You are standing on a planet with a radius 10,000kilometers. It's mass is 10^26 kg. What is the planet's escape velocity from where your standing? Ignore rotation of the planet.
(1/2) m Vescape^2 = G m M/R
The term on the right is the potential energy change necessary to escape.
m is the object's mass (which cancels out)
M is the planet's mass
G is the universal gravity constant
Vescape = sqrt(2G*M/R)
Do the numbers
vescape=sqrt(2g*m/r)
To calculate the escape velocity of a planet, we can use the formula:
Escape Velocity = √(2 * Gravitational Constant * Mass of the Planet / Radius of the Planet)
First, let's calculate the escape velocity using the given values:
Radius of the planet (r) = 10,000 kilometers = 10,000,000 meters
Mass of the planet (m) = 10^26 kg
Gravitational Constant (G) = 6.67430 × 10^-11 m^3 kg^−1 s^−2
Substituting these values into the formula, we get:
Escape Velocity = √(2 * 6.67430 × 10^-11 m^3 kg^−1 s^−2 * 10^26 kg / 10,000,000 meters)
Simplifying further:
Escape Velocity = √(2 * 6.67430 × 10^-11 * 10^26 / 10,000,000)
Escape Velocity = √(2 * 6.67430 × 10^15)
Escape Velocity ≈ √(1.33486 × 10^16)
Escape Velocity ≈ 3.65 × 10^7 m/s
So, the escape velocity from the surface of this planet is approximately 3.65 × 10^7 meters per second.