Answer :
The weight of the person is [tex]3.85 \times 10^5 \ N[/tex] or [tex]8.66 \times 10^4\ pounds[/tex].
The weight is the force by which the earth pulls any object.
[tex]W=mg[/tex]
Given:
Mass of the person, [tex]m=67\ kg[/tex]
Radius of the orbit, [tex]r=263\ km[/tex]
The weight of the person is computed as:
[tex]W= \frac{GMm}{r^2}\\W=\frac{6.67 \times 10^{-11} \times 5.972 \times 10^{24} \times 67}{(263 \times 10^3)^2}\\W = 3.85 \times 10^5 \ N[/tex]
The weight in pounds is computed as:
[tex]W = 3.85 \times 10^5 \ N\\W = \frac{3.85 \times 10^5}{4.44}\\W= 8.66 \times 10^4\ pounds[/tex]
Therefore, the weight of the person is [tex]3.85 \times 10^5 \ N[/tex] or [tex]8.66 \times 10^4\ pounds[/tex].
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Final answer:
For calculating the weight of a 67-kg man in orbit, we'd use Newton's universal law of gravitation with the gravitational constant, the masses involved, and the distance to the center of the Earth, including the spacecraft's altitude. Then,the weight should be converted from newtons to pounds.
Explanation:
For calculating the a 67-kg man's weight W (gravitational force with respect to the earth) in a spacecraft traveling in a circular orbit 263 km above the Earth's surface, we use Newton's universal law of gravitation:
F = G * ([tex]m_{1}[/tex] * [tex]m_{2}[/tex]) / r²
where:
F is the gravitational force between two masses (weight of the man in this case),
G is the gravitational constant (6.674 x 10⁻¹¹ N(m/kg)²),
[tex]m_{1}[/tex] is the mass of the man (67 kg),
[tex]m_{2}[/tex] is the mass of the Earth (5.97 x 10²⁴ kg), and
r is the distance from the center of the Earth to the man in the spacecraft, which is the radius of the Earth plus the altitude of the spacecraft (6.38 x 10⁶ m + 263 x 10³ m).
Plugging in the values:
F = (6.674 x 10⁻¹¹ N(m/kg)²) * (67 kg * 5.97 x 10²⁴ kg) / (6.38 x 10⁶ m + 263 x 10³ m)²=3.85 x 10⁵ N
After calculating the above expression, we get the weight in newtons. To convert the weight to pounds, we use the conversion 1 newton = 0.224809 pounds. so the weight of the person in pounds will be 8.66 x 10⁴
