A planet moves around the sun. At a gıven point P, it is closest from the sun at a distance d1 and has a speed v1 . At another point Q, when it is farthest from the sun at a distance d2, its speed will be

Question

A planet moves around the sun. At a gıven point P, it is closest from the sun at a distance d1 and has a speed v1 . At another point Q, when it is farthest from the sun at a distance d2, its speed will be (A) (d12 v1/d22) (B) (d2 v1/d1) (C) (d1 v1/d2) (D) (d22 v1/d12)

Tardigrade Admin · Accepted Answer

Angular momentum remains constant m v1 d1=m v2 d2 ⇒ v2=(v1 d1/d2)

Q. A planet moves around the sun. At a gıven point $P$ , it is closest from the sun at a distance $d_{1}$ and has a speed $v_{1} .$ At another point $Q$ , when it is farthest from the sun at a distance $d_{2}$ , its speed will be

$\frac{d _{1}^{2} v _{1}}{d _{2}^{2}}$

$\frac{d _{2} v _{1}}{d _{1}}$

$\frac{d _{1} v _{1}}{d _{2}}$

$\frac{d _{2}^{2} v _{1}}{d _{1}^{2}}$

Angular momentum remains constant
$m v_{1} d_{1} = m v_{2} d_{2}$
$\Rightarrow v_{2} = \frac{v _{1} d _{1}}{d _{2}}$

Q. A planet moves around the sun. At a gıven point P, it is closest from the sun at a distance d1​ and has a speed v1​. At another point Q, when it is farthest from the sun at a distance d2​, its speed will be

d22​d12​v1​​

d1​d2​v1​​

d2​d1​v1​​

d12​d22​v1​​