Calculating Gravity and Weight on Krypton

[Cicima]

Im not sure if this is done right...

The planet Krypton has a moon that circles the planet in a circle that has a period of 40 days (watch units) and is 6 x 10^8 m from the planet's center. The planet's radius is 6.4 x 10^6 m. What would you weigh on Krypton if your mass is 70 KG? Show a free body diagram.

Im guessing use Net force = ma
The net force is the Gravitational force, Gm1m2 / r^2 is = m2 4 (pie)^2 r/ T^2

for the 4 (pie)^2 r/ T^2 r is the distance form the planet's center, to the moon, for T, find how many second 40 days is.

and the other r is the planet's radius

m2 cancels

solve for m1, and yo uhave the mass of the planet.

I guess plug in numbers after that, into the equaltion Fg = Gm1 m2 / r^2

m2 would be the 70 kg







Can someone help me out and tell me if what i am doing looks right?

 

[OlderDan]

Im not sure if this is done right...

Im guessing use Net force = ma
The net force is the Gravitational force, Gm1m2 / r^2 is = m2 4 (pie)^2 r/ T^2

for the 4 (pie)^2 r/ T^2 r is the distance form the planet's center, to the moon, for T, find how many second 40 days is.

and the other r is the planet's radius ?

m2 cancels

solve for m1, and yo uhave the mass of the planet.

I guess plug in numbers after that, into the equaltion Fg = Gm1 m2 / r^2

m2 would be the 70 kg

Can someone help me out and tell me if what i am doing looks right?

All the r in your first equation are the same. r is the distance from the center of Krypton to the center of its moon. The r in the second equation is the radius of the planet. I assume that Fg is the force of gravity, or weight at the planet's surface. If that is what you mean, then you should have the correct result.

 

[Cicima]

Yes that's what i meant. The other r (the one in the 2nd equation) is the radius. So i know how to set it up, the problem is I am not good at plugging it in. What am i doing wrong?

Gm1m2 / r^2 is = m2 4 (pie)^2 r/ T^2
for the 4 (pie)^2 r/ T^2 r is the distance form the planet's center, to the moon, for T, find how many second 40 days is.
m2 cancels
so it would be...

m1/3.6x10^17=39.47 r/t^2
m1/3.6x10^17=39.47 (6x10^8)/1.194x10^13
when i solve for m1 i get 6.84x10^14...that doesn't seem right?

Fg = Gm1 m2 / r^2

m2 would be the 70 kg

and if its right, how do u multiply that times 70 kg...which is m2?

 

[Cicima]

So am i wrong? And if so, where am i plugging them in wrong?

 

[OlderDan]

Yes that's what i meant. The other r (the one in the 2nd equation) is the radius. So i know how to set it up, the problem is I am not good at plugging it in. What am i doing wrong?

m1/3.6x10^17=39.47 r/t^2
m1/3.6x10^17=39.47 (6x10^8)/1.194x10^13
when i solve for m1 i get 6.84x10^14...that doesn't seem right?

and if its right, how do u multiply that times 70 kg...which is m2?

It doesn't look right, but you have not included enough steps to find out what you are doing. I suggest you solve the equation algebraically for m1 before entering any numbers,

 

[Cicima]

It doesn't look right, but you have not included enough steps to find out what you are doing. I suggest you solve the equation algebraically for m1 before entering any numbers,

m1/r^2=4pi^2 r/t^2
thats basically as far as i can solve it...
plug in 345600 for t, and 6x10^8 for r, then its just basic calculator plug ins from there getting m1/r^2=.0019...so what am i doing wrong?

 

[OlderDan]

m1/r^2=4pi^2 r/t^2
thats basically as far as i can solve it...
plug in 345600 for t, and 6x10^8 for r, then its just basic calculator plug ins from there getting m1/r^2=.0019...so what am i doing wrong?

What became of G? Why not multiply both sides by r² ?

 

[Cicima]

What became of G? Why not multiply both sides by r² ?

Oops forgot G.


Gm1=4pi^2 r^3/t^2

That would be simplified then...so why does my answer look so wrong when i plug in 345600 for t, and 6x10^8?

 

[Cicima]

Oops forgot G.


Gm1=4pi^2 r^3/t^2

That would be simplified then...so why does my answer look so wrong when i plug in 345600 for t, and 6x10^8?

Then...
Gm1=39.478 r^3/3456000^2
Gm1=39.478 r^3/1.194x10^13
then you divide each side by G...so what am i doing wrong? Maybe I am taking r^3 wrong? How do you do that just to make sure I am doing it right.

 

[OlderDan]

Oops forgot G.


Gm1=4pi^2 r^3/t^2

That would be simplified then...so why does my answer look so wrong when i plug in 3456000 for t, and 6x10^8?

Gm1=4pi²*r³/t²
m1=4*pi²*r³/(t²*G) = 1.07 x 10^25 kg on my calculator

Edit: The original value posted was incorrect because it used the OP's value for t that was off by a factor of 10. The value in the quote has been corrected, and the correction for m1 made here

 

[Cicima]

1.07 x 10^27 kg now needs to be multiplied by m12 which is 70kg. so can i just multiply 1.07x10^27 by 70, then divide it by r^2 and that's it?

Quick question, if I am doing R^2, would that mean if r is 6.4x10^6 that r^2 is 6.4x10^12?

 

[Cicima]

Gm1=4pi²*r³/t²
m1=4*pi²*r³/(t²*G) = 1.07 x 10^27 kg on my calculator

can u show me the steps because i still can't get that answer, after that i know how to do it...thanks.

 

[OlderDan]

Quick question, if I am doing R^2, would that mean if r is 6.4x10^6 that r^2 is 6.4x10^12?

NO

(6.4x10^6)^2 = 6.4x10^6x6.4x10^6 = (6.4)^2x10^12 = 40.96x10^12 = 4.096x10^13

Maybe this is your problem??

 

[Cicima]

can u show me the steps because i still can't get that answer...i get like 7.139x10^13, then i multiply it by 70 and 9.8 and divide it by (6.4x10^6)^2 and get 1195. Howd u get 1.07x10^27? What do you do after you get it? if u plug it into the 2nd equation you get a crazy number.

 

[OlderDan]

can u show me the steps because i still can't get that answer...i get like 7.139x10^13, then i multiply it by 70 and 9.8 and divide it by (6.4x10^6)^2 and get 1195. Howd u get 1.07x10^27? What do you do after you get it? if u plug it into the 2nd equation you get a crazy number.

t = 40days*(24hr/day)*(60min/hr)*(60sec/min) = 3.456x10^6 s <== You had this as 3.456x10^5 and I used your number, so my exponent was a bit off

t² = (3.456x10^6 s)(3.456x10^6 s) = 3.456²x10^12 s² = 1.194x10^13 s²

t²*G = (1.194x10^13 s²)*(6.673x10^-11 N m²/kg²) = 7.97x10² N m² s²/kg² = 7.97x10² m³/kg


m1 = 4*pi²*r³/(t²*G) = 4*3.14²*(6x10^8 m)³/(7.97x10² m³/kg)

m1 = 4*9.870*6³x10^24 m³/(7.97x10² m³/kg)

m1 = 8.527 x10^27 kg/(7.97x10²)

m1 = 1.07 x10^25 kg