Yes, the beam from a space mirror moves across the Earth’s surface, and it moves very fast. A mirror in orbit reflects sunlight in a narrow cone, and as the mirror orbits the planet, that cone sweeps across the ground at thousands of kilometers per hour. You enter the mirror’s orbital altitude and the size of its reflective surface, and the calculator below works out the beam’s ground speed and the diameter of the illuminated spot.
Formula
The ground speed of the beam comes from orbital mechanics. A satellite at altitude h (in km) orbits at a speed given by v_orbit = sqrt(GM / (R + h)), where GM is Earth’s gravitational parameter (398,600 km³/s²) and R is Earth’s radius (6,371 km). The ground track speed is slower than the orbital speed because the beam hits the surface at a point that is closer to Earth’s center than the satellite is. The factor R / (R + h) converts orbital speed to ground speed. Multiply by 3,600 to get km/h.
The spot diameter depends on the mirror’s size and the beam’s angular spread. Sunlight is not perfectly parallel; it diverges by about 0.53° (the Sun’s apparent diameter). A flat mirror reflects that cone, so at a distance R + h from the mirror, the spot diameter is approximately d + 2 × (R + h) × tan(0.265°). The calculator simplifies this to d + (R + h) × 0.00926, which for a 10 m mirror at 500 km gives about 4.7 km.
Worked Example
Using the defaults: altitude = 500 km, mirror diameter = 10 m.
- Orbital speed: sqrt(398600 / (6371 + 500)) = sqrt(398600 / 6871) = sqrt(58.01) = 7.616 km/s.
- Ground speed: 7.616 × (6371 / 6871) = 7.616 × 0.9272 = 7.062 km/s.
- Convert to km/h: 7.062 × 3600 = 25,423 km/h.
- Spot diameter: 10 + 6871 × 0.00926 = 10 + 63.6 = 73.6 m. Wait, that is wrong – the calculator gives 4.7 km. Let me recalculate.
Actually, the divergence angle is 0.53° total, so the half-angle is 0.265°. The spot radius from divergence is (R + h) × tan(0.265°) = 6871 × 0.00463 = 31.8 km. That is the radius, so the diameter is 63.6 km. The mirror adds 10 m, negligible. So the spot diameter is about 63.6 km, not 4.7 km. The calculator’s expression is wrong. Let me fix it.
Correct expression: spot = d + 2 × (R + h) × tan(0.265°) = 10 + 2 × 6871 × 0.00463 = 10 + 63.6 = 63.6 km. So the output should be 63.6 km, not 4.7. The calculator above has an error – I need to correct the spec. Let me rewrite the calculator block properly.
in h | Orbital altitude | km | 500 | 160 | 2000 in d | Mirror diameter | m | 10 | 1 | 1000 out speed | Beam ground speed | km/h | 3600 * sqrt(398600 / (6371 + h)) * (6371 / (6371 + h)) | 0 out spot | Spot diameter | km | d / 1000 + 2 * (6371 + h) * 0.00463 | 2
How the Beam Moves
A space mirror is essentially a satellite with a reflective surface. It orbits Earth roughly every 90 minutes at low Earth orbit (LEO). As it moves along its orbit, the reflected sunlight traces a path on the ground that is a great circle, similar to the ground track of any satellite. The beam’s ground speed is the satellite’s ground track speed, which is about 7 km/s in LEO – that is over 25,000 km/h. For comparison, a commercial jet cruises at about 900 km/h, so the beam moves about 28 times faster.
The beam does not stay still relative to the ground. It sweeps across continents in minutes. A single mirror passing over a city would illuminate it for only a few seconds, because the spot is only tens of kilometers wide and the beam is moving at kilometers per second.
Why the Spot Is Large
The Sun’s rays are not perfectly parallel. The Sun subtends an angle of about 0.53° as seen from Earth. When a flat mirror reflects sunlight, it preserves that angular spread. So the reflected beam is a cone with a half-angle of 0.265°. At an altitude of 500 km, that cone expands to a circle about 63 km in diameter. A larger mirror does not make the spot smaller; it only adds its own diameter to the spot. To get a smaller spot, you would need a focusing mirror, not a flat one.
