A rocket is used to place a synchronous satellite in orbit about the earth. What is the speed of the satellite in orbit?
Well, the satellite is moving at a speed that can be described as "out of this world!" It's actually traveling at a whopping 11,186 kilometers per hour (6,951 miles per hour) to stay synchronized with the Earth's rotation. That's faster than a cheetah on roller skates! Just be careful not to challenge it to a race, or you might end up feeling a little bit spaced out!
To determine the speed of a satellite in orbit around the Earth, we can use the following equation:
v = √(G * M / r)
Where:
- v is the speed of the satellite in orbit,
- 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),
- r is the distance from the center of the Earth to the satellite.
The satellite in question is a synchronous satellite, which means it stays fixed in a particular position relative to the Earth's surface. This implies that the satellite's orbit has a radius equal to the Earth's radius.
The Earth's radius is approximately 6,371 kilometers (6.371 × 10^6 meters). We can use this value as the distance, r.
Substituting the known values into the equation, we have:
v = √(6.67430 × 10^-11 * 5.972 × 10^24 / 6.371 × 10^6)
Calculating this expression, we find:
v ≈ 3,070 meters per second (m/s)
Therefore, the speed of the satellite in orbit is approximately 3,070 m/s.
To calculate the speed of a satellite in orbit around the Earth, we need to use the formula for the velocity of a satellite in circular motion. The formula is as follows:
v = √(G * M / r)
Where:
v = Velocity of the satellite in m/s
G = Universal gravitational constant (6.6743 × 10^-11 N m^2/kg^2)
M = Mass of the Earth (5.972 × 10^24 kg)
r = Distance from the center of the Earth to the satellite's orbit (radius of the orbit)
Since a synchronous satellite is in geostationary orbit, it orbits at a distance of approximately 42,164 km (or 26,199 miles) from the center of the Earth.
First, let's convert the distance from km to meters:
r = 42,164 km = 42,164,000 meters
Now we can substitute the values into the formula and calculate the velocity:
v = √(G * M / r)
v = √((6.6743 × 10^-11 N m^2/kg^2) * (5.972 × 10^24 kg) / 42,164,000 meters)
By plugging in the values and solving the equation, you will obtain the velocity of the satellite in its orbit around the Earth.
Period is 24 hrs. Convert that to seconds.
The distance they travel in one period is 2PI*radius. Find the radius of the Earth in meters, then add the altitude.
veloicty=distance/period