Question

what would be the weight of a 59.3 - kg astronaut on a planet twice as massive as earth and having twice earths radius?
a) 118 n
b) 1200 n
c) 580 n
d) 1160 n
e) 340 n
f) 290 n

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force is \(F = \frac{GMm}{R^{2}}\), where \(G\) is the gravitational constant, \(M\) is the mass of the planet, \(m\) is the mass of the object (astronaut), and \(R\) is the radius of the planet.

Step2: Analyze the change in mass and radius

Let the mass of Earth be \(M_E\) and radius be \(R_E\). For the new planet, \(M = 2M_E\) and \(R = 2R_E\).
Substitute into the formula: \(F=\frac{G(2M_E)m}{(2R_E)^{2}}=\frac{2GM_Em}{4R_E^{2}}=\frac{1}{2}\frac{GM_Em}{R_E^{2}}\)
The weight of the astronaut on Earth is \(F_E=\frac{GM_Em}{R_E^{2}} = mg_E\) (where \(g_E = 9.8\ m/s^{2}\)). The weight on the new planet \(F=\frac{1}{2}F_E\)
Given \(m = 59.1\ kg\), \(F_E=59.1\times9.8 = 579.18\ N\approx580\ N\)

Answer:

C. 580 N