Question

If half of the earth were taken off by the impulse of a comet then what change would be produced in the moon's orbit?


Need full clarification.​

Answer 1

ANSWER:

• Radius of moon's orbit will double.

GIVEN:

• Half of the earth were taken off by the impulse of a comet.

TO FIND:

• The chnge produced in the moon's orbit.

EXPLANATION:

$\boxed{ \bold{ \large{ \gray{Total \ Energy = K.E + P.E}}}}$

BEFORE IMPACT:

Let mass of moon be m and mass of earth be M.

$\sf \leadsto K.E = \dfrac{1}{2} mv^2$

Let the distance between earth and moon be r.

$\sf \leadsto P.E = - \dfrac{GMm}{r}$

$\sf \leadsto T. E= \dfrac{1}{2} mv^2 - \dfrac{GMm}{r}$

AFTER IMPACT:

Now mass of earth will be M/2 and mass of moon will be m.

$\sf \leadsto K.E = \dfrac{1}{2} mv^2$

Now let the distance between earth and moon be r'.

$\sf \leadsto P.E = - \dfrac{GMm}{2r'}$

$\sf \leadsto T. E= \dfrac{1}{2} mv^2 - \dfrac{GMm}{2r'}$

By law of conservation of energy, energy before and after impact will be the same.

$\sf \leadsto \dfrac{1}{2} mv^2 - \dfrac{GMm}{r} = \dfrac{1}{2} mv^2 - \dfrac{GMm}{2r'}$

$\sf \leadsto \dfrac{GMm}{r} = \dfrac{GMm}{2r'}$

$\sf \leadsto \dfrac{1}{r} = \dfrac{1}{2r'}$

$\sf \leadsto r'= \dfrac{r}{2}$

HENCE THE RADIUS OF MOON's ORBIT WILL DOUBLE.