Imagine a table: Earth is about 150 million kilometres from the Sun, Mars about 228 million. Subtract them and you get roughly 78 million kilometres. That seems to give the distance to Mars. But both planets move, and the table said nothing about which side of the Sun they occupy.
Two planets have no single fixed separation: their distance depends on their positions in their orbits. For Earth and Mars, it is tens or hundreds of millions of kilometres. In a simplified model with circular orbits of radii 1 and 1.52 astronomical units, the separation varies from approximately 78 to 377 million kilometres. This is the range of a teaching model, not the precise limits of real encounters. Let’s see where those numbers come from. JPL: orbital sizes and shapes.
The astronomical unit: a convenient ruler
Numbers with many zeros are hard to compare. Within the Solar System, astronomers therefore often use the astronomical unit, internationally written au. One au is exactly 149,597,870,700 metres, or about 149.6 million kilometres. That is close to the characteristic Earth–Sun distance, but it does not mean Earth always lies at precisely that distance. The unit’s definition is fixed; the planet’s position changes. JPL: definition of the au.
Instead of “Jupiter is about 778 million kilometres from the Sun,” we can say “its orbit has a characteristic size of about 5.2 au.” It is then easier to see that Jupiter orbits roughly five times farther from the Sun than Earth. This compares distances, not the sizes of the planets themselves.
Real orbits are not perfect circles. They are described by ellipses, and the semi-major axis, half the ellipse’s longest axis, sets an orbit’s characteristic size. Tables often call this the “average distance from the Sun.” It is neither the current distance nor exactly the time-averaged distance. The table below uses rounded semi-major axes; the teaching diagram replaces the ellipses with circles of those radii.
Walking through a scale Solar System
Imagine a scale of 1 au = 10 metres. Earth would be about 10 metres from the Sun marker, Mars 15.2 metres, and Jupiter 52 metres. Reaching Neptune would take you roughly 301 metres away. All four rocky planets fit into the first 15.2 metres; most of the model extends beyond them.
If 1 au were 10 metres
| Planet | Orbit size, au | From the Sun in the model, m |
|---|---|---|
| Mercury | 0.39 | 3.9 |
| Venus | 0.72 | 7.2 |
| Earth | 1 | 10 |
| Mars | 1.52 | 15.2 |
| Jupiter | 5.2 | 52 |
| Saturn | 9.54 | 95.4 |
| Uranus | 19.19 | 191.9 |
| Neptune | 30.07 | 300.7 |
The table lays out orbital sizes along one ruler. It does not claim that all the planets currently stand in a line. Subtracting two marks gives the gap between the corresponding circular orbits along one direction. Finding the distance between the planets themselves also requires their positions.
There is a reason book illustrations show large planets almost touching. At our scale, Earth’s diameter would be about 0.85 millimetres. At a distance of 10 metres, such a speck would be hard to see, while Neptune must be hundreds of metres away. Diagrams therefore often enlarge bodies or compress distances; check which scale they preserve. JPL: building a scale model, planetary diameters.
The same Mars, a different distance
Put the Sun at the centre, Earth on a circle of radius 1 au, and Mars on a circle of radius 1.52 au. While they lie on the same side of the Sun along the same ray, their separation is the difference in radii: 1.52 − 1 = 0.52 au, or about 78 million kilometres.
If Mars moves to the other side of the Sun, the separation is the sum of the radii: 1.52 + 1 = 2.52 au, about 377 million kilometres. At an intermediate position, the connecting segment runs diagonally. Even though each planet’s distance from the Sun is fixed in this model, their mutual separation changes.
Predict the result: what happens to the distance as the angle at the Sun changes from 0° to 180°? Then try another pair, such as Jupiter and Saturn. The walking scale changes only how many metres we would walk in the model.
Two planets: change their configuration
Predict: will the Earth–Mars distance stay fixed if you turn the direction to Mars? Choose a pair, change the angle or select a reference configuration. A and B identify the selected planets.
Without the interaction, Earth and Mars are shown at 0°. The reference values below are always available.
