Question

Find the escape speed of a body from the
surface of Mars. (Radius of Mars = 3392 km,
gMars = 3.724 m/s?]
​

Answer 1

Answer:

Explanation:

Given :

Escape velocity of body from earth ( ) = 11.2 km/s

Radius of Mars = (1/2) Radius of Earth

Mass of Mars = (1/9) mass of Earth

Let :

Mass of Earth = M

Radius of Earth = R

To find :

Escape velocity of body from Mars

Formula used :

Escape velocity  =  

Here

M = Mass of planet

R = Radius of planet

G = Gravitational's constant

Solution :

✪ For earth

◕ Escape velocity ( )=  

➝ 11.2 km/s =  ...... equation 1

Escape velocity of body from Mars = 5.27 km/h

Answer 2

The escape velocity of any object from a planet with a mass of M and radius R is given by the relatively simple equation:

ve=2GMR−−−−√ .

G is the universal gravitational constant, G=6.674∗10−11N⋅kg−2⋅m2 . Unfortunately, we only have the radius and G, so we still need to get the mass. We can get that from the given gravitational acceleration and the radius using another equation which relates the local gravitational acceleration to the mass of the planet, the radius, and the gravitational constant:

g=GMr2

Picky or pedantic readers may notice that I have omitted a negative sign, and also have opted to ignore the intrinsic vector nature of this equation. To them I say “Pshaw!” because anyone familiar enough to recognize the error in my equation should easily know why I don’t care.

Rearranging the above equation and plugging in the given numbers gives us a planetary mass of about 6.420∗1023kg , not too far from the 6.39∗1023kg that Google claims; so we’re in good shape.

Now, we can go back to that first equation with this new mass in hand, and very quickly find the escape velocity. Crunching it through gives ve=5026ms.