Question

1. John detects a distant meteoroid moving toward earth on a straight line that is 3R_e from earth center as shown. She is assigned by NASA to find out if the meteoroid will be deflected toward earth and if so to what value its speed must be increased to avoid coming to earth.

What minimum speed did John calculate for the meteoroid to be moving in order not to be deflected toward earth by earth

Answer 1

See, over here we are Equating the accelration due to cetripetal force due to gravity pull of earth to its acceleration(force/pull) towards earth.

Assume it like a thread tied to a stone scenario.

There the closest the stone can be to the hand (while rotating) so that the string is taut and the stone follows a specific trajectory (circular).

The force on meterioit by earth = m g

And the point from where it starts getting deflected i.e., there is a pull towards earth.

So if it is moving then the centripetal acceleration on equals the accelerational pull then we get the minimum speed.

Hence, we can say :

V(meteor)² / R (meteor) = g

=> V(meteor) =

But g also changes for major height of the objects ( comparable to Re) , the relation is stated as:

Thus g (meteroite) = g * (Re /(Re + 2 Re) ) ^2 = g * (1/9) = g/9

Thus in the previous equation :-> V(meteor) = =

here g is acceleration due to gravity on earth's surface.