by the speed of light, and it is a critical factor in planning communications with distant spacecraft such as Mars rovers.

Distance Measurement

Distance measurement involves determining the separation between two points, which in space communications can be vast and is often expressed in units like millions of kilometers. Accurate distance measurements are essential for calculating communication delays and ensuring proper timing in signal transmission.

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