Question

As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite side after completing a lap of 25.2 km. You hold a hammer and a falcon feather at a height of 1.49 m, release them, and observe that they fall together to the surface in 28.8 s. Determine the mass of the planet.

Answer #1

circumference of the planet = 2r = 25.2 km = 25.2 x 1000 m

r = radius of planet

2 (3.14) r = 25200

**r = 4012.74 m**

distance travelled by hammer = **d = 1.49 m**

time taken = **t = 28.8 sec**

initial velocity = **V _{i} = 0 m/s**

using the kinematics equation ::

d = V_{i} t + (0.5)a t^{2}

1.49 = 0 (28.8) + (0.5) a (28.8)^{2}

**a = 0.0036 m/s ^{2}**

acceleration due to gravity is given as ::

a = GM/r^{2}

**M = mass of planet** , r = radius of
planet = **4012.74 m , a = acceleration = 0.0036**

inserting the values

0.0036 = (6.67 x 10^{-11}) M / (4012.74)^{2}

**M = 8.7 x 10 ^{14} kg**

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