
How to calculate the mass of the Sun?
Answer
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Hint:The gravitational attraction between the Sun and the Earth is due to the centripetal force which is causing the circular motion of the Earth around the Sun. We can use Newton’s law of universal gravitation to find the mass of the Sun.
Complete step-by-step solution:
From Newton’s Law of Gravitation, we can find the mass of the Sun without even visiting the Sun. This same technique can be employed to find the mass of other stars like Cygnus X-1.
Now we can say that,
where Universal Gravitational constant, mass of the Sun, mass of the Earth and orbital radius of the earth distance between the Sun and the Earth.
where mass of the Earth, velocity of the Earth around the Sun and orbital radius of the earth distance between the Sun and the Earth.
Comparing both equation and we get,
Eliminating from both sides we get,
Arranging the equation we get,
The known values are,
where is the time required for the Earth to complete one revolution around the Sun.
Now,
Substituting all the values in equation we get,
Thus, the mass of the Sun is .
Note:The orbital radius between the Sun and the Earth is a mean radius. The path of orbit between the Sun and the Earth is not circular. It is elliptical, so we have to take the mean radius. It must be made sure that the distance measurement must be in meters, time in seconds in order to find the proper result.
Complete step-by-step solution:
From Newton’s Law of Gravitation, we can find the mass of the Sun without even visiting the Sun. This same technique can be employed to find the mass of other stars like Cygnus X-1.
Now we can say that,
Comparing both equation
Eliminating
Arranging the equation we get,
The known values are,
Now,
Substituting all the values in equation
Thus, the mass of the Sun is
Note:The orbital radius between the Sun and the Earth is a mean radius. The path of orbit between the Sun and the Earth is not circular. It is elliptical, so we have to take the mean radius. It must be made sure that the distance measurement must be in meters, time in seconds in order to find the proper result.
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