# Planet Z is 12,000 km in diameter. The free-fall acceleration on Planet Z is 9.0 m/s2.?

(a) What is the mass of Planet Z?

(b) What is the free-fall acceleration 10,000 km above Planet Z's north pole?

• (a) g=Gm/r^2 where G=6.67 * 10^-11 Nm^2/kg^2, m is the mass of the planet, r is the radius of the planet.

9.0 = (6.67 10^-11)/(6000^2) m

m= (6000000^2 9.0)/(6.67 10^-11)

m~4.85757*10^24 kg

(b) g=Gm/r^2. This time, the radius is 6000+10000 = 16000km

g=(6.67 10^-11 4.85757*10^18)/(16000^2)

g ~1.26562 m/s^2

To the person below thanks for reminding me.

• Planet Z

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• gearth= G* Mearth/ (earth radius)^2

gplanetZ=G* Mplanetz/ (planetz radius)^2

G is a universal constant

(a)

gearth=9.8 m/s^2

gplanetz=9 m/s^2

earth radius= 6371 * 10^3 m

planetz radius= 6000 *10 ^3 m

Mearth=5.9742 × 10^24 kg

Divide both equations you get

Mplanetz= gplanetz/gearth (radius planet z)^2/(radius earth)^2 Mearth

Mplanetz=4.87 x 10^24 kg

b)

gplantz= G*Mplanetz/(radius planet z)^2

gatheight= G*Mplanetz/(radius planet z + h)^2

gatheight=gplanetz (radius planet z)^2/(radius planet z + h)^2= 9 6000^2/16000^2

gatheight=1.26 m/s^2

catsponge: you forget to convert to meter in part a