What Are the Escape Velocities for Callisto and a Neutron Star?

[warmfire540]

Determine the escape speed from (a) Jupiter’s moon Callisto with a mass of 1.07 × 10^23 kg and radius 2.4 Mm and (b) a neutron star twice the mass of the sun and a radius of 6 km.

I want to make sure I'm doing this and have the correct equations..

For part a)
Okay, so escape speed is found using the equation
v=sqrt(2GM/r)
G=6.67 x 10^-11
M=1.07 × 10^23
r=2.4 x 10^6

v=sqrt(1.427 x 10^13/2.4 x 10^6)
v=srt(5947416.667)
v=2438.73 m/s

For part b)
v=sqrt(2GM/r)
G=6.67 x 10^-11
M=2(1.9891 ×10^30) = 3.9782 x 10^30
r=6000

v=sqrt(5.301 x 10^20/6000)
v=sqrt(8.845 x 10^16)
v=297403171.9 m/s

 

[SporadicSmile]

Yep, you have the right formulae, and the right answers too.

and incase it is mentioned, your neutron star is VERY nearly a black hole too.

 

[Moetasim]

Your calculations for both parts are correct. The escape velocity from Callisto is 2438.73 m/s and from the neutron star is 297403171.9 m/s. These calculations are important in understanding the minimum speed an object needs to escape the gravitational pull of a celestial body. It is also useful in spacecraft missions, as the escape velocity determines the amount of energy and fuel needed to leave a planet or moon's orbit. Additionally, these equations can also be used to calculate the escape velocity for other celestial bodies, providing valuable information for future space exploration.