EBK LOOSE-LEAF VERSION OF UNIVERSE
EBK LOOSE-LEAF VERSION OF UNIVERSE
11th Edition
ISBN: 9781319227975
Author: KAUFMANN
Publisher: VST
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Chapter 15, Problem 44Q

(a)

To determine

The orbital period Sun grazing comets whose aphelion distance is 100au.

(a)

Expert Solution
Check Mark

Answer to Problem 44Q

Solution:

The orbital period and lifetime of Sun grazing comets are 353.55years and 35355years, respectively.

Explanation of Solution

Given data:

The aphelion distance is 100au and the comet can only survive 100 perihelion passages.

Formula used:

Write the expression for the orbital period from the Kepler law.

T=a3/2

Here, the orbital time period is T and the semi major axis is a.

Write the expression for the lifetime.

L=T×t

Here, the lifetime is L and the life of the comet is t.

Explanation:

Calculate the semi major axis of the orbit.

a=y2

Here, the aphelion distance is y.

Substitute 100au for y.

a=100au2=50au

Write the expression for the orbital period.

T=a3/2

Substitute 50au for a.

T=(50 au)3/2=353.55years

The comet can survive for 100 perihelion passages. Therefore, the value of t is 100.

Write the expression for the lifetime.

L=T×t

Substitute 353.55years for T and 100 for t.

L=(353.55years)(100)=35355years

Conclusion:

Hence, the orbital period and lifetime of Sun grazing comets is 353.55years and 35355years, respectively.

(b)

To determine

The orbital period and lifetime of Sun grazing comets whose aphelion distance is 1000au.

(b)

Expert Solution
Check Mark

Answer to Problem 44Q

Solution:

The orbital period and lifetime of Sun grazing comets are 11180.34years and 1118034years, respectively.

Explanation of Solution

Given data:

The aphelion distance is 1000au and the comet can only survive 100 perihelion passages.

Formula used:

Write the expression for the orbital period.

T=a3/2

Here, the orbital time period is T and the semi major axis is a.

Write the expression for the lifetime.

L=T×t

Here, the lifetime is L and the life of the comet is t.

Explanation:

Calculate the semi major axis of the orbit.

a=y2

Here, the aphelion distance is y.

Substitute 1000au for y.

a=1000au2=500au

Write the expression for the orbital period.

T=a3/2

Substitute 500au for a.

T=(500 au)3/2=11180.34years

Write the expression for the lifetime.

L=T×t

Substitute 11180.34years for T and 100 for t.

L=(11180.34years)(100)=1118034years

Conclusion:

Hence, the orbital period and lifetime of Sun grazing comets are 11180.34years and 1118034years, respectively.

(c)

To determine

The orbital period and lifetime of Sun grazing comets whose aphelion distance is 10000au.

(c)

Expert Solution
Check Mark

Answer to Problem 44Q

Solution:

The orbital period and lifetime of Sun grazing comets are 353553.4years and 1118034years, respectively.

Explanation of Solution

Given data:

The aphelion distance is 10000au and the comet can only survive 100 perihelion passages.

Formula used:

Write the expression for the orbital period.

T=a3/2

Here, the orbital time period is T and the semi major axis is a.

Write the expression for the lifetime.

L=T×t

Here, the lifetime is L and the life of the comet is t.

Explanation:

Calculate the semi major axis of the orbit.

a=y2

Here, the aphelion distance is y.

Substitute 10000au for y.

a=10000au2=5000au

Write the expression for the orbital period.

T=a3/2

Substitute 5000au for a.

T=(5000)3/2=353553.4years

Write the expression for the lifetime.

L=T×t

Substitute 353553.4years for T and 100 for t.

L=(353553.4years)(100)=35355340years

Conclusion:

Hence, the orbital period and lifetime of Sun grazing comets are 353553.4years and 35355340years, respectively.

(d)

To determine

The orbital period and lifetime of Sun grazing comets whose aphelion distance is 100000au.

(d)

Expert Solution
Check Mark

Answer to Problem 44Q

Solution:

The orbital period and lifetime of Sun grazing comets are 11180339.9years and 1118033990years, respectively.

Explanation of Solution

Given data:

The aphelion distance is 100000au and the comet can only survive 100 perihelion passages.

Formula used:

Write the expression for the orbital period.

T=a3/2

Here, the orbital time period is T and the semi major axis is a.

Write the expression for the lifetime.

L=T×t

Here, the lifetime is L and the life of the comet is t.

Explanation:

Calculate the semi major axis of the orbit.

a=y2

Here, the aphelion distance is y.

Substitute 100000au for y.

a=100000au2=50000au

Write the expression for the orbital period.

T=a3/2

Substitute 50000au for a.

T=(50000 au)3/2=11180339.9years

Write the expression for the lifetime.

L=T×t

Substitute 11180339.9years for T and 100 for t.

L=(11180339.9years)(100)=1118033990years

Conclusion:

Hence, the orbital period and lifetime of Sun grazing comets are 11180339.9years and 1118033990years, respectively.

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