Question

Question 6The Sun has a mass of about 1.99 x 10^30 kg. A relatively unknownplanet named Earth orbits the Sun with a mean orbital radius of about1.496 x 10^11 meters.Calculate the orbital speed of the Earth, in m/s, as it orbits the Sun

Answer 1

The formula for calculating the orbital speed of the eqrth as it orbits the sun is expressed as

`V\text{ = }\sqrt[]{(GM)/(R)}`

Where

G is the gravitational constant whose value is 6.673 x 10^- 11 Nm^2/kg^2

M is the mass of the central body about which the satelite orbits

R is the ardius of orbit of the satelite

From the information given,

M = 1.99 x 10^30 kg

R = 1.496 x 10^11

By substituting these values into the formula, we have

`\begin{gathered} V\text{ = }\sqrt[]{\frac{6.673\text{ }*10^(-11)*1.99\text{ }*10^(30)}{1.496\text{ }*10^(11)}} \\ V\text{ = 29793.48 m/s} \end{gathered}`

The orbital speed of the Earth, in m/s, as it orbits the Sun is 29793.48 m/s