anonymous
  • anonymous
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?
Physics
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SOLVED
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katieb
  • katieb
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IrishBoy123
  • IrishBoy123
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
  • IrishBoy123
"duh" we are comparing things so it ought to cancel out...
UnkleRhaukus
  • UnkleRhaukus
\[W_\oplus=F_\oplus = G\frac{M_\oplus m}{R_\oplus^2}=mg_\oplus\]\[W_x=F_x = G\frac{M_x m}{R_x^2}=mg_x\] \[R_x=2R_\oplus,\qquad M_x=8M_\oplus \] \[W_x=F_x = G\frac{(8M_\oplus) m}{(2R_\oplus)^2}=\dots%\left(\frac84\right)G\frac{M_\oplus m}{R_\oplus^2}=2W_\oplus \]

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