Universal gravitation to find the mass of a star

AI Thread Summary
To find the mass of a distant star with a planet orbiting at a radius of 3.51X10^11m and a period of 853 days, the universal gravitation formula T^2 = (4π^2 * R^3) / (G * m) is used. Initial calculations yielded incorrect mass values due to errors in exponent handling and the application of the formula. A suggestion was made to recheck calculations, particularly focusing on the orders of magnitude, which should be around 10^30 for the mass. The discussion emphasizes the importance of accuracy in calculations and the correct application of gravitational equations. Accurate results are crucial for understanding stellar masses in astrophysics.
BoldKnight399
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A distant star has a single plante orbiting at a radius of 3.51X10^11m. The period of the planet's motion around the star is 853 days. What is the mass of the star? The universal gravitational constant is 6.67259X10^-11N m^2/kg^2. Answer in kg.

Alrighty. So I tried to find the mass by using the equation:
T^2=(4pi)^2 X R^2/Gm

so that became:
(73699200sec)^2=(4pi)^2 X (3.51X10^11)/(6.67259X10^-11)X(mass star)

(5.43157X10^15)=(5.5427X10^13)/(6.67253X10^-11)X(m)
thus m=6.5388X10^-9

Even I noticed that the answer shouldn't work and doesn't make sense. Can anyone see where I went wrong, or have a better approach?
 
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The R should be cubed (R^3). Also, rather than (4*pi)^2, you would have 4(pi)^2.
 
Ok so I did that and got:
5.4315X10^15 =(4.2875X10^34)/(6.67259X10^-11 X m)
and that m=2.178X10^12

that was wrong. So where in there did I go wrong?
 
M = (4*(pi)2*R3)/(G*T2)
 
ok, I did that and got: 38214641.16 kg and that answer is still wrong. I did it so that:
m=(39.4784176)(3.51X10^11)^3/(6.67259X10^-11)(73699200s)^2

so where am I going wrong?
 
BoldKnight399 said:
Ok so I did that and got:
5.4315X10^15 =(4.2875X10^34)/(6.67259X10^-11 X m)
and that m=2.178X10^12

that was wrong. So where in there did I go wrong?

It would seem that you have mixed up some orders of magnitude. Just from looking at the exponents of the 10s' above, one should be able to see that the order of magnitude should be around 30 (i.e. x10^30). Perhaps the most logical step now would be to recheck your calculations.
 
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