21st Century Astronomy 6E
21st Century Astronomy 6E
6th Edition
ISBN: 9780393690675
Author: Laura Kay, Stacy Palen, George Blumenthal
Publisher: W. W. Norton
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Chapter 12, Problem 41QP

(a)

To determine

The number of times the Halley’s Comet reappeared in the sky since its early sighting.

(a)

Expert Solution
Check Mark

Answer to Problem 41QP

The Halley’s Comet has reappeared for 29 times since its first observed appearance in the sky.

Explanation of Solution

The Halley’s Comet was first observed in the sky in 240BCE. The time since the first appearance of the Halley’s Comet is the sum of the years passed and the 240years BCE.

Write the expression for the time elapsed since the first appearance of comet.

  T=n+240years        (I)

Here, T is the time elapsed and n is the number of years passed after BCE.

Write the expression for the number of reappearance of the Halley’s Comet.

  N=TTHalley        (II)

Here, N is the number of reappearance of the comet and THalley is the orbital time period of the comet Halley.

Conclusion:

Substitute 2019 for n in equation (I).

  T=2019+240years=2259years

Substitute 2259years for T and 76.4years for THalley in equation (II).

  N=2259years76.4years=29.5629

Thus, the Halley’s Comet has reappeared for 29 times since its first observed appearance in the sky.

(b)

To determine

The mass lost by the comet since its first appearance in 240BCE.

(b)

Expert Solution
Check Mark

Answer to Problem 41QP

The total mass lost by the comet since its early sighting is 8.7×1012kg.

Explanation of Solution

The every comet when comes near the sun, the comet action takes place and the body losses some of material as the action occurs.

The Halley’s Comet has appeared for 29 times since its first appearance in the sky.

Write the expression for the mass lost by the comet during all its appearance.

  m=NmL        (III)

Here, m is the total mass lost by the comet and mL is the mass lost by the comet each time it passes near the sun.

Conclusion:

Substitute 29 for N and 3×1011kg for mL in equation (III).

  m=29(3×1011kg)=8.7×1012kg

Thus, the total mass lost by the comet since its early sighting is 8.7×1012kg.

(c)

To determine

The percentage of the comet’s total mass lost by the comet.

(c)

Expert Solution
Check Mark

Answer to Problem 41QP

The mass lost by the Halley’s Comet is about 4% of the total mass of comet.

Explanation of Solution

Write the expression for the total mass of the comet at its first sight.

  M=m+mH        (IV)

Here, M is the total mass of the comet and mH is the current mass of the Halley’s Comet.

Write the expression for the percentage of mass of the comet as of its initial mass.

  x=mM×100%        (V)

Here, x is the percentage of mass.

Conclusion:

Substitute 8.7×1012kg for m and 2.2×1014kg for mH in equation (IV).

  M=8.7×1012kg+2.2×1014kg=2.287×1014kg

Substitute 2.287×1014kg for M and 8.7×1012kg for m in equation (V).

  x=8.7×1012kg2.287×1014kg×100%=3.8%4%

Thus, the mass lost by the Halley’s Comet is about 4% of the total mass of comet.

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