In 1993 the spacecraft Galileo sent home an image of asteroid 243 Ida and an orb

Question

In 1993 the spacecraft Galileo sent home an image of asteroid 243 Ida and an orbiting tiny moon (now known as Dactyl), the first confirmed example of an asteroid moon system. Other such systems have since been discovered. Assume an asteroid's moon is 1.6 km wide, and that its center is 116 km from the center of the asteroid, which is 55 km long. The moon's orbit is circular with a period of 24 h. (a) What is the mass of the asteroid? kg (b) The volume of the asteroid is 14, 100 km^3. What is the density of the asteroid? kg/m^3

Explanation / Answer

r = 116 km

t = 24 hours

v = 116 *2*pi /24 hour

v = 30.35 km/hr

v = 8.43 m/sec

a = v^2/r

a = 0.0006126 m/s^2

Now to the Universal law of gravitation

F= G Mm/r^2

a = GM /r^2 ... for a satellite orbiting a main body.

M = a r^2/G

M =( 0.0006126 m/s^2 x (116000m)^2/ (6.673 x 10^-11 m3/kg s^2 )

M = 1.2353 x 10^17 kg

b)

Density = Mass/volume

= (1.2353 x 10^17 kg / 14100 km^3

= 8.76 x10^12 kg/km

= 8.76 x 10^3 kg/m^3

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