Question 207: Gravitation

Question

Figure shows elliptical path abcd of a planet around the sun S such that the area of triangle csa is $${1 \over 4}$$ the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If t
1
is the time taken for planet to go over path abc and t
2
for path taken over cda then :

Accepted Answer

Let the area of ellipse = A
$$ 	herefore $$   Area of abcSa = $${A \over 2} + {A \over 4}$$ = Area of half of the ellipse + Area of the triangle  =  $${{3A} \over 4}$$
Area of adcSa = $${A \over 2} - {A \over 4}$$ = $${A \over 4}$$
$$ 	herefore $$   $${{{t_1}} \over {{t_2}}}$$ = $${{{{3A} \over 4}} \over {{A \over 4}}}$$ = 3
$$ 	herefore $$   t
1
= 3t
2

Answer

t
1
= t
2

Answer

t
1
= 2t
2

Answer

t
1
= 3t
2

Answer

t
1
= 4t
2

Gravitation

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