Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How to calculate the mass of the Sun?

Answer
VerifiedVerified
425.7k+ views
1 likes
like imagedislike image
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,
Fgravitational=Fcentripetal
Fgravitational=GMmr2(1) where G= Universal Gravitational constant, M= mass of the Sun, m= mass of the Earth and r= orbital radius of the earth= distance between the Sun and the Earth.
Fcentripetal=mv2r(2) where m= mass of the Earth, v= velocity of the Earth around the Sun and r= orbital radius of the earth= distance between the Sun and the Earth.
Comparing both equation (1) and (2) we get,
GMmr2=mv2r
Eliminating m from both sides we get,
GMr=v2
Arranging the equation we get,
M=rv2G(3)
The known values are,
G=6.67×1011 N.m2kg
r=1.5×1011 m
v=2πrT where T is the time required for the Earth to complete one revolution around the Sun.
T=365.25×24×60×60=3.15×107 s
Now, v=2×3.14×1.5×10113.15×107=3×104 ms
Substituting all the values in equation (3) we get,
M=1.5×1011×(3×104)26.67×1011=1.989×1030 kg
Thus, the mass of the Sun is 1.989×1030 kg.


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.


Latest Vedantu courses for you
Grade 10 | MAHARASHTRABOARD | SCHOOL | English
Vedantu 10 Maharashtra Pro Lite (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for MAHARASHTRABOARD students
PhysicsPhysics
BiologyBiology
ChemistryChemistry
MathsMaths
₹36,600 (9% Off)
₹33,300 per year
Select and buy