Universal gravitation to find the mass of a star

In summary, the conversation discusses an attempt to find the mass of a distant star using the equation T^2=(4pi)^2 X R^2/Gm. However, the resulting mass does not make sense and the individual is seeking help in finding where they went wrong in their calculations.
  • #1
BoldKnight399
79
0
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?
 
Physics news on Phys.org
  • #2
The R should be cubed (R^3). Also, rather than (4*pi)^2, you would have 4(pi)^2.
 
  • #3
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
M = (4*(pi)2*R3)/(G*T2)
 
  • #5
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
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.
 

1. How is universal gravitation used to find the mass of a star?

To find the mass of a star, scientists use the universal law of gravitation, which states that the force of attraction between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. By measuring the orbital period and distance of a smaller object, like a planet or moon, orbiting around a star, scientists can calculate the mass of the star using this equation: M = (4π²r³)/G(T²), where M is the mass of the star, r is the distance between the star and the smaller object, G is the gravitational constant, and T is the orbital period.

2. What role does the gravitational constant play in determining the mass of a star?

The gravitational constant, denoted by G, is a fundamental constant in physics that relates the force of gravity to the masses and distances of objects. In the equation used to find the mass of a star, G is in the denominator, meaning that as its value increases, the mass of the star decreases. Therefore, scientists must have an accurate value for G in order to accurately calculate the mass of a star.

3. Can universal gravitation be used to find the mass of any type of star?

Yes, universal gravitation can be used to find the mass of any type of star as long as there is a smaller object orbiting around it. This includes main sequence stars, white dwarfs, neutron stars, and even black holes. However, the accuracy of the calculation may vary depending on the type of star and the distance and orbital period of the smaller object.

4. How do scientists measure the orbital period and distance of objects orbiting a star?

Scientists use a variety of techniques to measure the orbital period and distance of objects orbiting a star. These techniques include using telescopes to observe the movement of the object over time, analyzing the Doppler shift of the star's light caused by the gravitational pull of the orbiting object, and using spacecrafts to directly measure the distance and velocity of the object.

5. What other factors may affect the accuracy of using universal gravitation to find the mass of a star?

Aside from the distance and orbital period of the smaller object, other factors that may affect the accuracy of using universal gravitation to find the mass of a star include the presence of other massive objects that may also affect the orbit of the smaller object, the shape and size of the star, and any external forces acting on the system. These factors must be carefully considered and accounted for in order to obtain an accurate calculation of the star's mass.

Similar threads

Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
956
  • Introductory Physics Homework Help
Replies
3
Views
851
  • Introductory Physics Homework Help
Replies
2
Views
3K
  • Introductory Physics Homework Help
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
23
Views
2K
Replies
8
Views
798
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
883
  • Introductory Physics Homework Help
Replies
11
Views
1K
Back
Top