Mars Lag

It takes time for a radio signal to travel from Earth to Mars and back. The one-way travel time is equal to d/c, where d is the distance between the planets and c is the speed of light in space (1806,000 miles per second).

Here's a question mission planners might ask: suppose the rover sends back a signal which NASA scientists review and then send some sort of instruction back to the rover on Mars. If we want to limit the total "lag" time (from the time the rover sends a signal to the time it receives an instruction) to 30 minutes, and it takes the scientists 10 minutes (600 seconds) to review the data, what's the maximum distance between Earth and Mars that will allow that?

The formula relating the communication lag time would be

Mars Lag

where
t = communication lag time in seconds
d = distance between Mars and Earth in miles
c = speed of light = 186,000 miles/second
To find the distance at which t = 30 minutes (1800 seconds), you would plug in the appropriate values of t and c, and solve for d.

Use the formula above and apply laws of equations to solve for the unknown.

Subject: Mathematics
Topics: Algebra—Expressions and Equations
Grades: 6 – 12
Knowledge and Skills:
- Can evaluate expressions by substituting values for variables
- Can simplify expressions using correct order of operations
- Can do basic operations on both sides of an equation in such a way as to preserve the equality

Download Teacher Guide: Mars Lag (PDF)
Download Student Lesson: Mars Lag (PDF)

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Running time 1:41 minutes.

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