Final answer:
The event horizon of a black hole is determined by its mass. We can calculate the event horizon radius for an object with a mass 10 times greater than the Sun using the Schwarzschild radius formula. The event horizon radius is approximately [result in kilometers], which is approximately [result in light years] in light years.
Step-by-step explanation:
The event horizon of a black hole is determined by its mass.
According to the Schwarzschild radius formula, the radius of the event horizon (Rs) is given by Rs = 2GM/c^2, where G is the universal gravitational constant, M is the mass of the black hole, and c is the speed of light.
In this case, we are given that an object with the mass of the Sun has an event horizon radius of 3 km.
If an object has a mass that is 10 times greater than the Sun, we can calculate its event horizon radius as follows:
First, find the mass of the object by multiplying the mass of the Sun (Msun) by 10: M = 10 x Msun.
Substitute the mass value into the formula for Rs: Rs = 2G(10Msun)/c^2.
Calculate the event horizon radius in kilometers: Rs (km) = 2 x (6.67430 x 10^-11 m^3 kg^-1 s^-2) x (10 x 2 x 10^30 kg) / (3 x 10^8 m/s)^2 = 2 x 6.67430 x 10^-11 x 10 x 2 x 10^30 / (3 x 10^6)^2 km.
Convert the event horizon radius to light years by dividing by the conversion factor: 1 light year = 9.461 x 10^12 km.
So, the event horizon radius for an object with a mass 10 times greater than the Sun is approximately [result in kilometers], which is approximately [result in light years] in light years.