Question

9. In 1993 the Galileo spacecraft sent home an image of asteroid “243 Ida” and a...

9. In 1993 the Galileo spacecraft sent home an image of asteroid “243 Ida” and a tiny moon “Dactyl” orbiting the asteroid. Assume that the small moon orbits in a circle with a radius of r = 100 km from the center of the asteroid with an orbital period of T = 27 hours.

a) Show and explain how we derived Kepler’s 3rd law in class using Newton’s 2nd Law, the definition for centripetal acceleration, and the equation for the gravitational force.

b) Use your result for Kepler’s 3rd Law from part a) to determine the mass of the asteroid.

c) If the asteroid has a radius of about 16 km calculate the approximate value for the acceleration due to gravity, g, on its surface. (Ignore that this is a poor approximation for radius)

d) What velocity would you need to achieve in order to lift off and leave this asteroid?

e) Use Newton’s 2nd Law, the definition for centripetal acceleration, and the equation for gravitational force (again) to determine an expression for circular orbital velocity.

f) What is the orbital velocity of the small moon if we assume it is in a circular orbit?