PRINTABLE ACTIVITIES / SIGNAL TRAVEL TIME
Send a Signal.
Wait for the Reply.
Compare Moon, L2 and idealized Mars separations, calculate both travel legs and distinguish static geometry from a live spacecraft link.
Download printable worksheet & educator notes · PDF ↓Open the Signal travel time interactive tool →
Print learner pages 1–2; answers and educator notes are on pages 3–4. The complete activity is also readable below. Optional data and code downloads are inside the offline-verification section.
CHECK THIS RESULT / TEACHING METHOD 1.0
Check the near-side Mars example.
Use the Spacecraft signal delay interactive tool. Choose Mars, which starts at Near-side alignment / shorter separation. The model places Earth on a 1 AU circle and Mars on a 1.524 AU circle. Their separation in this alignment is 0.524 AU, not Mars’s distance from the Sun.
Reference inputs and generated arithmetic: the Moon and L2 comparisons use rounded distances; the Mars cases use chosen circular geometry informed by a rounded JPL orbital size. These are not today’s planetary positions, spacecraft telemetry or measured communications delays. Extra decimal places let you repeat the arithmetic; they do not improve a rounded distance.
| Step | Reference result | What to check |
|---|---|---|
| Circle radii | Earth 1 AU; Mars 1.524 AU | These are adopted teaching radii, not current positions. |
| Sender–receiver separation | |1.524 − 1| = 0.524 AU | Use the separation between sender and receiver. |
| Convert to kilometers | 78389284.2468 km | 0.524 × 149,597,870.7 km per AU. |
| Equivalent distance in miles | 48708843.011065 miles | Divide kilometers by 1.609344. |
| One-way time t = d/c | 261.478507 s ≈ 4 min 21.479 s | Use c = 299,792.458 km/s with kilometers. |
| Hypothetical immediate reply | 522.957013 s ≈ 8 min 42.957 s | Two equal travel legs: 2d/c, with zero remote waiting. |
The vacuum speed c is fixed by the SI definition; in kilometers per second it is exactly 299,792.458. The adopted distance remains approximate. A real link also depends on motion, visibility, transmission duration, processing, scheduling, plasma and other corrections. This calculation isolates propagation time.
Repeat the calculation in a spreadsheet
- Compute the near-side separation with
=ABS(1.524-1). Convert AU to kilometers with=0.524*149597870.7. - Calculate the one-way time using
=78389284.2468/299792.458. Double it for an immediate reply, or use=2*78389284.2468/299792.458directly. - For minutes and seconds, divide total seconds by 60, keep the whole minutes, then subtract 60 times that whole-minute count from the original seconds. For case 3, 261.478507 s is 4 min 21.478507 s, not 4.357975 minutes written as minutes-and-seconds.
- Change the lab’s Distance unit between miles, kilometers and AU. It converts the number while preserving separation, so the delay stays the same. A different numerical value in another unit does not mean the destination moved.
Use the CSV’s higher-precision generated values for software comparisons. Stored digits and display rounding are not measurement uncertainties. The international mile conversion is exactly 1.609344 km.
Why is the opposite-side case not a usable direct radio link?
Choose Opposite-side alignment / longer separation after Mars. This circular model gives 1 + 1.524 = 2.524 AU, about 1259.488 s one way and 2518.976 s for the doubled path. This is a geometric comparison. At exact opposite-side alignment, the Sun blocks a direct path between Earth and Mars.
These two cases are not actual closest/farthest Mars distances or a prediction for any date. Real planetary orbits are elliptical and tilted, and a spacecraft has its own position. Knowing an orbital size from the Sun does not by itself give the Earth–receiver range.
What changes if the receiver waits before answering?
If the receiver waits 30 s before sending its reply, the stationary-path total becomes =2*78389284.2468/299792.458+30 ≈ 552.957013 s, or 9 min 12.957 s. This optional paper calculation adds a remote wait; the live tool displays the zero-wait comparison.
Higher bandwidth can carry more information per second. It does not increase the speed of the signal front in vacuum. Faster processing can reduce a processing delay, while the propagation time for the same path still applies. Neither simple total predicts a mission’s full command/response schedule.
Verify the reference inputs and generated cases offline
Extract the kit and run python3 verify_analysis.py --data-dir . (Windows: py -3 verify_analysis.py --data-dir .). Python 3.9+ and its standard library are sufficient. Compare the emitted JSON with worked-result.json.
The script checks eight pinned reference rows, five generated cases (four core cases plus the Proxima extension), near/far circle geometry, one-way and doubled times, and the same separation expressed in four units. It makes no network request and changes no input files. It checks a recipe and stored transcriptions, not a live ephemeris or mission telemetry.
Keep the assumptions: straight propagation through vacuum, constant separation and an instantaneous hypothetical reply. The Moon value is a rounded mean center-to-center separation; actual surface-station range varies. The 1.5-million-km L2 value is a rounded Earth–L2 region reference for Roman’s orbital design, not the telescope’s live range or a distance from the Sun. The other two Scale Lab tools remain separate comparisons.
