EBK FOUNDATIONS OF ASTRONOMY
EBK FOUNDATIONS OF ASTRONOMY
14th Edition
ISBN: 8220106820612
Author: Backman
Publisher: YUZU
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Chapter 18, Problem 12P
To determine

The number of impacts expected to strike a 100m2 region in one hour during Earth’s formation.

Expert Solution & Answer
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Answer to Problem 12P

The number of impacts expected to strike a 100m2 region in one hour during Earth’s formation is 133.

Explanation of Solution

Write the expression for the total particles needed.

    totalparticleneeded=MEmp        (I)

Here, ME is the mass of Earth and mp is the average mass of each particle.

Write the expression for the particles captured by Earth.

    ParticlescapturedbyEarth=Totalparticlesneededt        (II)

Here, t is the time required to capture the particles.

Write the expression for the surface area of the Earth.

    A=4πRE2        (III)

Here, RE is the radius of the Earth.

Write the expression for the fraction of the total surface area.

    fractionoftotalsurfacearea=SrSE        (IV)

Here, Sr is the surface area of the region and SE is the surface area of Earth.

Write the expression for the number of impacts in the given region.

    numberofimpactsin100m2/sec=[(fractionoftotalsurfacearea)×(particlescapturedbyEarth/sec)]        (V)

Conclusion:

Refer to Table A-10, “Properties of the planets” to obtain the value of ME as 5.97×1024kg.

Substitute 5.97×1024kg for ME and 100gm for mp in equation (I) to find the total particles needed.

    totalparticleneeded=5.97×1024kg100gm×(1kg1000gm)=5.97×1025

Substitute 5.97×1025 for total particles needed and 10 million years for t in equation (II) to find the particles captured by Earth.

    ParticlescapturedbyEarth=5.97×102510millionyears×(106year1millionyears)×(3.15×107sec1year)=5.97×10253.15×1014sec=1.9×1011particles/sec

Substitute 6.38×106m for RE in equation (III) to find the surface area of the Earth.

    A=4π(6.38×106m)2=4π×40.7044×1012m2=5.12×1014m2

Substitute 100m2 for Sr and 5.12×1014m2 for SE in equation (III) to find the fraction of the total surface area.

    fractionoftotalsurfacearea=100m25.12×1014m2=1.95×1013

Substitute 1.95×1013 for fraction of the total surface area and 1.9×1011particles/sec for particlescapturedbyEarth/sec in equation (V) to find numberofimpactsin100m2/sec.

    numberofimpactsin100m2/sec=[1.95×1013×1.9×1011particles/sec]=3.705×102particles/sec=3.705×102particlessecond×(1second13600hr)=133.38particles/hr133particles/hr

Therefore, the number of impacts expected to strike a 100m2 region in one hour during Earth’s formation is 133.

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Chapter 18 Solutions

EBK FOUNDATIONS OF ASTRONOMY

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