A large asteroid of mass 98700 kg is at rest far away from any planets or stars. A much smaller asteroid, of mass 780 kg, is in a circular orbit about the first at a distance of 201 meters as a result of their mutual gravitational attraction. What is the speed of the second asteroid?

Question

contestada

Respuesta :

Vespertilio Vespertilio · Answer 1 · 2019-09-15T03:38:31+02:00

Answer:

1.81 x 10^-4 m/s

Explanation:

M = 98700 kg

m = 780 kg

d = 201 m

Let the speed of second asteroid is v.

The gravitational force between the two asteroids is balanced by the centripetal force on the second asteroid.

[tex]\frac{GMm}{d^{2}}=\frac{mv^2}{d}[/tex]

[tex]v=\sqrt{\frac{GM}{d}}[/tex]

Where, G be the universal gravitational constant.

G = 6.67 x 10^-11 Nm^2/kg^2

[tex]v=\sqrt{\frac{6.67 \times 10^{-11}\times 98700}{201}}[/tex]

v = 1.81 x 10^-4 m/s