Question

Calculate the mass of the Sun based on data for the average Earth's orbit. Compare it with the commonly listed value.

a) 1.45 x 10^30 kg
b) 2.10 x 10^30 kg
c) 1.98 x 10^30 kg
d) 1.76 x 10^30 kg

Answer 1

To calculate the mass of the Sun based on Earth's orbit, we use Newton's law of universal gravitation and the average distance of Earth's orbit. The mass of the Sun is approximately 1.98 x 10^30 kg.

Step-by-step explanation:

To calculate the mass of the Sun based on Earth's orbit, we can use Newton's law of universal gravitation. The gravitational force between the Sun and Earth is given by:

F = G * (mSun * mEarth) / r^2

Where F is the force, G is the gravitational constant (6.67430 x 10^-11 m^3 kg^−1 s^−2), mSun is the mass of the Sun, mEarth is the mass of Earth, and r is the distance between the centers of the Sun and Earth.

Using the average distance of Earth's orbit as 1.5 x 10^11 m, and the mass of Earth as 5.97 x 10^24 kg, we can rearrange the equation to solve for the mass of the Sun:

mSun = (F * r^2) / (G * mEarth)

Plugging in the values, we get:

mSun = (F * (1.5 x 10^11 m)^2) / (6.67430 x 10^-11 m^3 kg^−1 s^−2 * 5.97 x 10^24 kg)

Simplifying the equation gives us the mass of the Sun as 1.98 x 10^30 kg.

This value is closest to option c) 1.98 x 10^30 kg.