Ask Questions, Get Answers
Menu
X
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
studyplans
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
mobile
exams
ask
sample papers
tutors
pricing
sign-in
Download our FREE mobile app with 1000+ tests for CBSE, JEE MAIN, NEET
X
Search
Topics
Want to ask us a question?
Click here
Browse Questions
Student Questions
Ad
Home
>>
TN XII Math
>>
Analytical Geometry
0
votes
The orbit of the planet mercury around the sun is in elliptical shape with sun at a focus. The semi-major axis is of length $36$ million miles and the eccentricity of the orbit is $0.206$ Find how close the mercury gets to sun?
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p218
q9
q9-1
modelpaper
oct-2009
Share
asked
Apr 11, 2013
by
poojasapani_1
retagged
Jul 19, 2013
by
balaji.thirumalai
Please
log in
or
register
to add a comment.
Can you answer this question?
Do not ask me again to answer questions
Please
log in
or
register
to answer this question.
1 Answer
0
votes
Toolbox:
Standard forms of equation of the ellipse with major axes 2a, minor axis 2b $(a >b)$ eccentricity e and $b^2=a^2(1-e^2)$ or $e^2=1-\large\frac{b^2}{a^2}$
$\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$
http://clay6.com/mpaimg/19_2_Toolbox.png
Foci$(\pm ae,o),$ center $(0,0)$,vertices $(\pm a,0)$
End points of Latus Rectum $\; (ae,\pm \large\frac{b^2}{a})$ and $(-ae,\pm \large\frac{b^2}{a})$
Directrices $x=\pm \large\frac{a}{e}$.
The major axis is $y=0$ (x- axis) and the minor axes is $x=0$ (y- axis)
$\large\frac{x^2}{b^2}+\frac{y^2}{a^2}$$=1$
http://clay6.com/mpaimg/19_2_Toolbox1.png
Foci$(0,\pm ae),$ center $(0,0)$,vertices $(0,\pm a)$
End points of Latus Rectum $(\pm \large\frac{b^2}{a}$$,ae)$ and $(\pm \large\frac{b^2}{a}$$,-ae)$
Directrices $y=\pm \large\frac{a}{e}$.
The major axis is $x=0$ (y- axis) and the minor axes is $y=0$ (x- axis)
If a point moves so that the sum of its distances from two fixed points is a constant,then the path traced as an ellipse with major axis of length equal to the constant sum and foci at the two fixed points.
Step 1:
http://clay6.com/mpaimg/1_sec2q9.png
In the orbit of mercury,$e=0.206$ and semi-major axis $a=36$(in millions of miles).
Let $F(ae,0),F'(-ae,0)$ be the foci and $A(a,0),A'(-a,0)$ be the vertices of the elliptical path with the sun at $F$.
Step 2:
Mercury is closest to the sun at $A$.
Distance from the sun =$FA=a(1-e)$
$\qquad\qquad\qquad\qquad=36(1-0.206)$
$\qquad\qquad\qquad\qquad=36\times 0.794$
$\qquad\qquad\qquad\qquad=28.584$ million miles.
answered
Jun 18, 2013
by
sreemathi.v
edited
Jun 18, 2013
by
sreemathi.v
Please
log in
or
register
to add a comment.
Related questions
0
votes
1
answer
The orbit of the planet mercury around the sun is in elliptical shape with sun at a focus. The semi-major axis is of length $36$ million miles and the eccentricity of the orbit is $0.206$ The greatest possible distance between mercury and sun.
asked
Apr 11, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p218
q9
q9-2
0
votes
1
answer
A satellite is travelling around the earth in an elliptical orbit having the earth heat a focus and of eccentricity $\large\frac{1}{2}.$ The shortest distance that the satellite get to the earth is $400kms.$ Find the longest distance that the satellite gets from the earth.
asked
Apr 11, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p217
q8
modelpaper
jun-2007
jun-2008
0
votes
1
answer
The arch of a bridge is in the shape of a semi-ellipse having a horizontal span of $40ft$ and $16ft$ high at the centre. How high is the arch $9ft$ from the right or left of the centre .
asked
Apr 11, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p218
q10
0
votes
1
answer
Find the equation of the ellipse if the length of the semi major axis, and the latus rectum are $7$ and $\large\frac{80}{7}$ respectively, the centre is $(2 , 5 )$ and the major axis is parallel to y- axis.
asked
Apr 10, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p217
q1
q1-6
0
votes
1
answer
Find the equation of the ellipse if the centre at the origin, the major axis is along $x$-axies,$e=\large\frac{2}{3}$ and passes through the point $(2 , \large\frac{-5}{3})$
asked
Apr 10, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p217
q1
q1-5
0
votes
1
answer
Find the eccentricity, centre, foci, vertices of the following ellipses and draw the diagram:$ 16x^{2}+9y^{2}+32x-36y=92$
asked
Apr 10, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p217
q6
q6-4
modelpaper
jun-2009
0
votes
1
answer
Find the equations and length of major and minor axes of $16x^{2}+9y^{2}+32x-32y-92=0$
asked
Apr 10, 2013
by
poojasapani_1
tnstate
class12
bookproblem
ch4
sec-1
exercise4-2
p217
q4
q4-4
Ask Question
Tag:
Math
Phy
Chem
Bio
Other
SUBMIT QUESTION
►
Please Wait
Take Test
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
JEEMAIN
350+ TESTS
NEET
320+ TESTS
CBSE XI MATH
50+ TESTS
CBSE XII MATH
80+ TESTS
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...