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High School Math Algebra Glencoe Algebra 2 Student Edition C2014

Write an equation for the orbit of each planet.

Write an equation for the orbit of each planet.

Glencoe Algebra 2 Student Edition C2014

Glencoe Algebra 2 Student Edition C2014

1st Edition

ISBN: 9780076639908

Author: McGraw-Hill Glencoe

Publisher: MCG

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Question

Chapter 11.4, Problem 62SR

a.

To determine

Write an equation for the orbit of each planet.

a.

Expert Solution

Answer to Problem 62SR

$x2(67.685)2+y2(67.684)2=1$

$x2(483.685)2+y2(483.13)2=1$

Explanation of Solution

Given information:

The table at the right shows the closest and farthest distances of Venus and Jupiter from the Sun in millions of miles.

$PlanetClosestFarthestVenus66.867.7Jupiter460.1507.4$

Write an equation for the orbit of each planet. Assume that the centre of the orbit is the origin and the centre of the Sun is a focus that lies on the $x−axis$ .

Calculation:

Consider the standard equation of the horizontal ellipse which is centred to the origin,

$x2a2+y2b2=1$

Length of major axis, $2a$ units, length of minor axis $2b$ unit and foci are at $(c,0)$ and $(−c,0)$

The valid equation is,

$c2=a2−b2......(1)$

Consider the table for distances,

Assume that planet Venus revolves around the Sun in an elliptical orbit with the Sun at its one of its focus on $x−axis$ .

The length of major axis will be the sum of closest and farthest distances and diameter of the Sun which is $0.87million$ miles. So now,

$2a=66.8+0.87+67.72a=135.37a=135.372a=67.685$

Now find $c$ which is the distance from centre of ellipse to the focus, equal to minus the close sets distance and radius of the Sun $(0.87/2=0.435)$ .

$c=67.685−66.8−0.435c=0.45$

Now put values of $a=67.685,c=0.45$ in equation $(1)$ .

$(0.45)2=(67.685)2−b2b2=4581.056725b=67.684$

Now put $a=67.685,b=67.684$ in $x2a2+y2b2=1$ we get,

$x2(67.685)2+y2(67.684)2=1$

Hence, the equation of the orbit of Venus is , $x2(67.685)2+y2(67.684)2=1$ .

Now consider the closest and farthest distance of Jupiter from the Sun,

$2a=460.1+0.870506.42a=967.37a=483.685$

$c=483.685−460.1−0.435c=23.15$

Now substitute $a=483.685$ , $c=23.15$ in equation $(1)$ .

$(23.15)2=(483.685)2−b2b2=233,415.2567b=483.13$

Now put $a=483.685,b=483.13$ in $x2a2+y2b2=1$ we get,

$x2(483.685)2+y2(483.13)2=1$

Hence equation for orbit of Jupiter is $x2(483.685)2+y2(483.13)2=1$

b.

To determine

Which planet has an orbit that is closer to the circle?

b.

Expert Solution

Answer to Problem 62SR

$Venus$

Explanation of Solution

Given information:

The table at the right shows the closest and farthest distances of Venus and Jupiter from the Sun in millions of miles.

$PlanetClosestFarthestVenus66.867.7Jupiter460.1507.4$

Which planet has an orbit that is closer to the circle?

Calculation:

Consider the standard equation of eccentricity of ellipse is,

$e=ca$

For Venus planet put $a=67.685,c=0.45$ in above equation,

$ev=0.4567.685ev=6.6484×10−3$

For Jupiter planet, $a=483.685$ , $c=23.15$ ,

$eJ=23.15483.685eJ=47.8617×10−3$

Thus lesser the value of $e$ more circular the orbit of ellips,

Hence, the orbit of $Venus$ is more circular.

Chapter 11.4, Problem 61SR

Chapter 11.4, Problem 63SR

Chapter 11 Solutions

Glencoe Algebra 2 Student Edition C2014

Ch. 11.1 - Prob. 1AGP Ch. 11.1 - Prob. 1BGP Ch. 11.1 - Prob. 2AGP Ch. 11.1 - Prob. 2BGP Ch. 11.1 - Prob. 3AGP Ch. 11.1 - Prob. 3BGP Ch. 11.1 - Prob. 4GP Ch. 11.1 - Prob. 5GP Ch. 11.1 - Prob. 6GP Ch. 11.1 - Prob. 1CYU

Ch. 11.1 - Prob. 2CYU Ch. 11.1 - Prob. 3CYU Ch. 11.1 - Prob. 4CYU Ch. 11.1 - Prob. 5CYU Ch. 11.1 - Prob. 6CYU Ch. 11.1 - Prob. 7CYU Ch. 11.1 - Prob. 8CYU Ch. 11.1 - Prob. 9CYU Ch. 11.1 - Prob. 10PPS Ch. 11.1 - Prob. 11PPS Ch. 11.1 - Prob. 12PPS Ch. 11.1 - Prob. 13PPS Ch. 11.1 - Prob. 14PPS Ch. 11.1 - Prob. 15PPS Ch. 11.1 - Prob. 16PPS Ch. 11.1 - Prob. 17PPS Ch. 11.1 - Prob. 18PPS Ch. 11.1 - Prob. 19PPS Ch. 11.1 - Prob. 20PPS Ch. 11.1 - Prob. 21PPS Ch. 11.1 - Prob. 22PPS Ch. 11.1 - Prob. 23PPS Ch. 11.1 - Prob. 24PPS Ch. 11.1 - Prob. 25PPS Ch. 11.1 - Prob. 26PPS Ch. 11.1 - Prob. 27PPS Ch. 11.1 - Prob. 28HP Ch. 11.1 - Prob. 29HP Ch. 11.1 - Prob. 30HP Ch. 11.1 - Prob. 31HP Ch. 11.1 - Prob. 32HP Ch. 11.1 - Prob. 33STP Ch. 11.1 - Prob. 34STP Ch. 11.1 - Prob. 35STP Ch. 11.1 - Prob. 36STP Ch. 11.1 - Prob. 37SR Ch. 11.1 - Prob. 38SR Ch. 11.1 - Prob. 39SR Ch. 11.1 - Prob. 40SR Ch. 11.1 - Prob. 41SR Ch. 11.1 - Prob. 42SR Ch. 11.1 - Prob. 43SR Ch. 11.1 - Prob. 44SR Ch. 11.1 - Prob. 45SR Ch. 11.1 - Prob. 46SR Ch. 11.1 - Prob. 47SR Ch. 11.1 - Prob. 48SR Ch. 11.1 - Prob. 49SR Ch. 11.1 - Prob. 50SR Ch. 11.1 - Prob. 51SR Ch. 11.1 - Prob. 52SR Ch. 11.1 - Prob. 53SR Ch. 11.1 - Prob. 54SR Ch. 11.1 - Prob. 55SR Ch. 11.1 - Prob. 56SR Ch. 11.1 - Prob. 57SR Ch. 11.1 - Prob. 58SR Ch. 11.1 - Prob. 59SR Ch. 11.1 - Prob. 60S Ch. 11.1 - Prob. 61S Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.2 - Prob. 1GP Ch. 11.2 - Prob. 2GP Ch. 11.2 - Prob. 3GP Ch. 11.2 - Prob. 4GP Ch. 11.2 - Prob. 1CYU Ch. 11.2 - Prob. 2CYU Ch. 11.2 - Prob. 3CYU Ch. 11.2 - Prob. 4CYU Ch. 11.2 - Prob. 5PPS Ch. 11.2 - Prob. 6PPS Ch. 11.2 - Prob. 7PPS Ch. 11.2 - Prob. 8PPS Ch. 11.2 - Prob. 9PPS Ch. 11.2 - Prob. 10PPS Ch. 11.2 - Prob. 11PPS Ch. 11.2 - Prob. 12PPS Ch. 11.2 - Prob. 13HP Ch. 11.2 - Prob. 14HP Ch. 11.2 - Prob. 15HP Ch. 11.2 - Prob. 16HP Ch. 11.2 - Prob. 17STP Ch. 11.2 - Prob. 18STP Ch. 11.2 - Prob. 19STP Ch. 11.2 - Prob. 20STP Ch. 11.2 - Prob. 21SR Ch. 11.2 - Prob. 22SR Ch. 11.2 - Prob. 23SR Ch. 11.2 - Prob. 24SR Ch. 11.2 - Prob. 25SR Ch. 11.2 - Prob. 26S Ch. 11.2 - Prob. 27S Ch. 11.2 - Prob. 28S Ch. 11.2 - Prob. 29S Ch. 11.3 - Prob. 1AGP Ch. 11.3 - Prob. 1BGP Ch. 11.3 - Prob. 2GP Ch. 11.3 - Prob. 3GP