The practice portal carries the arithmetic, algebra, logarithms and calculus this article uses, with worked solutions that explain the reasoning rather than just the answer.
Open the practice portal →The pause before an answer comes back from Mars is at least nine minutes, and it can be forty two. Working that out takes one division, and the result is the reason a Mars rover has to think for itself while a Moon rover does not.
Every child who has waited for a video call to catch up knows what a delay feels like. Space has the same problem, except that nothing can be done about it, because the delay is not caused by a slow connection. It is caused by the speed of light, which is the fastest anything can go, and it is fixed at 299,792,458 metres every second by definition.
This article works out how long the pause is when you talk to the Moon, to Mars and to Voyager 1, using nothing but division. The answers decide something real: whether a machine can be driven from Earth, or whether it has to be able to think for itself.
The Moon is on average 384,400 kilometres away. Light covers 299,792.458 kilometres every second. To find how long the trip takes, divide the distance by the speed:
384,400 ÷ 299,792.458 = 1.282 seconds
That is the one way trip. A conversation needs the message to go there and the answer to come back, so double it: 2.564 seconds.
Two and a half seconds is a pause you would notice, but it is not a pause that stops you working. It is about as long as it takes to say a short sentence out loud. If a rover on the Moon started rolling towards a hole, a driver on Earth could see it and stop it, because the news of the hole and the instruction to stop together take less than three seconds.
Mars is harder, and it is harder in a way that changes. Both planets go round the Sun at different speeds, so the distance between them is never the same twice. At its closest Mars is about 78 million kilometres away, and at its furthest, when it is on the far side of the Sun, it is about 378 million.
Do the same division twice.
78,000,000 ÷ 299,792.458 = 260 seconds = 4.3 minutes
378,000,000 ÷ 299,792.458 = 1,261 seconds = 21 minutes
Doubling both gives a round trip of between 8.7 minutes and 42 minutes.
Now the consequence. A rover on Mars cannot be driven. Not because the engineering is difficult, but because by the time a picture of a hole has arrived on Earth and an instruction to stop has got back, at least nine minutes have gone by and the rover has been sitting in the hole for eight and a half of them. That single division is the reason Mars rovers are built to notice obstacles and decide for themselves, while Moon rovers do not have to be.
Voyager 1 is the furthest human object from Earth. NASA publishes its distance and updates it constantly. On 18 November 2026 it was 25,902,068,356 kilometres away, and NASA describes that distance as one light day.
That claim can be checked, and checking it is the best part of this exercise, because it is a claim by NASA that an eleven year old can test.
25,902,068,356 ÷ 299,792.458 = 86,400 seconds
And 86,400 seconds is 24 hours exactly, because 60 × 60 × 24 = 86,400. The distance NASA publishes is not a rounded figure that happens to be near a light day. It is defined so that it is a light day, to the last digit.
So a message to Voyager 1 takes a day to arrive, and the reply takes another day. Anyone who sends a command has to wait two days to learn whether it worked.
This is one of the few pieces of real engineering that needs only a single division, which makes it unusually good for a child who is confident with numbers but has never used them for anything that matters.
Three things are worth drawing out. The first is that the answer changes the design. Nobody decided that Mars rovers should be clever. The arithmetic decided it, and the engineers followed. The second is that a very large number divided by a very large number can give a small, ordinary answer, which is a genuinely useful intuition to build early. The third is that a published figure can be checked. Children are used to being told facts. Being handed a NASA number and finding that it comes out to exactly 86,400 seconds is a different experience entirely.
A good extension question, for a child who has finished the three above: how far away would something have to be for the round trip to take a whole year? The method is identical, and the answer, about half a light year, is further than any spacecraft will travel in a lifetime.
Because both planets are moving. Earth takes a year to go round the Sun and Mars takes about 687 days, so sometimes they are on the same side of the Sun and sometimes on opposite sides. The distance between them swings from about 78 million kilometres to about 378 million, and the delay swings with it, from 8.7 minutes to 42 minutes for a round trip.
No. Radio waves are light, and light travels at one fixed speed through empty space. A bigger antenna makes a faint signal easier to hear, which matters enormously for a distant spacecraft, but it cannot make the signal arrive sooner. The delay is set by distance alone.
They are given a destination rather than a set of steering instructions. The rover takes its own pictures, works out where the rocks are and picks its own path, checking in when it has finished or when it is unsure. Engineers plan a day of work, send it, and see the results the following day.
Defined. Since 1983 the metre has been defined as the distance light travels in one 299,792,458th of a second, so the speed of light is exactly 299,792,458 metres per second by construction. It is one of the few numbers in science with no measurement uncertainty at all.
The practice portal carries the arithmetic, algebra, logarithms and calculus this article uses, with worked solutions that explain the reasoning rather than just the answer.
Open the practice portal →