Respuesta :
Answer:
4 times
Explanation:
[tex]M[/tex] = mass of the earth
[tex]R[/tex] = radius of the earth
[tex]g_{e}[/tex] = acceleration due to gravity on earth
acceleration due to gravity on the earth is given as
[tex]g_{e} =\frac{GM}{R^{2}}[/tex]
[tex]w_{e}[/tex] = weight of the astronaut on earth
weight of the astronaut on earth is given as
[tex]w_{e} = m g_{e} = \frac{GMm}{R^{2}}[/tex]
[tex]M_{p}[/tex] = mass of the planet = [tex]4 M[/tex]
[tex]R_{p}[/tex] = radius of the planet = R
[tex]g_{p}[/tex] = acceleration due to gravity on earth
acceleration due to gravity on the planet is given as
[tex]g_{p} =\frac{GM_{p}}{R_{p}^{2}}\\g_{p} = \frac{4GM}{R^{2}}\\g_{p} = 4 g_{e}[/tex]
[tex]w_{p}[/tex] = weight of the astronaut on planet
weight of the astronaut on planet is given as
[tex]w_{p} = m g_{p}\\w_{p} = m (4) g_{e}\\w_{p} = 4 w_{e}[/tex]
hence the weight of the astronaut on the planet is four times.
The astronaut's weight on the given planet would be 39.2m (4mg).
The given parameters;
- radius of Earth = R
- mass of Earth = m
- mass of the planet = 4M
The weight of object is calculated as follows;
[tex]W = mg_p[/tex]
where;
- m is the mass of the astronaut
- [tex]g_p[/tex] is the acceleration due to gravity on the planet
The acceleration due to gravity on Earth is given as;
[tex]g = \frac{GM}{R^2} \\\\let \ \frac{G}{R^2} = k\\\\g = kM\\\\k = \frac{g}{M} \\\\\frac{g_1}{M_1} = \frac{g_2}{M_2} \\\\when \ M_2 = 4M_1\\\\\frac{g_1}{M_1} =\frac{g_2}{4M_1} \\\\g_2M_1 = 4M_1g_1\\\\g_2 = 4g_1[/tex]
The acceleration due to gravity on the planet = 4g
The weight of the astronaut is calculated as;
W = m x 4g
W = 4mg
W = (4 x 9.8) m
W = 39.2m
Thus, the astronaut's weight on the planet would be 39.2m.
Learn more here: https://brainly.com/question/8843404
