How Much Does a Shadow Weigh?
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Radiation pressure lets light create an effective force on matter, so illuminated areas can be treated as having a tiny momentum-driven “weight” increase.
Briefing
A shadow can’t be weighed directly, but the physics behind it can: wherever light hits matter, it transfers momentum, creating a tiny force that adds up over large areas. On Earth, sunlight exerts about one-billionth of a pound of force per square inch, which seems negligible at small scales. Over a city-sized surface, though, that momentum transfer becomes measurable—Chicago would effectively “weigh” about 300 pounds more on a sunny day because the incoming light is pushing on the ground and buildings.
In space, the effect grows because sunlight is no longer filtered or deflected by Earth’s atmosphere and magnetic environment. A spacecraft traveling from Earth to Mars can be nudged off course by light by roughly 1,000 km, a real navigation concern that mission planners must account for. Engineers have even turned this pressure into propulsion using giant reflective solar sails, which are pushed by sunlight.
That momentum-transfer idea also reframes what a shadow means. An area covered in shadow receives less incoming light, so it experiences less of the light’s push than the surrounding illuminated regions. In that technical sense, a shadowed patch corresponds to “less push” and therefore “weighs less” than its sunlit neighbors—an accounting trick grounded in radiation pressure rather than the shadow itself being a physical object.
The discussion then pivots from everyday sunlight to astronomical shadows bright enough for humans to see. Three bodies can cast visible shadows on Earth: the Sun, the Moon, and—surprisingly—Venus. Pete Lawrence investigated Venus’s shadow using a “digital sky” approach and a tube fitted with a cutout shaped like Venus’s astronomical symbol. By aiming the tube at nearby sky regions and then at Venus itself, the setup produced a Venus-shaped shadow, demonstrating that Venus can cast a detectable silhouette under the right observational conditions.
From there, the focus shifts to how light interacts with matter and how “speed” works in physics. Light travels at c in vacuum, but in air it moves slightly slower (298,925,574 m/s). That distinction matters for phenomena like Cherenkov radiation: when charged particles move through a medium faster than light can travel in that medium (but still not faster than c), they generate a “photonic boom” analogous to a sonic boom. The key mechanism is interference—at lower speeds, emitted photon waves cancel out; at higher speeds, they constructively interfere, producing visible flashes.
Finally, the transcript tackles a common “faster-than-light” puzzle: pushing a button a lightyear away. Even if a rigid board is one lightyear long, the far end doesn’t respond instantly because pushing a rigid object transmits information through compression waves, which travel at the speed of sound in the material—not at the speed of light. The “speed of push” is therefore limited by mechanical wave propagation, not by c. The closing takeaway ties everything together: light can push, shadows mark where that push is reduced, and the relevant speeds depend on whether the situation involves photons or compression waves.
Cornell Notes
Light can’t be weighed, but it can push. Sunlight exerts a tiny force per unit area (about one-billionth of a pound per square inch), and over large surfaces that momentum transfer becomes significant—Chicago would gain roughly 300 pounds of effective “weight” in sunlight. In space, where Earth’s atmosphere and magnetic field don’t filter solar effects, light pressure can deflect spacecraft by about 1,000 km on a Earth-to-Mars trip, which is why solar sails exist. A shadow corresponds to reduced incoming light pressure, so shadowed areas “weigh less” than illuminated ones in a technical momentum sense. The transcript also connects these ideas to Cherenkov radiation and clarifies that pushing information through a rigid object travels via compression waves at the speed of sound, not at the speed of light.
How can a shadow be linked to “weight” if shadows aren’t physical objects?
Why does sunlight’s force become noticeable at city scale?
What makes light pressure matter for space travel?
How can Venus cast a visible shadow on Earth?
What is a “photonic boom,” and how does it relate to Cherenkov radiation?
Why doesn’t pushing a lightyear-long board transmit information instantly?
Review Questions
- What physical quantity links sunlight to an effective “weight” difference between illuminated and shadowed regions?
- Under what condition does Cherenkov radiation occur, and why does interference change with particle speed?
- In the “lightyear-long board” thought experiment, what sets the speed of the response at the far end?
Key Points
- 1
Radiation pressure lets light create an effective force on matter, so illuminated areas can be treated as having a tiny momentum-driven “weight” increase.
- 2
Sunlight’s force is minuscule per square inch (about one-billionth of a pound) but becomes significant when multiplied across large areas like cities.
- 3
In space, unfiltered sunlight can deflect spacecraft by large distances (about 1,000 km on an Earth-to-Mars trajectory), so navigation must account for light pressure.
- 4
A shadow corresponds to reduced incoming light pressure, meaning shadowed regions experience less push than surrounding illuminated areas in a technical sense.
- 5
Venus can cast a visible silhouette on Earth under suitable observational methods, alongside the Sun and Moon.
- 6
Cherenkov radiation occurs when charged particles move faster than light’s speed in a medium, producing constructive interference of emitted photon waves.
- 7
The “speed of push” in a rigid object is limited by compression-wave propagation (speed of sound in the material), not by the speed of light.