Question

Need help!!! A rocket scientist is designing a rocket to visit the planets in the solar system. The velocity that is needed to escape a planet’s gravitational pull is called the escape velocity. The escape velocity depends on the planet’s radius and its mass, according to the equation V escape=square root(2gR where R is the radius and g is the gravitational constant for the particular planet. The rocket’s maximum velocity is exactly double Earth’s escape velocity. The earth’s gravitational pull is 9.8 m/s^2 The earth’s radius is 6.37 x10 ^6 For which planets will the rocket have enough velocity to escape the planet’s gravity?

Answer 1

Mercury, Venus, Earth, Mars, and Uranus

Explanation:

Calculate the escape velocity for each planet, using the equation v = √(2gR).

`\left[\begin{array}{cccc}Planet&R(m)&g(m/s^(2))&v(m/s)\\Mercury&2.43*10^(6)&3.61&4190\\Venus&6.07*10^(6)&8.83&10400\\Earth&6.37*10^(6)&9.80&11200\\Mars&3.38*10^(6)&3.75&5030\\Jupiter&6.98*10^(7)&26.0&60200\\Saturn&5.82*10^(7)&11.2&36100\\Uranus&2.35*10^(7)&10.5&22200\\Neptune&2.27*10^(7)&13.3&24600\end{array}\right]`

The rocket's maximum velocity is double the Earth's escape velocity, or 22,400 m/s. So the planets the rocket can escape from are Mercury, Venus, Earth, Mars, and Uranus.