Question

What would be the weight of a 59.1-kg astronaut on a planet with the same density as Earth and having twice Earth's radius? . . I am getting 290, but I dont know if that is correct... . A) 580N. B) 290N. C) 1160N. D) 2320N. E) 1200N

Answer 1

The astronaut's weight on the Earth's surface can be  determined from  
F = m g = 579.2 N subsituting  mass equal to 59.1 kg and acceleration due to gravity equal to 9.8 m/s². When the variables are mass of the earth and the radius of the earth, F = k m / r². Thus, doubling the mass of the earth would double his weight and doubling the radius would decrease the original weight by 1/4.  Hence, 579.2 N* 2* 1/4 equal to 290 N. Answer is B.

Answer 2

The weight of a 59.1-kg astronaut on a planet would be about

C) 1160 N

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Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

$\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }$

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem !

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Given:

mass of the astronaut = m = 59.1 kg

density of Earth = density of Planet = ρ

radius of Earth = R₁ = R

radius of Planet = R₂ = 2R

Asked:

weight of the astronaut on planet = w₂ = ?

Solution:

We will compare the weight of the astronaut on planet and earth as follows:

$w_2 : w_1 = mg_2 : mg_1$

$w_2 : w_1 = g_2 : g_1$

$w_2 : w_1 = G\frac{m_2}{(R_2)^2} : G\frac{m_1}{(R_1)^2}$

$w_2 : w_1 = G\frac{\rho V_2}{(R_2)^2} : G\frac{\rho V_1}{(R_1)^2}$

$w_2 : w_1 = \frac{V_2}{(R_2)^2} : \frac{V_1}{(R_1)^2}$

$w_2 : w_1 = \frac{\frac{4}{3} \pi (R_2)^3}{(R_2)^2} : \frac{\frac{4}{3} \pi (R_1)^3}{(R_1)^2}$

$w_2 : w_1 = R_2 : R_1$

$w_2 : w_1 = 2R : R$

$w_2 : w_1 = 2 : 1$

$w_2 = 2w_1$

$w_2 = 2m g_1$

$w_2 = 2(59.1)(9.8)$

$w_2 \approx 1160 \texttt{ Newton}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields