Answer:
W = 661.6 N
Explanation:
The weight of a body is the force of attraction of the plant on the body, so we must use the law of gravitational attraction
F = G m M / r²
Where G is the gravitational attraction constant that values 6.67 10-11 N m² / kg², M is the mass of the planet and r is the distance from the center of the planet.
Let's look for the mass of the planet, for this we write Newton's second law for the landing craft
F = m a
Acceleration is centripetal a = v² / r
G m M / r² = m (v² / r)
The ship rotates rapidly (constant velocity module), let's use uniform kinematic relationships
v = d / t
The distance of a circle is
d = 2π r
v = 2π r / t
We replace
G m M / r² = m (4π² r² / t² r)
G M = 4 π² r³ / t²
M = 4π² r³ / G t²
The measured distance r from the center of the plant is
r = R orbit + R planet
r = 5.90 10⁵ + ½ 9.80 10⁶
r = 5.49 10⁶ m
M = 4 π² (5.49 10⁶)³ / (6.67 10⁻¹¹ (5.900 10³)²)
M = 6,532 10²¹ / 2,321 10⁺³
M = 2.814 10²⁴ kg
With this data we calculate the astronaut's weight
W = (G M / R²) m
W = (6.67 10⁻¹¹ 2,816 10²⁴ /(4.90 10⁶)2) 84.6
W = 7.82 84.6
W = 661.57 N
