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 25.1 km.
You hold a hammer and a falcon feather at a height of 1.40 m, release them, and observe that they fall together to the surface in 29.4 s.

Determine the mass of the planet.

The mass of the planet is M = 7.75 × 10^14 kg

Explanation:

From the Newton's law of gravitation;

F = GMm/r^2

Where

F = gravitational force

G = gravitational constant

M = mass of planet

m = mass of other object

r = radius

And note that;

F = mg = GMm/r^2

g = GM/r^2

Making M the subject of formula,

M = gr^2/G 1

g = acceleration due to gravity in the planet.

From h = 0.5gt^2

g = 2h/t^2

given; h = 1.40 m

t = 29.4s

g = (2×1.4/29.4^2)m/s

Circumference of the planet is = 2πr =25.1km = 25100m

r = (25100/2π)m

G = 6.67 10-11m3kg-1s-2

Substituting the values to equation 1

M = (2×1.4/29.4^2)×((25100/2π)^2)/(6.67 × 10^-11)

M = 7.75 × 10^14 kg

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