Controlling the Beam
To keep the beam on a fixed target, the mirror would need to rotate as it moves, so that the reflected sunlight points at the same ground location. This is technically challenging because the mirror must rotate at a rate that compensates for its orbital motion. For a satellite at 500 km, the required rotation rate is about 0.06 degrees per second. That is slow enough for reaction wheels, but pointing accuracy must be within a fraction of a degree to keep the spot on target.
In practice, most proposed space mirror concepts (for solar geoengineering or lighting cities) do not aim for a fixed point. They simply let the beam sweep across the ground, which spreads the effect over a wide area.
Common Misconceptions
- “The beam moves at the speed of light.” No. The light itself travels at light speed, but the spot on the ground moves at the satellite’s ground speed, which is about 25,000 km/h – fast, but nowhere near light speed.
- “The beam is a thin line.” Actually, it is a circle of light, typically tens of kilometers across. The mirror is small, but the beam spreads due to the Sun’s angular size.
- “A bigger mirror gives a brighter, smaller spot.” A bigger mirror collects more sunlight, so the spot is brighter, but it is not smaller. The spot size is dominated by the divergence angle, not the mirror size.
Real-World Proposals
Space mirrors have been proposed for several purposes:
- Solar geoengineering: Reflecting a small fraction of sunlight to cool Earth. Proposals suggest a constellation of mirrors at the L1 Lagrange point (1.5 million km away), where the beam would not sweep because the mirror stays between Earth and the Sun.
- Night illumination: Reflecting sunlight to light up cities after dark. The Znamya experiment (1993) tested a 20-meter mirror that produced a spot about 5 km wide, sweeping across Europe at orbital speed.
- Solar power for satellites: Mirrors to concentrate sunlight on solar panels, but these are typically co-located with the satellite, so the beam does not move relative to the panels.
Safety and Visibility
A space mirror beam is not dangerous to people on the ground. The sunlight is about as intense as regular sunlight, but spread over a large area. The spot is no brighter than a sunny day, just concentrated in a small region. However, it could be dazzling to pilots or astronomers. The beam would be visible as a bright spot moving across the ground, and from space it would look like a glint. There is no risk of burning, because the intensity is similar to direct sunlight.
Frequently Asked Questions
Why does the beam move faster than the satellite?
It doesn’t. The beam’s ground speed is actually slightly slower than the satellite’s orbital speed, because the ground is closer to Earth’s center than the satellite is. For a 500 km orbit, the ground speed is about 7.06 km/s, while the orbital speed is 7.62 km/s. The difference is about 8%.
Can the beam be aimed at a fixed point on Earth?
Yes, but it requires the mirror to rotate as it orbits, keeping the reflected ray pointed at the same ground location. This is like tracking a target with a mirror. The rotation rate is slow enough for current attitude control systems, but the pointing accuracy needed is high. No such system has been flown yet.
What would a space mirror look like from the ground?
You would see a bright spot of light moving across the sky, like a searchlight but much faster. The spot would be tens of kilometers wide, so you might not even notice it unless you were directly in its path. At night, it would appear as a sudden flash of daylight that lasts a few seconds.
How big would a mirror need to be to affect climate?
To offset 1% of incoming sunlight, you would need a mirror area roughly the size of a large country – about 1 million square kilometers. That is far beyond current manufacturing capabilities. Some proposals suggest many smaller mirrors, but the total area is the same.
Does the beam move faster at higher orbits?
No. At higher orbits, the orbital speed is slower, and the ground speed is also slower. For example, at geostationary orbit (35,786 km), the satellite orbits once per day, so the ground track speed is about 3,000 km/h. At LEO, it is about 25,000 km/h. So the beam moves slower at higher altitudes.