Calculate the speed of a satellite moving in a circular orbit about the Earth at a height of 2700×103 m. The mass of the Earth is 5.98×1024 kg and the mass of the satellite is 1400 kg.

use the masses of the Earth and the satellite to find the gravitational force

... this force equals the centripetal force

(m * v^2) / r = gravitational force

the distance in the gravitational formula is between the centers of the masses

To calculate the speed of a satellite in a circular orbit around the Earth, we can use the equation for gravitational force and centripetal force.

The force of gravity between the Earth and the satellite is given by:

F = (G * m1 * m2) / r^2

where G is the gravitational constant (6.67 × 10^-11 N*m^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the satellite, and r is the distance between the centers of the Earth and the satellite.

The centripetal force required to keep the satellite in orbit is given by:

F = m * v^2/r

where m is the mass of the satellite, v is its velocity, and r is the radius of the orbit.

Since the gravitational force and the centripetal force are equal, we can set the two equations equal to each other:

(G * m1 * m2) / r^2 = m * v^2 / r

Rearranging the equation and solving for v, we get:

v = √((G * m1) / r)

Let's substitute the given values into the formula:

G = 6.67 × 10^-11 N*m^2/kg^2
m1 = 5.98 × 10^24 kg
r = 2700 × 10^3 m

v = √((6.67 × 10^-11 N*m^2/kg^2 * 5.98 × 10^24 kg) / (2700 × 10^3 m))

Calculating the equation:

v = √(3.98 × 10^14 N*m/kg * 7.41 × 10^26 N*m)

v = √(2.95 × 10^41 N^2*m^2/kg^2)

v ≈ 1.71 × 10^5 m/s

Therefore, the speed of the satellite in a circular orbit around the Earth at a height of 2700 × 10^3 m is approximately 1.71 × 10^5 m/s.

To calculate the speed of a satellite moving in a circular orbit, we can use the formula for gravitational force and centripetal force.

The gravitational force between the satellite and the Earth is given by the equation:

F = G * (m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (approximately 6.674 × 10^-11 N*m^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the satellite, and r is the distance between the centers of the Earth and the satellite.

The force required to keep the satellite in orbit is the centripetal force, which is given by the equation:

F = (m * v^2) / r

where m is the mass of the satellite, v is the speed of the satellite, and r is the distance between the centers of the Earth and the satellite.

Since both equations are equal to the gravitational force, we can equate them and solve for v.

G * (m1 * m2) / r^2 = (m * v^2) / r

Rearranging this equation, we get:

v^2 = (G * m1 * m2) / r

Taking the square root of both sides, we get:

v = sqrt((G * m1 * m2) / r)

Now, we can substitute the given values into the equation to calculate the speed of the satellite:

G = 6.674 × 10^-11 N*m^2/kg^2
m1 = 5.98 × 10^24 kg
m2 = 1400 kg
r = 2700 × 10^3 m

Plugging in the values, we have:

v = sqrt((6.674 × 10^-11 N*m^2/kg^2 * 5.98 × 10^24 kg * 1400 kg) / (2700 × 10^3 m))

Now, let's calculate the value using a calculator:

v = sqrt(796.77426) = 28.224 m/s

Therefore, the speed of the satellite moving in a circular orbit around the Earth at a height of 2700 × 10^3 m is approximately 28.224 m/s.