Problem Set
Sizing Up Pluto
This activity is related to a Teachable Moment from July 16, 2015. See "NASA's New Horizons Mission Flies by Pluto."
Overview
Using measurements taken by the New Horizons spacecraft as it flew by Pluto in July 2015, students have an opportunity to see how new data can change scientific understanding and practice their math skills in a real-world application.Materials
Background
On July 14, 2015 at 4:49 a.m. PDT, NASA's New Horizons spacecraft sped past Pluto – a destination that took nearly nine and a half years to reach – and collected scientific data along with images of the dwarf planet.
This illustration shows Pluto's orbit (in yellow) inside the Kuiper Belt, a disc-shaped region beyond the orbit of Neptune that is home to hundreds of thousands of icy bodies and comets. Image credit: NASA
Pluto, famous for once being the ninth planet, was reclassified as a dwarf planet in 2006 after new information emerged about the outer reaches of our solar system. Worlds similar to Pluto were discovered in the region of our solar system known as the Kuiper Belt. The Kuiper Belt – named for astronomer Gerard Kuiper – is a doughnut-shaped area beyond the orbit of Neptune that is home to Pluto, other dwarf planets such as Eris, Makemake and Haumaea, as well as hundreds of thousands of other large, icy bodies, and perhaps trillions of comets orbiting our sun. In 2019, the New Horizons spacecraft is expected to visit one more Kuiper Belt object.
Through careful measurements of new images, scientists have determined that Pluto is actually larger than previously thought: 2,370 kilometers in diameter. This is important information for scientists as it helps them understand the composition of Pluto. Because of the orbital interactions between Pluto and its moon Charon, Pluto’s mass is well known and understood. Having a more precise diameter gives scientists the ability to more accurately calculate Pluto's average density. A greater diameter means Pluto’s density is less than we thought. If you do the math, you’ll see that Pluto’s calculated density dropped from 2,051 kg/m3 to 1,879 kg/m3 with this new finding. Most rock has a density between 2,000-3,000 kg/m3 and ice at very cold temperatures has a density of 927 kg/m3, so we can also conclude that Pluto is a bit more icy than previously believed. In addition to helping scientists calculate the density of Pluto, this measurement confirms that Pluto is the largest known object in the Kuiper Belt.
Procedures
- Hand out copies of the Student Worksheet and have students solve the following problems:
- Find the radius(r) of Pluto.
2,370 kilometers ÷ 2 = 1,185 km - Find the circumference of Pluto.
C = 2 π r = 7,446 km - Find the surface area of Pluto.
SA = 4 π r2 = 17,646,012 km2 - Find the volume of Pluto.
4/3 π r3 = 6,970,174,651 km3 - Find the density of Pluto in kg/m3.
Pluto mass = 1.31 × 1022 kg
Convert volume in km3 to m3: 6,970,174,651 × 1,000,000,000 = 6.970174651 × 1018 m3
1.31 × 1022 kg / 6.970174651 × 1018 m3 = 1,879 kg/m3 - How does this new density calculation compare to the previous calculation when Pluto’s diameter was thought to be 2,302 km?
Pluto's density is 172 kg/m3 less than previously thought. - Most rock has a density between 2,000-3,000 kg/m3 and ice at very cold temperatures has a density of 927 kg/m3. What can we conclude about Pluto’s composition based on the new density measurement?
The new density measurement tells us that Pluto is more icy than previously believed.
Assessment
- Check student work against the Teacher Guide.
Extensions
- Video: What is a Dwarf Planet? (K-12)
- Activity: Solar System Bead Activity (4-8)
- Activity: How Far? How Faint? (9-12)
- Resource: Pluto Facts and Figures
- Interactive: Eyes on Pluto – Ride along with New Horizons in this simulation of its closest approach to Pluto!
- News and Images: NASA New Horizons Website