This activity is related to a Teachable Moment from Jan. 13, 2016. See "Cruising to Jupiter: A Powerful Math Lesson."
- Download the Student Worksheet from the materials list and make copies of both problems in the set or individual problems to hand out to students.
- This activity takes place in a darkened room, which can pose slip, trip and fall hazards. Keep walking paths clear and minimize unnecessary student movement in the darkened room.
- LED flashlights or light from a mobile device is recommended. If using a non-LED flashlight with the reflector housing removed, take safety measures to avoid accidental burns from a hot bulb.
NASA’s Juno mission, the first solar-powered mission to Jupiter, has become the farthest solar-powered spacecraft ever! Juno, and its eight science instruments designed to study the interior of Jupiter, has passed the mark previously held by the European Space Agency’s Rosetta mission and reached a distance of 5.3 astronomical units from the sun (an astronomical unit is equal to the average distance between Earth and the sun – about 149.6 million kilometers). Using only power from the sun, Juno will complete the five-year trip to Jupiter in July 2016 and begin studying the solar system’s most massive world in an attempt to better understand the origins of the planet, and in turn, our solar system.
What Made It Possible?
Just as a bright source of light dims as you move away from it, sunlight becomes less intense the farther a spacecraft travels from the sun, limiting the amount of power that can be generated using solar cells. Previous missions that visited Jupiter, like Galileo, Voyager 1 and Voyager 2, couldn’t use solar power and instead used radioisotope thermoelectric generators (RTGs) to supply power.
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.
Engineers designed Juno with three massive solar panels, each nearly 30 feet long. Combined, they provide Juno with 49.7 m2 of active solar cells. Once it reaches Jupiter, Juno will generate more than 400 watts of power, which may not sound like a lot, but it’s an impressive feat at so great a distance. For comparison, Juno’s solar panels can generate about 14 kilowatts near Earth.
Calculating Energy for Juno
Understanding how much sunlight the Juno spacecraft is receiving, and by extension how much energy the solar panels can generate at any point on its journey to Jupiter is as simple as understanding division and exponents. We use these math concepts to describe a relationship between Earth, the sun and the spacecraft in a law known as the inverse square law. We express this law as: 1/d2, where d equals the distance between the spacecraft and the sun as compared to Earth’s distance from the sun.
Let’s start at home. Earth’s orbit is not a perfect circle, but an ellipse that brings Earth as close as 147,090,000 km from the sun, and as far as 152,100,000 km from the sun. To make the math a little easier, astronomers define the average distance between Earth and the sun as one astronomical unit (AU). For our problem, astronomical units will be our measure of distance.
Knowing that Juno became the farthest solar powered spacecraft when it was 5.3 AU from the sun allows us to use the inverse square law to calculate how much sunlight is received at that distance. Substituting 5.3 AU for d gives us 1/5.32, or 0.036 – this tells us that at this distance, only 3.6 percent of the solar energy received at Earth is reaching Juno.
But just how much energy is that? In order to answer that question, we need to know how much energy is coming from the sun. The total solar irradiance (TSI) is a measure of the average amount of solar energy that reaches the top of Earth’s atmosphere. It was recorded by the SORCE satellite to be 1360.8 w/m2. So at 1 AU, Juno’s solar panels would receive 1360.8 w/m2. Taking 3.6 percent gives us 48.99 w/m2. With 49.7 m2 of active cells, there is a great deal of energy falling on the solar panels. Of course, even with improved technology, solar panels are not 100 percent efficient, which is why the spacecraft doesn’t convert all the energy it receives into usable power.
Testing the Inverse Square Law in the Classroom
Students can put the inverse square law to the test using a mobile device with a simple light meter app that measures lux or any lux measurement tool and a source of light. If you’re using an app or lux measurement tool for the first time, it would be a good idea to try this out first to see how accurate the sensor is before having students attempt the activity.
- Start with a dark classroom. The darker the better, as any stray light will affect the lux reading and change your results.
Safety reminder! Dark rooms can pose a slip, trip and fall hazard. Keep walking paths clear and minimize unnecessary student movement in the darkened room.
- Stand the device upright as close to vertical as you can with the light sensor (typically on the front) facing the light source. You may need to brace it with books to keep it perpendicular to the surface.
- Place the light source one foot away and record the lux reading. Readings will vary depending on how bright the light source is that you are using. If you have a second mobile device with an LED light, that can be used as a light source pointing toward the first device with the lux meter app.
Safety reminder! LEDs from mobile devices provide an even output of very low temperature light compared to flashlights with incandescent bulbs and reflectors. If you use a flashlight and have removed the reflector housing to create an even light source, the exposed bulb can become very hot. Take safety measures to avoid accidental burns from a hot bulb. LED flashlights are much cooler and minimize the risk of burns.
- Based on the one-foot reading, have students predict what the light reading will be at two, three, four and five feet away by substituting the distance in 1/d2 and solving for that fraction of the measurement at one foot.
- Move the light source an additional foot away. Because the distance is doubled from our first measurement, the inverse square law shows that the lux measurement should be 1/4 that of the first measurement. Have students check to see if the measurement matches their prediction. Because there may be stray light reaching the light sensor, the measurement may not be exactly 1/4 of the first measurement. Again, the darker the room, the better.
- Continue recording light measurements at the three, four and five foot marks, comparing measurements to predictions.
In addition to checking for accuracy on the student worksheet, assess students' ability to apply what they have learned to other locations in the solar system by asking them to calculate the percent of energy received at the following locations:
- Saturn: 9.54 AU
- Uranus: 19.18 AU
- Neptune: 30.06 AU
- Pluto (min.): 29.69 AU
- Pluto (avg.): 39.44 AU
- Pluto (max.): 49.19 AU
Pluto's highly eccentric orbit causes the dwarf planet to cross the orbital path of Neptune and be closer to the sun than Neptune at certain points in its orbit.
- Juno mission website - News, resources and updates on NASA's mission to Jupiter.
- Eyes on the Solar System - Take a virtual journey to Jupiter with Juno (scroll to "Solar System Tours" and click on Juno).
- To Jupiter with JunoCam! - Find out how classrooms can participate in the Juno mission to Jupiter using the spacecraft's on-board educational camera.
- Infographic: Solar Power Explorers - This graphic shows how NASA’s Juno mission to Jupiter became the most distant solar-powered explorer and influenced the future of space exploration powered by the sun.