Ch. 11.3 - Prob. 4GP Ch. 11.3 - Prob. 5GP Ch. 11.3 - Prob. 1CYU Ch. 11.3 - Prob. 2CYU Ch. 11.3 - Prob. 3CYU Ch. 11.3 - Prob. 4CYU Ch. 11.3 - Prob. 5CYU Ch. 11.3 - Prob. 6PPS Ch. 11.3 - Prob. 7PPS Ch. 11.3 - Prob. 8PPS Ch. 11.3 - Prob. 9PPS Ch. 11.3 - Prob. 10PPS Ch. 11.3 - Prob. 11PPS Ch. 11.3 - Prob. 12PPS Ch. 11.3 - Prob. 13PPS Ch. 11.3 - Prob. 14PPS Ch. 11.3 - Prob. 15PPS Ch. 11.3 - Prob. 16PPS Ch. 11.3 - Prob. 17PPS Ch. 11.3 - Prob. 18PPS Ch. 11.3 - Prob. 19HP Ch. 11.3 - Prob. 20HP Ch. 11.3 - Prob. 21HP Ch. 11.3 - Prob. 22HP Ch. 11.3 - Prob. 23HP Ch. 11.3 - Prob. 24HP Ch. 11.3 - Prob. 25STP Ch. 11.3 - Prob. 26STP Ch. 11.3 - Prob. 27STP Ch. 11.3 - Prob. 28STP Ch. 11.3 - Prob. 29SR Ch. 11.3 - Prob. 30SR Ch. 11.3 - Prob. 31SR Ch. 11.3 - Prob. 32SR Ch. 11.3 - Prob. 33SR Ch. 11.3 - Prob. 34SR Ch. 11.3 - Prob. 35SR Ch. 11.3 - Prob. 36SR Ch. 11.3 - Prob. 37SR Ch. 11.3 - Prob. 38SR Ch. 11.3 - Prob. 39SR Ch. 11.3 - Prob. 40SR Ch. 11.3 - Prob. 41SR Ch. 11.3 - Prob. 42S Ch. 11.3 - Prob. 43S Ch. 11.3 - Prob. 44S Ch. 11.3 - Prob. 1MCQ Ch. 11.3 - Prob. 2MCQ Ch. 11.3 - Prob. 3MCQ Ch. 11.3 - Prob. 4MCQ Ch. 11.3 - Prob. 5MCQ Ch. 11.3 - Prob. 6MCQ Ch. 11.3 - Prob. 7MCQ Ch. 11.3 - Prob. 8MCQ Ch. 11.3 - Prob. 9MCQ Ch. 11.3 - Prob. 10MCQ Ch. 11.3 - Prob. 11MCQ Ch. 11.3 - Prob. 12MCQ Ch. 11.4 - Prob. 1AGP Ch. 11.4 - Prob. 1BGP Ch. 11.4 - Prob. 2GP Ch. 11.4 - Prob. 3GP Ch. 11.4 - Prob. 4GP Ch. 11.4 - Prob. 1CYU Ch. 11.4 - Prob. 2CYU Ch. 11.4 - Prob. 3CYU Ch. 11.4 - Prob. 4CYU Ch. 11.4 - Prob. 5CYU Ch. 11.4 - Prob. 6CYU Ch. 11.4 - Prob. 7PPS Ch. 11.4 - Prob. 8PPS Ch. 11.4 - Prob. 9PPS Ch. 11.4 - Prob. 10PPS Ch. 11.4 - Prob. 11PPS Ch. 11.4 - Prob. 12PPS Ch. 11.4 - Prob. 13PPS Ch. 11.4 - Prob. 14PPS Ch. 11.4 - Prob. 15PPS Ch. 11.4 - Prob. 16PPS Ch. 11.4 - Prob. 17PPS Ch. 11.4 - Prob. 18PPS Ch. 11.4 - Prob. 19PPS Ch. 11.4 - Prob. 20PPS Ch. 11.4 - Prob. 21PPS Ch. 11.4 - Prob. 22PPS Ch. 11.4 - Prob. 23PPS Ch. 11.4 - Prob. 24PPS Ch. 11.4 - Prob. 25PPS Ch. 11.4 - Prob. 26PPS Ch. 11.4 - Prob. 27PPS Ch. 11.4 - Prob. 28PPS Ch. 11.4 - Prob. 29PPS Ch. 11.4 - Prob. 30PPS Ch. 11.4 - Prob. 31PPS Ch. 11.4 - Prob. 32PPS Ch. 11.4 - Prob. 33PPS Ch. 11.4 - Prob. 34PPS Ch. 11.4 - Prob. 35PPS Ch. 