An astronaut has weight W on Earth. The astronaut travels to a planet that has a mass 8 times greater than Earth's mass, and its radius is 2 times greater than Earth's radius. What is the astronaut's weight on the planet?

Question

irishboy123 · Answer

from Newton's Law for gravitation, we know that:

$\huge F = \frac{G \ M \ m}{r^2}$   [F is the proxy for weight]

so:

$\huge G = \frac{F \ r^2 }{\ Mm} = const.$

so

$\huge \frac{F_1 \ r_1^2 }{\ M_1m} = \frac{F_2 \ r_2^2 }{\ M_2m}$

thus:

$\huge \frac{F_1 \ r_1^2 }{\ M_1} = \frac{F_2 \ r_2^2 }{\ M_2}$

that's weird, m is irrelevant......

$\huge F_2 = F_1 (\frac{M_2}{M_1})( \frac{r_1}{r_2})^2$

so his actual mass is meaningless.

irishboy123 · Answer

"duh"

we are comparing things so it ought to cancel out...

unklerhaukus · Answer

$$W_\oplus=F_\oplus = G\frac{M_\oplus m}{R_\oplus^2}=mg_\oplus$$$$W_x=F_x = G\frac{M_x m}{R_x^2}=mg_x$$

$$R_x=2R_\oplus,\qquad M_x=8M_\oplus $$

$$W_x=F_x = G\frac{(8M_\oplus) m}{(2R_\oplus)^2}=\dots%\left(\frac84\right)G\frac{M_\oplus m}{R_\oplus^2}=2W_\oplus
$$