Calculate the velocity of a satellite moving in a stable circular orbit about the Earth at a height of 2600 km.
assuming Newtons law of gravity...
Force=mv^2/r
GMe m/(r^2)
GMe/r=v^2
where r=re+altidtude
v^2 = GM/r = 6.67*10^-11 * 5.97*10^24 / ((6371+2300)*1000) = 4.59*10^10
v = 6.776 km/s
typo - v^2 = 4.59*10^7
To calculate the velocity of a satellite in a stable circular orbit, we need to use the formula for the orbital speed. The orbital speed of a satellite is given by:
V = sqrt((G * M) / R)
where:
V is the orbital speed
G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2)
M is the mass of the Earth (5.972 x 10^24 kg)
R is the distance between the center of the Earth and the satellite
In this case, the distance between the center of the Earth and the satellite is the sum of the radius of the Earth (6,371 km) and the height of the satellite (2,600 km). So, the value of R would be:
R = 6,371 km + 2,600 km = 8,971 km = 8,971,000 meters
Now, we can plug in the values into the formula and calculate the velocity:
V = sqrt((6.67430 x 10^-11 m^3 kg^-1 s^-2 * 5.972 x 10^24 kg) / (8,971,000 m))
Calculating this equation will give us the velocity of the satellite in meters per second.