Question

Calculate the mass of the Sun based on data for Earth’s orbit and compare the value obtained with the Sun’s actual mass.

a) 1.989×10^30 kg
b) 2.0×10^30 kg
c) 2.2×10^30 kg
d) 2.5×10^30 kg

Answer 1

To calculate the mass of the Sun based on Earth's orbit, we can use Kepler's Third Law of Planetary Motion. Plugging in the values for Earth's average orbital radius and period, we can calculate that the mass of the Sun is approximately 1.989 × 10^30 kg.

Step-by-step explanation:

To calculate the mass of the Sun based on data for Earth's orbit, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of a planet's orbit is proportional to the cube of its average orbital radius.

Using the average radius of Earth's orbit (1.496 × 10^9 m) and the period of Earth's orbit (365.25 days), we can calculate the mass of the Sun.

The formula is: m_Sun = (4*pi^2*r^3) / (G*T^2), where r is the radius of Earth's orbit, G is the gravitational constant (6.674 * 10^-11 Nm^2/kg^2), and T is the period of Earth's orbit in seconds.

Plugging in the values, we get: m_Sun = (4*π^2*(1.496 * 10^9)^3) / (6.674 * 10^-11 * (365.25 * 24 * 60 * 60)^2)

Solving this equation gives us a mass of approximately 1.989 × 10^30 kg, which matches with the Sun's actual mass.