# Universal gravitation to find the mass of a star

1. Jan 27, 2010

### BoldKnight399

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?

2. Jan 27, 2010

### Gear300

The R should be cubed (R^3). Also, rather than (4*pi)^2, you would have 4(pi)^2.

3. Jan 27, 2010

### BoldKnight399

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?

4. Jan 27, 2010

### Gear300

M = (4*(pi)2*R3)/(G*T2)

5. Jan 27, 2010

### BoldKnight399

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?

6. Jan 27, 2010

### inutard

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.