14 Given that the mass and radius of Jupiter are respectively 1 90 1027kg and 7 15 104km, calculate the escape velocity from the surface of the planet
To calculate the escape velocity from the surface of a planet, you can use the formula:
v = √(2GM/r)
Where:
- v is the escape velocity
- G is the gravitational constant (approximately 6.674 × 10^(-11) N m^2/kg^2)
- M is the mass of the planet
- r is the radius of the planet
In this case, the given values for Jupiter are:
- Mass (M) = 1.90 × 10^27 kg
- Radius (r) = 7.15 × 10^4 km
To solve the problem, we need to convert the radius from kilometers to meters:
r = 7.15 × 10^4 km × 10^3 m/km = 7.15 × 10^7 m
Now, let's plug the values into the formula:
v = √(2 × 6.674 × 10^(-11) N m^2/kg^2 × 1.90 × 10^27 kg / 7.15 × 10^7 m)
Simplifying the equation:
v = √(2 × 6.674 × 1.90 / 7.15) × 10^(-11) × 10^27 / 10^7 m/s
v = √(2 × 6.674 × 1.90 × 10^(16) / 7.15) m/s
v ≈ √(2.54 × 10^17) m/s
Using a calculator, we find:
v ≈ 5.04 × 10^8 m/s
Therefore, the escape velocity from the surface of Jupiter is approximately 5.04 × 10^8 m/s.