Answer:
The mass of the galaxy is 2.096 × 10⁴¹ kg
Explanation:
Newton's Version of Kepler's Third law of motion II is:
p² = 4π² a³ / G(M + m) (1)
where
Step 1:
The orbital period of the sun around the galaxy is:
p = 230×10⁶ years × (3.15×10⁷ s / 1 year)
p = 7.25 × 10¹⁵ s
Step 2:
The average distance between the sun and the galactic centre is :
a = 28000 light-years × (9.46×10¹⁵ m / 1 light-year)
a = 2.65×10²⁰ m
Step 3:
Substitute the values of p and a into equation (1):
Rearranging equation (1) to make M the subject of the formula, we get:
M = (4π² a³ / G p²) - m
M = (4π²(2.65×10²⁰ m)³ / (6.67×10⁻¹¹ m)(7.25 × 10¹⁵ s)²) - 1.9891 × 10³⁰ kg
M = 2.096 × 10⁴¹ kg
Therefore, the mass of the galaxy is 2.096 × 10⁴¹ kg
Answer:
mass of the galaxy = 1.05 * 10^11 solar masses
Explanation:
According to Kepler’s third law, A^3 =P^2
Where A = Average distance of a planet from the sun, in AU
And P = The time taken by the planet to orbit the sun, in years.
Newton’s modification to Kepler’s third law applies to any two objects orbiting a common mass
According to Newton, M1+ M2 = (A^3) / (P^2)
Where M1 and M2 are the masses of the two objects in Solar mass
From the question,
Let M1 = the mass of the sun
and M2= the mass of the milky way galaxy
Distance, A = 28,000 light years
1 light year = 63241.1 AU
A = 28000 * 63241.1
A = 1,770,750,800 AU
Time taken for the orbit, P = 230,000,000 years
M1= 1 solar mass
M2 = ?
Using M1+ M2 = (A^3) / (P^2)
1 + M2 = (1770750800^3)/ (230,000,000^2)
1 + M2 = 1.05 * 10^11
M2 =( 1.05 * 10^11) – 1
M2 = 1.05 * 10^11 solar masses
