# Homework Help: Universal gravitation 4-determine the weight of astronaut on planet Z

1. Jun 14, 2012

### dani123

1. The problem statement, all variables and given/known data

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.

2. Relevant 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]

3. 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!

2. Jun 14, 2012

### Staff: Mentor

Wow, that is one complicated pile of equations! (Most of which are irrelevant.)

All you need is this:
To find Fg on the planet, just replace the mass and radius of the earth with the mass and radius of the planet and compare. (Hint: Almost no calculation is required.)

3. Jun 14, 2012

### cepheid

Staff Emeritus
A lot of the relevent equations that you posted are actually totally irrelevant. In fact, Newton's universal law of gravitation is all you need, and a couple of the other equations you have there are just Newton's universal law of gravitation applied to specific situations.

For me, step 1 would be to find the mass of the astronaut. It is certainly not 1.7 kg! Think about that for a second. How can a human being have a mass of only 1.7 kg?

Getting the mass shouldn't be too hard, since you know the weight on Earth, and you know g on Earth.

Then the second step, once you have the mass, would be to multiply it by the gp value that you computed to get the weight on the planet.

EDIT: Er, yeah, or you could do what Doc Al said, which is even smarter.

4. Jun 14, 2012

### dani123

do I multiply the gp with the mass of the astronaut on earth in order to find out the value of his mass on the planet Z? Just want to make sure I understood that correctly...

5. Jun 14, 2012

### Staff: Mentor

You can certainly do it that way. The mass is the same everywhere, of course. But you'll have to redo your calculation of gp. You can do that easily by just comparing the calculation to that of ge. (Again, hardly any calculation needed. But more than if you followed my original method.)

6. Jun 14, 2012

### dani123

ok so i tried to do what you said but i just ended up getting mass=84.99kg.... which is only 0.1kg off from what the mass is on earth...

7. Jun 14, 2012

### Staff: Mentor

I don't quite understand what you mean. There's only one mass. If you calculate the astronaut's mass on earth then that is also his mass on the planet. (But that value for mass looks OK.)

8. Jun 15, 2012

### dani123

so why do they even ask what the mass on planet Z is, if they are both the same?

9. Jun 15, 2012

### BruceW

The question asked for weight, not mass. Weight and mass are two different things in physics, even though in everyday language they are often used interchangeably. You just need to use the physics definition of mass and weight.

10. Jun 15, 2012

### Staff: Mentor

As BruceW already pointed out, they don't ask for the mass on planet Z. They ask for the weight on planet Z.

The only purpose in finding the mass would be to use it to find the weight via Wp = mgp. Which is OK, but, as I have tried to point out, that's the hard way of doing the problem.

11. Jun 23, 2012

### dani123

so is it just g of the planet which I found to be 489.95N/kg, and times that by 85kg (which is the mass of the astronaut)? If I do that I get weight=force due to gravity=41646.12N

12. Jun 23, 2012

### Staff: Mentor

As I said earlier, you'll need to redo your calculation of g on the planet as it is incorrect. But once you have the correct value of g, then you can multiply it by the mass to find the weight on the planet. (That's the hard way, but perfectly OK.)

13. Jun 23, 2012

### dani123

I don't see how my value for g of the planet is wrong though...

14. Jun 23, 2012

### Staff: Mentor

Just for fun, try the easy way. Answer this: If the mass of the planet is increased by a factor of 50, what would happen to the weight of the astronaut? Would it go up or down? By what factor? (Imagine everything else is held fixed.)

Note that this is equivalent to asking: If the mass of the planet is increased by a factor of 50, what would happen to the value of g at the surface?

Last edited: Jun 23, 2012
15. Jun 23, 2012

### Staff: Mentor

Check the number of zeroes in that last calculation.

16. Jun 23, 2012

### dani123

OPS! thank you for noticing that!

17. Jun 23, 2012

### dani123

so the answer should be weight=416.46N?

18. Jun 23, 2012