Question

Определите первую космическую скорость в условиях планеты Марс, считая ее радиус равным 3400 км и ускорение свободного падения - 3,8 М/с^2

Answer 1

G = 3,8 м/с^2
R = 3400 км = $3,4*10 ^{6}$ м
$v _{1} -?$

$v _{1} = \sqrt{gR}$

$v _{1} = \sqrt{3,8*3,4*10 ^{6} } =3594$ м/с

Answer 2

Calculation of the First Cosmic Velocity on Mars

To determine the first cosmic velocity on Mars, we need to consider the radius of Mars and the acceleration due to gravity on its surface.

Given: - Radius of Mars (R) = 3400 km - Acceleration due to gravity on Mars (g) = -3.8 m/s^2 The first cosmic velocity (v1) is the minimum velocity required for an object to escape the gravitational pull of a celestial body. It can be calculated using the formula:

v1 = sqrt(2 * g * R)

Substituting the values for Mars:

v1 = sqrt(2 * (-3.8 m/s^2) * (3400 km))

To perform the calculation, we need to convert the radius from kilometers to meters:

v1 = sqrt(2 * (-3.8 m/s^2) * (3400 km * 1000))

Simplifying the equation:

v1 = sqrt(2 * (-3.8 m/s^2) * (3.4 * 10^6 m))

v1 = sqrt(-25.76 * 10^6 m^2/s^2)

Taking the square root:

v1 ≈ 5087.1 m/s

Therefore, the first cosmic velocity on Mars, considering its radius as 3400 km and the acceleration due to gravity as -3.8 m/s^2, is approximately 5087.1 m/s.