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dani123
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Homework Statement
An astronaut weighs 833N on the surface of the Earth. Determine the weight of the astronaut on Planet Z if the planet's mass is 50.0 times the mass of the Earth and has a radius of 10.0 times the radius of the Earth.
Homework Equations
Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3
motion of planets must conform to circular motion equation: Fc=4∏2mR/T2
From Kepler's 3rd law: R3/T2=K or T2=R3/K
Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2
Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2
Newton's Universal Law of Gravitation: F=Gm1m2/d2
value of universal gravitation constant is: G=6.67x10-11N*m2/kg2
weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2
g=Gme/(Re)2
determine the mass of the Earth: me=g(Re)2/G
speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h
period of the Earth-orbiting satellite: T=2∏√R3/GMe
Field strength in units N/kg: g=F/m
Determine mass of planet when given orbital period and mean orbital radius: Mp=4∏2Rp3/GTp[Kepler's 3rd law: (Ta/Tb)2=(Ra/Rb)3
motion of planets must conform to circular motion equation: Fc=4∏2mR/T2
From Kepler's 3rd law: R3/T2=K or T2=R3/K
Gravitational force of attraction between the sun and its orbiting planets: F=(4∏2Ks)*m/R2=Gmsm/R2
Gravitational force of attraction between the Earth and its orbiting satelittes: F=(4∏2Ke)m/R2=Gmem/R2
Newton's Universal Law of Gravitation: F=Gm1m2/d2
value of universal gravitation constant is: G=6.67x10-11N*m2/kg2
weight of object on or near Earth: weight=Fg=mog, where g=9.8 N/kg
Fg=Gmome/Re2
g=Gme/(Re)2
determine the mass of the Earth: me=g(Re)2/G
speed of satellite as it orbits the Earth: v=√GMe/R, where R=Re+h
period of the Earth-orbiting satellite: T=2∏√R3/GMe
Field strength in units N/kg: g=F/m
Determine mass of planet SUP]2[/SUP]
The Attempt at a Solution
Fg=weight=833N on surface of the Earth
mp=50 * (5.98*1026 kg)
Rp=10*(6.38*106m)= 6380000 m
I used gp=GMp/(Rp)2=489.95 N/kg
I also used Fg=gxmo and manipulated the equation to solve for mo=1.7 kg
Just wondering if someone would be able to have a look at my attempt and let me know if its wrong and if it is maybe point out where it is that I made my mistake. It would be greatly appreciated! Thanks again so much in advance!