FOR EDUCATORS / INDEPENDENT LEARNERS
One trip to arrive.
Two trips for a reply.
Suggested use: ages 12+ through introductory college; allow 30–40 minutes. Learners need subtraction, multiplication, division and a calculator. Use the live tool or the printed cases; spreadsheet and Python checks are optional. No account, submitted answers or student information is required.
The four-page packet has two learner pages and two educator pages. The kit includes reference inputs, generated comparisons, worked results, an independent Python checker and the unchanged Scale Lab model with its helper dependency. The tasks and answer discussion below provide a text-first alternative. The printed timing sequence labels each event and does not rely on color.
Learning goals
- Choose sender–receiver separation rather than substituting a distance from the Sun.
- Distinguish one-way arrival from the total wait for an immediate reply.
- Keep the physical distance and delay fixed when changing units.
- Separate propagation time, other communication delays and the conditions for a usable link.
Investigation record
- Predict: rank Moon, L2 and the two Mars cases by signal time. Explain why the reply needs another travel leg.
- Calculate: use the four supplied separations below. Find d/c and 2d/c, expressing the Mars times as minutes and seconds.
- Compare: choose Moon, Sun–Earth L2 / Roman and Mars in the tool. Switch Mars alignment, read the model note, and identify which case is blocked at exact alignment.
- Test the units: keep the same case while changing miles, kilometers and AU. Explain why the numbers in the distance field change but the travel time does not.
- Explain: add a 30 s remote wait to case 3, then state a claim with two numerical clues, one assumption and one limit. Explain why bandwidth or a longer antenna does not remove propagation time.
| Case | Adopted sender–receiver separation | Input status |
|---|---|---|
| 1 / Moon | 384,400 km | Rounded mean center-to-center reference. |
| 2 / Sun–Earth L2 | 1,500,000 km | Rounded L2-region reference for the orbital design. |
| 3 / Mars, near-side | 0.524 AU | Chosen circles: |1.524 − 1| AU. |
| 4 / Mars, opposite-side | 2.524 AU | Chosen circles: 1.524 + 1 AU; direct path blocked by Sun at exact alignment. |
Educator notes and suggested answers
Timing: prediction 5 minutes; four cases 10; browser/unit comparison 8; remote-wait question 5; written explanation 7; optional extension 5. For 30 minutes, emphasize Moon and the two Mars cases.
Answers: Moon: 1.282220 s one way, 2.564441 s for an immediate reply. L2 reference: 5.003461 s and 10.006923 s. Near-side Mars: 261.478507 s (4 min 21.479 s) and 522.957013 s (8 min 42.957 s). Opposite-side Mars geometry: 1,259.488074 s (20 min 59.488 s) and 2,518.976149 s (41 min 58.976 s). The latter is not a usable direct path through the Sun.
Units and waiting: case 3 is about 48,708,843.011 miles or 78,389,284.247 km or 0.524 AU. All give the same propagation time. A 30 s remote wait raises the total to 552.957013 s (9 min 12.957 s); it does not change either leg’s vacuum propagation time.
Assessment: look for the right separation, consistent units, a doubled path for the reply and recognition of blockage/other delays. Reject a claim that this predicts current Mars range, Roman’s live range or a mission command schedule. More bandwidth changes information throughput, not c. Accept sensible rounding from the supplied inputs.
Proxima extension: the lab’s rounded 4.24-light-year preset gives 4.24 Julian years one way and 8.48 for an immediate hypothetical reply. One Julian year is 365.25 days = 31,557,600 s; a light-year is a distance. The receiver is hypothetical, not evidence of inhabitants or a detectable signal. This remains a static comparison. No formal curriculum alignment or independent scientific review is claimed.
Keep the units and source trail.
Suggested citation: The Last Transmission. “Scale Lab: Send a Signal. Wait for the Reply.” DarkScienceDocs.com. Teaching method 1.0, resource release 268; materials updated . https://darksciencedocs.com/exploration-guides/signal-travel-time/. Add your access date.
Definitions: BIPM, SI metre and exact c; Observatoire de Paris, IAU astronomical-unit definition; NIST, international mile conversion; JPL, Julian-year convention.
Rounded inputs and communications context: NASA, Moon Facts; NASA Roman observatory design paper; JPL orbital elements, Table 1; NASA’s 4.24-light-year Proxima reference; NASA, Telecom. JPL lists Mars’s J2000 semi-major axis as 1.52371034 AU; the lab rounds it to 1.524 and chooses Earth’s circle as 1 AU. It does not evaluate JPL’s ephemeris formulas.
Sources checked October 25, 2026. Original activity, timing diagram, generated cases and verifier by The Last Transmission. Not a NASA, JPL, BIPM, IAU or NIST product or endorsement. This package has not undergone independent scientific review. Corrections: select Scientific correction and include setting, result and evidence.