a 9.9*10^23 kg planet orbits a star in a circular orbit. The planet is 5.6 AU away from the star and has an orbital velocity of 32 km/s. What is the mass of the star. (1AU = 1.496*10^11m)
To find the mass of the star, we can use the formula for orbital velocity in a circular orbit:
v = √(G * M / r)
Where:
v = orbital velocity
G = gravitational constant (6.67430 × 10^-11 m^3/kg/s^2)
M = mass of the star
r = distance between the planet and the star
From the given information, we know:
v = 32 km/s = 32,000 m/s
r = 5.6 AU = 5.6 * 1.496 × 10^11 m
Rearranging the formula, we have:
M = (v^2 * r) / G
Now we can substitute the values and calculate the mass of the star.