11.4 - Prob. 36PPS Ch. 11.4 - Prob. 37PPS Ch. 11.4 - Prob. 38PPS Ch. 11.4 - Prob. 39PPS Ch. 11.4 - Prob. 40PPS Ch. 11.4 - Prob. 41PPS Ch. 11.4 - Prob. 42HP Ch. 11.4 - Prob. 43HP Ch. 11.4 - Prob. 44HP Ch. 11.4 - Prob. 45HP Ch. 11.4 - Prob. 46HP Ch. 11.4 - Prob. 47STP Ch. 11.4 - Prob. 48STP Ch. 11.4 - Prob. 49STP Ch. 11.4 - Prob. 50STP Ch. 11.4 - Prob. 51SR Ch. 11.4 - Prob. 52SR Ch. 11.4 - Prob. 53SR Ch. 11.4 - Prob. 54SR Ch. 11.4 - Prob. 55SR Ch. 11.4 - Prob. 56SR Ch. 11.4 - Prob. 57SR Ch. 11.4 - Prob. 58SR Ch. 11.4 - Prob. 59SR Ch. 11.4 - Prob. 60SR Ch. 11.4 - Prob. 61SR Ch. 11.4 - Prob. 62SR Ch. 11.4 - Prob. 63SR Ch. 11.4 - Prob. 64SR Ch. 11.4 - Prob. 65SR Ch. 11.4 - Prob. 66SR Ch. 11.4 - Prob. 67SR Ch. 11.4 - Prob. 68SR Ch. 11.4 - Prob. 69SR Ch. 11.4 - Prob. 70SR Ch. 11.4 - Prob. 71S Ch. 11.5 - Prob. 1GP Ch. 11.5 - Prob. 2GP Ch. 11.5 - Prob. 3GP Ch. 11.5 - Prob. 4GP Ch. 11.5 - Prob. 1CYU Ch. 11.5 - Prob. 2CYU Ch. 11.5 - Prob. 3CYU Ch. 11.5 - Prob. 4CYU Ch. 11.5 - Prob. 5CYU Ch. 11.5 - Prob. 6CYU Ch. 11.5 - Prob. 7CYU Ch. 11.5 - Prob. 8CYU Ch. 11.5 - Prob. 9PPS Ch. 11.5 - Prob. 10PPS Ch. 11.5 - Prob. 11PPS Ch. 11.5 - Prob. 12PPS Ch. 11.5 - Prob. 13PPS Ch. 11.5 - Prob. 14PPS Ch. 11.5 - Prob. 15PPS Ch. 11.5 - Prob. 16PPS Ch. 11.5 - Prob. 17PPS Ch. 11.5 - Prob. 18PPS Ch. 11.5 - Prob. 19PPS Ch. 11.5 - Prob. 20PPS Ch. 11.5 - Prob. 21HP Ch. 11.5 - Prob. 22HP Ch. 11.5 - Prob. 23HP Ch. 11.5 - Prob. 24HP Ch. 11.5 - Prob. 25HP Ch. 11.5 - Prob. 26HP Ch. 11.5 - Prob. 27STP Ch. 11.5 - Prob. 28STP Ch. 11.5 - Prob. 29STP Ch. 11.5 - Prob. 30STP Ch. 11.5 - Prob. 31SR Ch. 11.5 - Prob. 32SR Ch. 11.5 - Prob. 33SR Ch. 11.5 - Prob. 34SR Ch. 11.5 - Prob. 35SR Ch. 11.5 - Prob. 36SR Ch. 11.5 - Prob. 37SR Ch. 11.5 - Prob. 38S Ch. 11.5 - Prob. 1E Ch. 11.5 - Prob. 2E Ch. 11.5 - Prob. 3E Ch. 11.6 - Prob. 1GP Ch. 11.6 - Prob. 2GP Ch. 11.6 - Prob. 3AGP Ch. 11.6 - Prob. 3BGP Ch. 11.6 - Prob. 4GP Ch. 11.6 - Prob. 5GP Ch. 11.6 - Prob. 1CYU Ch. 11.6 - Prob. 2CYU Ch. 11.6 - Prob. 3CYU Ch. 11.6 - Prob. 4CYU Ch. 11.6 - Prob. 5CYU Ch. 11.6 - Prob. 6CYU Ch. 11.6 - Prob. 7CYU Ch. 11.6 - Prob. 8CYU Ch. 11.6 - Prob. 9PPS Ch. 11.6 - Prob. 10PPS Ch. 11.6 - Prob. 11PPS Ch. 11.6 - Prob. 12PPS Ch. 11.6 - Prob. 13PPS Ch. 11.6 - Prob. 14PPS Ch. 11.6 - Prob. 15PPS Ch. 11.6 - Prob. 16PPS Ch. 11.6 - Prob. 17PPS Ch. 11.6 - Prob. 18PPS Ch. 11.6 - Prob. 19PPS Ch. 11.6 - Prob. 20HP Ch. 11.6 - Prob. 21HP Ch. 11.6 - Prob. 22HP Ch. 11.6 - Prob. 23HP Ch. 11.6 - Prob. 24HP Ch. 11.6 - Prob. 25STP Ch. 11.6 - Prob. 26STP Ch. 11.6 - Prob. 27STP Ch. 11.6 - Prob. 28STP Ch. 11.6 - Prob. 29SR Ch. 11.6 - Prob. 30SR Ch. 11.6 - Prob. 31SR Ch. 11.6 - Prob. 32SR Ch. 11.6 - Prob. 33SR Ch. 11.6 - Prob. 34SR Ch. 11.6 - Prob. 35SR Ch. 11.6 - Prob. 36SR Ch. 11.6 - Prob. 37SR Ch. 11.6 - Prob. 38SR Ch. 11.6 - Prob. 39SR Ch. 11.6 - Prob. 40S Ch. 11.6 - Prob. 41S Ch. 11.6 - Prob. 42S Ch. 11 - Prob. 1QC Ch. 11 - Prob. 2QC Ch. 11 - Prob. 3QC Ch. 11 - Prob. 4QC Ch. 11 - Prob. 5QC Ch. 11 - Prob. 6QC Ch. 11 - Prob. 7QC Ch. 11 - Prob. 8QC Ch. 11 - Prob. 9QC Ch. 11 - Prob. 10QC Ch. 11 - Prob. 11QC Ch. 11 - Prob. 12QC Ch. 11 - Prob. 13QC Ch. 11 - Prob. 14QC Ch. 11 - Prob. 1SGR Ch. 11 - Prob. 2SGR Ch. 11 - Prob. 3SGR Ch. 11 - Prob. 4SGR Ch. 11 - Prob. 5SGR Ch. 11 - Prob. 6SGR Ch. 11 - Prob. 7SGR Ch. 11 - Prob. 8SGR Ch. 11 - Prob. 9SGR Ch. 11 - Prob. 10SGR Ch. 11 - Prob. 11SGR Ch. 11 - Prob. 12SGR Ch. 11 - Prob. 13SGR Ch. 11 - Prob. 14SGR Ch. 11 - Prob. 15SGR Ch. 11 - Prob. 16SGR Ch. 11 - Prob. 17SGR Ch. 11 - Prob. 18SGR Ch. 11 - Prob. 19SGR Ch. 11 - Prob. 20SGR Ch. 11 - Prob. 21SGR Ch. 11 - Prob. 22SGR Ch. 11 - Prob. 23SGR Ch. 11 - Prob. 24SGR Ch. 11 - Prob. 25SGR Ch. 11 - Prob. 26SGR Ch. 11 - Prob. 1PT Ch. 11 - Prob. 2PT Ch. 11 - Prob. 3PT Ch. 11 - Prob. 4PT Ch. 11 - Prob. 5PT Ch. 11 - Prob. 6PT Ch. 11 - Prob. 7PT Ch. 11 - Prob. 8PT Ch. 11 - Prob. 9PT Ch. 11 - Prob. 10PT Ch. 11 - Prob. 11PT Ch. 11 - Prob. 12PT Ch. 11 - Prob. 13PT Ch. 11 - Prob. 14PT Ch. 11 - Prob. 15PT Ch. 11 - Prob. 16PT Ch. 11 - Prob. 1E Ch. 11 - Prob. 2E Ch. 11 - Prob. 1STP Ch. 11 - Prob. 2STP Ch. 11 - Prob. 3STP Ch. 11 - Prob. 4STP Ch. 11 - Prob. 5STP Ch. 11 - Prob. 6STP Ch. 11 - Prob. 7STP Ch. 11 - Prob. 8STP Ch. 11 - Prob. 9STP Ch. 11 - Prob. 10STP Ch. 11 - Prob. 11STP Ch. 11 - Prob. 12STP Ch. 11 - Prob. 13STP Ch. 11 - Prob. 14STP Ch. 11 - Prob. 15STP Ch. 11 - Prob. 16STP

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