Find tha schwarzschild radius of tha earth ,whose mass 5.98×10^24kg
don't you have a handy formula for this problem?
Just plug in your value for M.
To find the Schwarzschild radius of the Earth, we will use the formula:
Rs = (2 * G * M) / c^2
Where:
Rs is the Schwarzschild radius
G is the gravitational constant (6.674 × 10^-11 N m^2 / kg^2)
M is the mass of the Earth (5.98 × 10^24 kg)
c is the speed of light (299,792,458 m/s)
Let's calculate it now:
Rs = (2 * 6.674 × 10^-11 N m^2 / kg^2 * 5.98 × 10^24 kg) / (299,792,458 m/s)^2
Rs = (2 * 6.674 × 5.98 × 10^13 N m^2) / (8.98755 × 10^16 m^2/s^2)
Rs = (79.79052 × 10^13 N m^2) / (8.98755 × 10^16 m^2/s^2)
Rs ≈ 8.8802 mm
Therefore, the Schwarzschild radius of the Earth is approximately 8.8802 millimeters.