Radii of the teaching circles: A · Earth = 1 au; B · Mars = 1.52 au.
- Between the planets
- 0.52 au77.8 million km
- Geometric light travel time
- 4.3 min
- At the selected scale
- 5.2 m
| Angle | Distance, au |
|---|---|
| 0° | 0.52 |
| 90° | 1.82 |
| 180° | 2.52 |
The angle is measured at the Sun between the directions to the two planets. It is not the angle between them in our night sky. The diagram is not tied to today’s date either: you choose a geometric configuration rather than scrolling through a calendar.
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Calculating the distance for any angle
The Sun and two planets form a triangle. Let r_(1) and r_(2) be the teaching circles’ radii, θ the angle between them, and d the required separation. The cosine rule gives:
(d)^(2) = (r_(1))^(2) + (r_(2))^(2) − 2r_(1)r_(2)cosθ.
If the radii are in au, d is in au too. At 0°, the cosine is 1, giving the absolute difference in radii; at 180°, the cosine is −1, giving their sum.
At 90°, the cosine is zero. For Earth and Mars:
d = √((1)^(2) + (1.52)^(2)) ≈ 1.82 au.
That is approximately 272 million kilometres. The angle changed; the radii did not. The whole triangle determines the distance, so subtracting table entries is not enough.
Why a real encounter can be closer
Our circular model does not reproduce orbital eccentricity, inclination or changes caused by other bodies’ gravity. Mars moves closer to and farther from the Sun; Earth does not keep a fixed radius either. Real distances are therefore not bounded by the numbers we obtained for two fixed circles.
There is a clear check. On 27 August 2003, during a Hubble exposure near a close encounter, Earth and Mars were about 55.8 million kilometres apart. That is less than the 78 million in our diagram. The observation does not disprove triangle geometry: it shows that radii of 1 and 1.52 au do not describe every real position. NASA: distance during Hubble’s 2003 exposure.
When asking “which planet is closest?”, specify today, at its closest approach, or averaged over a particular interval. These are different questions. A distance on a specific date requires calculated positions, called ephemerides. Precise models account for more than orbital radii; the teaching diagram cannot replace them. JPL: finding positions and Horizons.
Light takes minutes; a spacecraft takes much longer
Another way to grasp a distance is to ask how long light takes to cross it. In a vacuum, light travels at roughly 300,000 kilometres per second. For 1 au, that is about 8 minutes 19 seconds. Even such a fast signal does not make the Solar System close at hand. BIPM: the speed of light.
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From kilometres to minutes of delay
Estimate the time t for a given length d as t = d/c, where c is the speed of light. With d in kilometres and c ≈ 300 000 km/s, time comes out in seconds. For roughly 78 million kilometres:
t ≈ (78 000 000)/(300 000) = 260 s.
That is about 4 minutes 20 seconds one way. A reply sent immediately upon receipt would take roughly as long again to return; signal processing adds its own delay.
For 377 million kilometres, the same estimate gives about 21 minutes one way. This is a geometric time for a given length: it neglects motion during propagation and does not guarantee a direct radio link when the Sun is between the planets. These numbers are not a full communication model for a particular mission.
A spacecraft’s travel time is not found this way. It moves much more slowly than light, follows a trajectory under gravity, and must meet a planet that moves during the journey. Launch planning therefore considers relative positions, energy needs and arrival conditions, rather than simply picking the day of minimum current separation. The straight orange line in our diagram is the distance between two points, not a mission route. JPL: geometry of a Mars launch window.
Check your understanding: a table gives Earth as 1 au and Mars as 1.52 au. Can you say they are always 0.52 au apart?
No. That is the difference in the teaching circles’ radii, giving the separation only when the planets lie on the same ray from the Sun. On opposite sides, this model gives 2.52 au; on real elliptical orbits, distances from the Sun change too.
Planets are moving points in a vast system, not beads on a fixed string. The au helps us compare scale, geometry explains changes in separation, and a date plus a more precise model are needed for a particular measurement. Return to the map of the Solar System to connect these distances with its structure. Next in the course, we will travel beyond the planetary system.