Planet Motion: Calculate Star Mass

[myoplex11]

Homework Statement

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)

Homework Equations

G Mp Ms / r^2 = Mp V^2/r

The Attempt at a Solution

Ms = v^2 r /G
is my solution correct

 

[Janus]

Looks good to me.

 

[thomate1]

Your solution is partially correct. The equation you have written is the correct equation to use to calculate the mass of the star. However, you have not included all of the necessary variables and units in your equation. The correct equation should be:

Ms = (v^2 * r) / (G * Mp)

Where:
Ms = mass of the star (in kg)
v = orbital velocity of the planet (in m/s)
r = distance between the planet and the star (in m)
G = gravitational constant (6.67 * 10^-11 N*m^2/kg^2)
Mp = mass of the planet (9.9 * 10^23 kg)

To convert the given values to the correct units, we need to convert the orbital velocity from km/s to m/s and the distance from AU to m. This gives us:

v = 32 km/s * (1000 m/km) = 32,000 m/s
r = 5.6 AU * (1.496 * 10^11 m/AU) = 8.375 * 10^11 m

Plugging these values into the equation, we get:

Ms = (32,000^2 * 8.375 * 10^11) / (6.67 * 10^-11 * 9.9 * 10^23)
= 1.152 * 10^30 kg

Therefore, the mass of the star is approximately 1.152 * 10^30 kg. It is important to note that this is an estimated value, as we have rounded some of the values and the given values may not be exact.