Collecting Light: Inverse Square Law Demo
In this activity, students learn how light and energy are spread throughout space. The rate of change can be expressed mathematically, demonstrating why spacecraft like NASA’s Juno need so many solar panels.
- Students may want to work in groups of two in order to be able to handle the unsealed balloon while another student is measuring.
- Remind students not to tie off the balloon, as they will need to be able to continue to add and remove air throughout the activity.
- The square marked on the balloon will stretch at different rates depending on where it is drawn on the balloon. Ask students to share with the class where they drew the square and identify commonalities between square locations. It may help to standardize where the square is drawn after some student trial and error.
In order to travel millions of miles to other planets and orbit or rove around once they arrive, spacecraft need a source of power. For some spacecraft, this power comes from the Sun. Expansive solar arrays – wing- or arm-like structures attached to the spacecraft – convert light from the Sun into power.
Different spacecraft have different power needs, so some solar-powered spacecraft will have different size solar panels than others. The farther a spacecraft is traveling from the Sun, the larger its solar arrays need to be to meet its specific power needs. That’s because the farther you get from the Sun, the less light there is to be collected as solar energy. Most spacecraft traveling to very distant planets cannot rely on solar power because the size of the solar arrays needed would make them too heavy or large to even launch.
Advances in solar panel efficiency along with improvements in the way spacecraft and their instruments use power have recently made solar power a viable option for spacecraft heading as far as Jupiter – though going beyond will require further technological advances.
One such solar-powered mission is NASA’s Psyche spacecraft, which will visit an asteroid known as 16 Psyche. Located in the asteroid belt between Mars and Jupiter, the 16 Psyche asteroid orbits the Sun at a distance ranging from 378 million to 497 million kilometers (235 million to 309 million miles). That’s 2.5 to 3.3 times the distance between Earth and the Sun. To generate enough power at that distance, the Psyche spacecraft's solar panels are designed to have an area of 75 square meters (800 square feet).
The Europa Clipper mission will become the second solar-powered spacecraft to orbit Jupiter when it arrives to study the giant planet’s ice-covered moon Europa. To meet its power needs the spacecraft is equipped with solar arrays covering an area of over 90 square meters (960 square feet).
To find out how much solar power is required for these space journeys, scientists and engineers use the inverse square law.
Visible light, just like all frequencies of the electromagnetic spectrum, follows the inverse square law, which can be represented as one over the square of the distance from the light source, or 1/r2. Jupiter is 5 times farther away from the Sun than Earth, so using the inverse square law, 1/(5)2, we know that Jupiter has only 1/25 as much available light as Earth.
- Have students or student teams inflate a round balloon until it has a diameter of about 10 cm. Do not tie off the balloon. (You can use the binder clip to hold it closed.) Tell students to imagine the Sun is always in the center of their balloon.
- Using a marker, have students draw a 1-by-1 cm square on the balloon. Draw this square near the bottom of the balloon to really see the effect. This square represents light energy spreading out the farther away it is from the Sun (the middle of the balloon). As the balloon gets larger, the distance from the Sun increases.
- Inflate the balloon until it has a diameter of about 20 cm. The distance to the center of the balloon has now doubled. How has the area of the original square changed in size?
- Measure and record the size of the square on the balloon now.
- Inflate the balloon until it has a diameter of around 30 cm. Be careful not to pop it! The distance to the center of the balloon has now tripled.
- Measure and record the size of the square on the balloon once more.
- Record your observations and compare the radius of your balloon to the area of the square.
- Do your findings fit the inverse square law? If not, why?
- Why is the inverse square law important for scientists and engineers to understand when designing and operating missions far from the Sun?
- Which other forms of energy might follow the inverse square law? If visible light follows this relationship, what about other forms of electromagnetic radiation?
- How does the amount of available sunlight at Jupiter compare with the amount available at Saturn, which is about twice as far from the Sun as Jupiter?
- How does the amount of available sunlight at Jupiter compare with the amount available at asteroid 16 Psyche at its closest point to the Sun, which is about half as far as Jupiter?