Question

Искусственный спутник обращается по круговой орбите на высоте 600км от поверхности поанеты. Радиус планеты равен 3400км, ускорение свободного падения на поверхности планеты равно 4 м\с^2. какова скорость движения спутника по орбите?

Answer 1

V=√g(R+h)
v=√4(3400+600)*1000
v=√4*4000*1000
v=4000 м/с=4 км/с

Answer 2

Calculation of Satellite's Orbital Velocity

To calculate the velocity of a satellite in a circular orbit, we can use the formula:

v = √(GM/r)

Where: - v is the velocity of the satellite - G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2) - M is the mass of the planet - r is the distance between the center of the planet and the satellite

In this case, the radius of the planet is given as 3400 km, which is equivalent to 3,400,000 meters. The acceleration due to gravity on the surface of the planet is given as 4 m/s^2. The satellite is orbiting at a height of 600 km above the surface, which is equivalent to 600,000 meters.

To calculate the mass of the planet, we can use the formula:

g = GM/r^2

Where: - g is the acceleration due to gravity on the surface of the planet

Rearranging the formula, we get:

M = g * r^2 / G

Substituting the given values, we have:

M = 4 * (3,400,000)^2 / (6.67430 × 10^-11)

Now, we can calculate the mass of the planet using the above formula.

Let's calculate the mass of the planet first:

M = 4 * (3,400,000)^2 / (6.67430 × 10^-11) = 6.448 × 10^24 kg.

Now, we can calculate the velocity of the satellite using the formula mentioned earlier:

v = √(GM/r) = √((6.67430 × 10^-11) * (6.448 × 10^24) / (3,400,000 + 600,000))

Calculating the above expression, we find:

v ≈ 7,660 m/s

Therefore, the velocity of the satellite in its orbit is approximately 7,660 m/s.

Please note that the above calculation assumes a circular orbit and neglects factors such as atmospheric drag and the oblateness of the planet.