A polar satellite is launched at 850km above earth.Find its orbital speed.
assuming the Earth is a sphere? So g at the surface is the same at the polar cap as it is at the equator.
v^2/d= g(re/(re+h))^2
v^2= 9.8m/s^2 * re^2 (re+h)/(re+h)^2= 9.8 re^2/(re+h) insert your value of radius of Earth (re) and altitude h. Watch units, put all in meters.
solve for v in m/s
To find the orbital speed of a satellite, we can use the formula for orbital velocity, which is given by:
v = √(G * M / r)
where,
v is the orbital speed,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^−1 s^−2),
M is the mass of the Earth (approximately 5.972 × 10^24 kg),
and r is the distance between the center of the Earth and the satellite.
In this case, the satellite is at a height of 850 km above the Earth's surface. To calculate the distance from the center of the Earth to the satellite, we need to add the radius of the Earth (approximately 6,371 km) to the altitude of the satellite.
r = radius of the Earth + altitude of the satellite
r = 6,371 km + 850 km
r = 7,221 km
Now, we can substitute the values into the formula and solve for v:
v = √(G * M / r)
v = √((6.67430 × 10^-11 m^3 kg^−1 s^−2) * (5.972 × 10^24 kg) / (7,221 km))
Note: It is important to convert the distance to meters before calculation.
v = √((6.67430 × 10^-11 m^3 kg^−1 s^−2) * (5.972 × 10^24 kg) / (7,221,000 m))
Calculating this equation will give you the orbital speed of the polar satellite at a height of 850 km above the Earth's surface.