Comets orbit the Sun in highly elliptical orbits, and are mainly composed of frozen water and CO2. Short-period comets originate in the Kuiper belt, roughly we will investigate some of the impacts of comets on the early Earth. ~ 40 au distant. Here a Calculate the kinetic energy of a spherical comet of radius 4 km, composed of water ice, which travels from the Kuiper belt to the region of the Earth's orbit around the Sun. Assume that the density of water ice p = 0.92 g/cm°

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Comets orbit the Sun in highly elliptical orbits, and are mainly composed of frozen water
and CO2. Short-period comets originate in the Kuiper belt, roughly
we will investigate some of the impacts of comets on the early Earth.
~ 40 au distant. Here
a Calculate the kinetic energy of a spherical comet of radius 4 km, composed of
water ice, which travels from the Kuiper belt to the region of the Earth's orbit around
the Sun. Assume that the density of water ice p = 0.92 g/cm°
b Estimate the radius of the cylindrically shaped crater that such a comet creates when it
strikes the Moon. Assume that the crater, of depth 10 km, is formed by heating to 3,500 K,
and thus vaporizing, a cylindrical volume of moon rocks. Moon rocks are made of silicates,
which have molecular weights of ~ 30 (i.e., m ~
cm°. Ignore the latent heat required to melt and vapourize the rocks, and the energy involved
in vapourizing the comet itself.
30 mH), and mean solid densities p ~ 2 g/
c The number of craters per unit area in the relatively smooth 'mare' regions of the Moon, which
trace the impact history over the past - 3 Gyr, indicate a total of about 10 impacts, leaving 50
km radius craters, during this period. Based on the assumptions in b), these would be impacts
of objects with radii > 4 km. From geometrical considerations alone (i.e., the relative target
sizes posed by the Earth and by the Moon, and ignoring gravity), estimate how many such
objects have struck the Earth.
d What is the mean time interval between impacts? How does the impact you
found compare to ~ 60 Myr, the typical interval between large extinctions of species
on Earth? (The most recent large extinction, 65 Myr ago, eliminated the dinosaurs,
and marked the rise of the mammals.) Explain why you might find a different value.
Transcribed Image Text:Comets orbit the Sun in highly elliptical orbits, and are mainly composed of frozen water and CO2. Short-period comets originate in the Kuiper belt, roughly we will investigate some of the impacts of comets on the early Earth. ~ 40 au distant. Here a Calculate the kinetic energy of a spherical comet of radius 4 km, composed of water ice, which travels from the Kuiper belt to the region of the Earth's orbit around the Sun. Assume that the density of water ice p = 0.92 g/cm° b Estimate the radius of the cylindrically shaped crater that such a comet creates when it strikes the Moon. Assume that the crater, of depth 10 km, is formed by heating to 3,500 K, and thus vaporizing, a cylindrical volume of moon rocks. Moon rocks are made of silicates, which have molecular weights of ~ 30 (i.e., m ~ cm°. Ignore the latent heat required to melt and vapourize the rocks, and the energy involved in vapourizing the comet itself. 30 mH), and mean solid densities p ~ 2 g/ c The number of craters per unit area in the relatively smooth 'mare' regions of the Moon, which trace the impact history over the past - 3 Gyr, indicate a total of about 10 impacts, leaving 50 km radius craters, during this period. Based on the assumptions in b), these would be impacts of objects with radii > 4 km. From geometrical considerations alone (i.e., the relative target sizes posed by the Earth and by the Moon, and ignoring gravity), estimate how many such objects have struck the Earth. d What is the mean time interval between impacts? How does the impact you found compare to ~ 60 Myr, the typical interval between large extinctions of species on Earth? (The most recent large extinction, 65 Myr ago, eliminated the dinosaurs, and marked the rise of the mammals.) Explain why you might find a different value.
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