[tex]\huge{\color{lavender}{\underline{\color{white} {\underline{\color{white} {\textbf{\textsf{\colorbox{black}{Question:-}}}}}}}}}[/tex] Calculate the mass of the Sun.
The Sun's mass can be calculated by rearranging Kepler's third law equation to give M = 4π2a3/Gp2. Here M is the mass of the Sun; p is the orbital period; a is the orbit semi-major axis distance, and G is the gravitation constant.
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Answer:
The Sun's mass can be calculated by rearranging Kepler's third law equation to give M = 4π2a3/Gp2. Here M is the mass of the Sun; p is the orbital period; a is the orbit semi-major axis distance, and G is the gravitation constant.
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Sure! Here's a step-by-step explanation to calculate the mass of the Sun:
Step 1: Determine the orbital radius of the Earth around the Sun.
The average orbital radius of the Earth (r) is approximately 149.6 million kilometers or 93 million miles.
Step 2: Determine the orbital period of the Earth around the Sun.
The orbital period of the Earth (T) is approximately 365.25 days or 31,557,600 seconds.
Step 3: Calculate the gravitational constant (G).
The gravitational constant (G) is approximately 6.67430 × 10^-11 m^3/kg/s^2.
Step 4: Use the formula to calculate the mass of the Sun.
The formula is M = (4π^2 * r^3) / (G * T^2), where M represents the mass of the Sun.
Let's calculate step by step:
Step 1:
If we convert the average orbital radius of the Earth (r) to meters, it becomes:
r = 149.6 million kilometers * 1000 meters/kilometer = 149.6 billion meters.
Step 2:
The orbital period of the Earth (T) is already given as 31,557,600 seconds.
Step 3:
The gravitational constant (G) is approximately 6.67430 × 10^-11 m^3/kg/s^2.
Step 4:
Substitute the values into the formula:
M = (4π^2 * (149.6 billion)^3) / (6.67430 × 10^-11 * (31,557,600)^2).
Calculating this equation will give us the mass of the Sun in kilograms.
After performing the calculations, the mass of the Sun is approximately 1.989 x 10^30 kilograms.
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