Use the period of the earth (2.34 y), its
mean orbital radius (1.496 × 1011 m), and
the universal gravitational constant (6.673 × 10−11 N · m2/kg2) to calculate the mass of sun. Answer in units of kg.
First calculate the speed if earth in its orbit
V = 2 pi R / (3.1558*10^7 s)= ? m/s
(The denominator is 1 year expressed in seconds)
Then get the mass M of the sun from
M G/R^2 = V^2/R (centripetal acceleration)
so is the correct answer 3.632308558 X 10 ^29 ???
The Sun's mass is 1.99 x 10^30 kg.
You made a mistake somewhere.
V = 2pi R/ 2.34(3.1558X 10^7s)
(2pi R/ 2.34(3.1558X 10^7s)^2 / 1.496X10^11 = ANS
ANS/ G/R^2 - > Ans/ (6.673X10^-11/1.496X10^11)
= 3.632308558 X 10^29
i did everything right i believe
The problem is this: You used the wrong orbital period of the Earth. Did they really tell you it is 2.34 years? It is actually 1.000 years. That is the definition of a year!
The orbital radius and G value that you used are correct.
yes its given as 2.34 years. its an online hw generator that gives everyone different sets of numbers.
To calculate the mass of the Sun, you can use the following formula:
M = (4π² * r³) / (G * T²)
Where:
M = mass of the Sun
π = pi (approximately 3.14159)
r = mean orbital radius of the Earth around the Sun
G = universal gravitational constant
T = period of the Earth
Now let's plug in the values and calculate the mass of the Sun:
M = (4π² * (1.496 × 10^11)^3) / (6.673 × 10^−11 * (2.34 * 365.25 * 24 * 60 * 60)^2)
First, let's simplify the numerator:
Numerator = 4π² * (1.496 × 10^11)^3
= 4π² * (1.496 × 10^11 * 1.496 × 10^11 * 1.496 × 10^11)
= 4π² * (3.350867136 × 10^33)
Next, let's simplify the denominator:
Denominator = (6.673 × 10^−11 * (2.34 * 365.25 * 24 * 60 * 60)^2)
= (6.673 × 10^−11 * (2.34 * 31557600)^2)
= (6.673 × 10^−11 * 736381489.6^2)
= (6.673 × 10^−11 * 5.4198442 × 10^17)
Now, let's calculate the final result:
M = Numerator / Denominator
= (4π² * (3.350867136 × 10^33)) / (6.673 × 10^−11 * 5.4198442 × 10^17)
By performing this calculation, we obtain the mass of the Sun in units of kg.