How to Calculate the Mass of Jupiter Using Orbital Data

[bona0002]

Hi guys,

I'm not sure if I'm going about this the correct way, but it seems to be the only one that makes sense right now. The problem reads: Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22E5 km. From these data, determine the mass of Jupiter.

So, with that in mind, the equation that pops out at me is T^2 = (4*pi^2)(a^3)/(G*M_big_). Now, assuming that M_big_ is the size of jupiter, one can solve for M_big_: M_big_ = (4*pi^2)(a^3)/(T^2*G). Before substituition, I convered 1.77 days into 1.53E5 seconds. Then, I substituted: M_big_ = ((4*pi^2)*(4.22E5km)^3)/((1.53E5)^2)*(6.67E-11) = 1.07E7 kg.

So, is my process right and I'm simply punching it in wrong, or is it that my logic is flawed?

Thanks!

 

[rude man]

Hi guys,

I'm not sure if I'm going about this the correct way, but it seems to be the only one that makes sense right now. The problem reads: Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22E5 km. From these data, determine the mass of Jupiter.

So, with that in mind, the equation that pops out at me is T^2 = (4*pi^2)(a^3)/(G*M_big_). Now, assuming that M_big_ is the size of jupiter, one can solve for M_big_: M_big_ = (4*pi^2)(a^3)/(T^2*G). Before substituition, I convered 1.77 days into 1.53E5 seconds. Then, I substituted: M_big_ = ((4*pi^2)*(4.22E5km)^3)/((1.53E5)^2)*(6.67E-11) = 1.07E7 kg.

So, is my process right and I'm simply punching it in wrong, or is it that my logic is flawed?

Thanks!

Change km to m.

 

[bona0002]

Change km to m.

I did. The answer I get then is 1.07E10, which is supposedly incorrect.

 

[Dewgale]

I did. The answer I get then is 1.07E10, which is supposedly incorrect.

From what I can see, the formula you want is \frac{2πr}{T}=\sqrt{\frac{GM}{r}}

With M being the mass of Jupiter, G being the gravitational constant, r being the radius from the centre of Jupiter, and T being the period.

Good luck :)

 

[bona0002]

Alright, figured it out. Turns out I had the process down just fine, but just that when punching in the numbers on my calculator, I forgot to cube a. Thanks for the help guys!