On October 15, 2001, a planet was discovered orbiting around the star x. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days.

a. What is the mass of x?
b. Express your answer in terms of our sun's mass.

t^2=4(3.14)^2r^3

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GM

M=2.3*10^30kg

To calculate the mass of star X, you can use the third law of Kepler's planetary motion, which states that the square of a planet's orbital period is proportional to the cube of its average distance from the center of the star. The formula for this is:

(Mx + Mp) = (4π^2 / G) * (r^3 / T^2)

Where Mx is the mass of the star, Mp is the mass of the planet, G is the gravitational constant, r is the orbital distance, and T is the orbital period.

a. To find the mass of star X (Mx), we need to rearrange the formula to solve for Mx:

Mx = (4π^2 / G) * (r^3 / T^2) - Mp

In this case, we are assuming the mass of the planet (Mp) is negligible compared to the mass of the star, so we can ignore it in our calculations.

The value of G (Gravitational constant) is approximately 6.67430 x 10^-11 N(m/kg)^2.

Substituting the given values:
r = 10.5 million kilometers = 10.5 x 10^6 kilometers = 10.5 x 10^9 meters
T = 6.3 days = 6.3 x 24 x 60 x 60 seconds

Plugging these values into the equation and using the given values of π and G, we get:

Mx = (4 * 3.1416^2 / (6.67430 x 10^-11)) * (10.5 x 10^9)^3 / (6.3 x 24 x 60 x 60)^2

Evaluating this equation will give you the mass of star X.

b. To express the answer in terms of our Sun's mass (Msun), you can divide the mass of star X by the mass of the Sun:

Mx / Msun

The mass of our Sun, Msun, is approximately 1.989 x 10^30 kilograms.

By dividing Mx by Msun, you will get the mass of star X relative to that of our Sun.