Exploring the surface of a comet
On August 6, 2014 after a decadelong journey chasing its target, ESA’s
Rosetta has today become the first
spacecraft to rendezvous with a
comet, opening a new chapter in
Solar System exploration. Comet
67P/Churyumov–Gerasimenko and
Rosetta now lie 405 million kilometers
from Earth, about half way between
the orbits of Jupiter and Mars, rushing
towards the inner Solar System at
nearly 55,000 kilometers per hour.
This image shows the comet
close-up from a distance of
283 kilometers. The image has
a width of 5 kilometers.
Problem 1 – Approximate
the shape of the dumbbellshaped nucleus as two spheres.
What is the total volume of the
nucleus in cubic meters?
Problem 2 – If the average
density of the material is 300 kg/
m3, about what is the total mass
of the nucleus in metric tons?
Credit: ESA/Rosetta/MPS for OSIRIS Team
Answer Key
Problem 1 – Approximate the shape of the dumbbellshaped nucleus as two spheres. What is the total
volume of the nucleus in cubic meters?
Answer: The image shows one way to draw two spheres inside
the nucleus to represent the volume. From the scale of the
image the larger sphere has a radius of about 1200 meters
and the smaller sphere has a radius of about 840 meters.
From the volume of a sphere V = 4/3 π R3 ,we have
Large sphere = 1.3 x 3.1 x (1200)3
= 7.0 x 109 cubic meters
Small sphere = 1.3 x 3.1 x (840)3
= 2.4 x 109 cubic meters.
Problem 2 – If the average density of the
material is 300 kg/m3, about what is the total mass of the nucleus in metric tons?
Answer: The total volume is just 7.0 x 109 + 2.4 x 109 = 9.4 x 109 cubic meters.
From Mass = density x volume we then get
= 300 kg/m3 x 9.4x109 m3
= 2.8 x 1012 kg
Since 1 ton = 1000 kg, the mass is about 2.8 billion tons!
SpaceMath@NASA introduces students to the use of mathematics in today’s scientific discoveries. Through press
releases and other articles, it explores how many kinds of mathematics skills come together in exploring the universe.
Visit http://spacemath.gsfc.nasa.gov to discover hundreds of math problems you can solve on your own.
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