Question 432: Gravitation

Question

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then

Accepted Answer

According to KeplerÃ¢ÂÂs law, the areal velocity of a planet around the sun always remains constant.
SCD : A
1
Ã¢ÂÂ  t
1
(areal velocity constant)
SAB : A
2
Ã¢ÂÂ t
2
$${{{A_1}} \over {{t_1}}} = {{{A_2}} \over {{t_2}}}$$
$${t_1} = {t_2}.{{{A_1}} \over {{A_2}}}$$   (given A
1
= 2A
2
)
$$ = {t_2}.{{2{A_2}} \over {{A_2}}}$$
$$ 	herefore $$ $${t_1} = 2{t_2}$$

Answer

t1 = 4t2

Answer

t1 = 2t2

Answer

t1 = t2

Answer

t1 > t2

Gravitation

The figure shows elliptical orbit of a planet m about the sun S. The shaded area SCD is twice the shaded area SAB. If t1 is the time for the planet to move from C to D and t2 is the time to move from A to B then

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