COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
COLLEGE PHYSICS LL W/ 6 MONTH ACCESS
2nd Edition
ISBN: 9781319414597
Author: Freedman
Publisher: MAC HIGHER
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Chapter 10, Problem 65QAP
To determine

(a)

The semimajor axis of Apophis

Expert Solution
Check Mark

Answer to Problem 65QAP

Semimajor axis =0.9225au=1.38×1011m

Explanation of Solution

Given info:

Aphelion = 1.099au

Perihelion = 0.746au

Mass of Apophis = 2.7×1010kg

Formula used:

Semimajor axis =Ra+Rp2

  Ra= Aphelion

  Rp= Perihelion

  T=2πa3GM

  T= Time

  G= Gravitational constant

  M= Mass

  a= Semimajor axis

  v=2GMR

  v= Velocity

  R= Radius

Calculation:

Semimajor axis,

Semimajor axis =Ra+Rp2=1.099au+0.746au2=0.9225au

Semimajor axis =0.9225au×1.496×1011=1.38×1011m

Conclusion:

Semimajor axis =0.9225au=1.38*1011m

To determine

(b)

Time taken by Apophis to orbit the Sun

Expert Solution
Check Mark

Answer to Problem 65QAP

Time taken by Apophis to orbit the Sun =323.5days

Explanation of Solution

Given info:

Aphelion = 1.099au

Perihelion = 0.746au

Mass of Apophis = 2.7×1010kg

Formula used:

Semimajor axis =Ra+Rp2

  Ra= Aphelion

  Rp= Perihelion

  T=2πa3GM

  T= Time

  G= Gravitational constant

  M= Mass

  a= Semimajor axis

  v=2GMR

  v= Velocity

  R= Radius

Calculation:

Time taken by Apophis to orbit the Sun,

  T=2πa3GM=2π (1.38× 10 11 m)3(6.67× 10 11Nm2/kg2)×1.989× 10 30kg=2.80×107s=323.5days

Conclusion:

Time taken by Apophis to orbit the Sun =323.5days

To determine

(c)

Points of slowest and fastest of Apophis

Expert Solution
Check Mark

Answer to Problem 65QAP

Apophis travels fastest at perihelion and slowest at aphelion

Explanation of Solution

Given info:

Aphelion = 1.099au

Perihelion = 0.746au

Mass of Apophis = 2.7×1010kg

Formula used:

Semimajor axis =Ra+Rp2

  Ra= Aphelion

  Rp= Perihelion

  T=2πa3GM

  T= Time

  G= Gravitational constant

  M= Mass

  a= Semimajor axis

  v=2GMR

  v= Velocity

  R= Radius

Calculation:

Point Apophis travel fastest = at perihelion

Point Apophis travel slowest = at aphelion

Conclusion:

Apophis travels fastest at perihelion and slowest at aphelion

To determine

(d)

Ratio of its maximum speed to minimum speed

Expert Solution
Check Mark

Answer to Problem 65QAP

Ratio of the maximum speed to minimum speed =1.74

Explanation of Solution

Given info:

Aphelion = 1.099au

Perihelion = 0.746au

Mass of Apophis = 2.7×1010kg

Formula used:

Semimajor axis =Ra+Rp2

  Ra= Aphelion

  Rp= Perihelion

  T=2πa3GM

  T= Time

  G= Gravitational constant

  M= Mass

  a= Semimajor axis

  v=2GMR

  v= Velocity

  R= Radius

Calculation:

Ratio of the maximum speed to minimum speed,

  vα1Rv p va=R a Rp=1.099au0.746au=1.74

Conclusion:

Ratio of the maximum speed to minimum speed =1.74

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