Home
Class 11
PHYSICS
Let the speed of the planet at the perih...

Let the speed of the planet at the perihelion P in figure .(a) be `v_p` and the Sun - planet distance SP be `r_p` . Relate `{r_p, v_p}` to the corresponding quantities at the apphelion `{r_(A) , v_A}` . Will the planet take equal take equal times to traverse BAC and CPB ?

Text Solution

Verified by Experts

`implies` Suppose angular momentum of a planet at P is `L_p` .
`:. L_p = m_(p) r_(p) v_(p)` , where mass of planet is `m_p`
Because angle between `vecr_p and vecv_p` is `90^@` and similarly angular momentum at point A,
`L_(A) = m_(p) r_(A) v_(A)`
`:. m_(p) r_(p) v_(p) = m_(p) r_(A) v_(A)`
`:. (v_p)/(v_(A) )= r_A/r_p`
but `r_A gt r_p :. v_p gt v_A`
The area SBAC bounded by the ellipse and the radius vectors `vec(SB) and vec(SC)` is larger then SBPC. Form Kepler.s second law, equal areas are swept in equal times. Hence , the planet will take a longer time to traverse BAC and CPB.
Promotional Banner

Topper's Solved these Questions

  • GRAVITATION

    KUMAR PRAKASHAN|Exercise Section - B Numerical From Textual Exercise (Answer the following:)|21 Videos

  • GRAVITATION

    KUMAR PRAKASHAN|Exercise Section - B ADDITIONAL EXERCISE|4 Videos

  • GRAVITATION

    KUMAR PRAKASHAN|Exercise Section - A Try Yourself (VSQs)|76 Videos

  • LAW OF MOTION

    KUMAR PRAKASHAN|Exercise (QUESTION PAPER) SECTION-D|1 Videos

Similar Questions

Explore conceptually related problems

Let the speed of the planet at the perihelion P in figure be v_(P) and the Sun planet distance SP be r_(P) . Relater r_(P), v_(P) to the corresponding quantities at the aphelion (r_(A),v_(A)) . Will the planet take equal times to transverse BAC and CPB ?

Let the speed of the planet at the perihelion pin be vP and the Sun-planet distance SP be r_(P) . Relate {r_(P), v_(P)} to the corresponding quantities at the aphelion {r_(A), v_(A)} . Will the planet take equal times to traverse BAC and CPB ?

In the given figure, find tan P - cot R.

Let A = {p, q, r}. Which of the following is an equivalence relation on A?

Spacemen Fred's spaceship (which has negligible mass) is in an elliptical orbit about planet Bob. The minimum distance between the spaceship and the planet is R, the maximum distance between the spaceship and the planet is 2R. At the point of maximum distance, spaceman fred is traveling at speed v_(0) . he then fires his thrusters so that he enters a circular orbit of radius 2R. what is his new speed?

Show that the relation R in the set A of points in a plane give by R = {(P,Q) : distance of the point P from the origin is same as the distance of the point Q from the origin} , is an equivalence relation. Further , show that the set equivalence relation . Further , show that the set of all points related to a point P ne (0,0) is the circle passing through P with origin as centre.

The equivalent resistance between the point P and Q in the network given here is equal to (given r = (3)/(2) Omega)

Plot P -V, V-T graph corresponding to the P-T graph for an ideal has shown in figure. Explain your answers.