Calculate the speed of an artificial earth satellite, assuming that it is travelling at an altitude h of 140 Km above the surface of the earth where g=9.8m/s2. The radius of earth R is 6373Km.

To calculate the speed of an artificial earth satellite at an altitude of 140 km above the surface of the earth, we need to consider the gravitational force acting on the satellite.

The gravitational force can be calculated using the formula:

F = (G * m * M) / r^2

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2),
m is the mass of the satellite,
M is the mass of the earth,
r is the distance between the center of the earth and the satellite.

Since the satellite is traveling at a constant speed, the gravitational force acting on it is balanced by the centripetal force:

F = m * (v^2) / r

Where:
v is the speed of the satellite.

By equating the gravitational force and the centripetal force, we can solve for the speed of the satellite.

(G * m * M) / r^2 = m * (v^2) / r

Simplifying the equation:

(G * M) / r = v^2

Taking the square root:

v = √(G * M / r)

Now, we can substitute the given values into the equation:

G = 6.67430 x 10^-11 N(m/kg)^2
M = mass of the Earth = 5.972 × 10^24 kg
r = radius of the Earth + altitude of the satellite = (6373 km + 140 km) = 6513 km

Converting all the units to meters:
G = 6.67430 x 10^-11 N(m/kg)^2
M = 5.972 × 10^24 kg
r = (6373 km + 140 km) * 1000 = 6513000 m

Calculating the speed:

v = √((6.67430 x 10^-11 N(m/kg)^2 * 5.972 × 10^24 kg) / 6513000 m)

v ≈ 7836 m/s

Therefore, the speed of the artificial earth satellite is approximately 7836 m/s.

To calculate the speed of an artificial earth satellite at a given altitude, we can use the following mathematical relationship:

v = √(g * R / (R + h))

Where:
v = speed of the satellite
g = acceleration due to gravity on the surface of the Earth
R = radius of the Earth
h = altitude of the satellite

First, let's convert the altitude from Km to meters:

h = 140 Km = 140,000 m

Now, we can substitute the values into the formula:

v = √(9.8 m/s^2 * 6,373 Km / (6,373 Km + 140 Km))

Simplifying the equation:

v = √(9.8 m/s^2 * 6,373,000 m / 6,513,000 m)

v = √(63,862,740 m^2/s^2 / 6,513,000 m)

v ≈ √9.79828

v ≈ 3.129 Km/s

Therefore, the speed of the artificial earth satellite at an altitude of 140 Km above the surface of the Earth is approximately 3.129 Km/s.

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