Speed of a satellite orbit (physics problem)?
What is the speed of a satellite in a geosynchronous orbit about Earth?
_________m/s
Compare it with the speed of the Earth as it orbits the Sun.
_________m/s
There is a clear distinction between a geosynchronous orbit and a geostationary orbit. The early recognition of a geostationary orbit was made by the Russian Konstantin Tsiolkovsky early this century. Others referred to the unique orbit in writings about space travel, space stations, and communications. It was probably Arthur C. Clarke who was given the major credit for the use of this orbit for the purpose of worldwide communications.
The geostationary orbit is one where a spacecraft or satellite appears to hover over a fixed point on the Earth's surface. There is only one geostationary orbit in contrast to there being many geosynchronous orbits. What is the difference you ask? A geosycnchronous orbit is one with a period equal to the earth's rotational period, which, contrary to popular belief, is 23hr-56min-4.09sec., not 24 hours. Thus, the required altltude providing this period is ~22,238 miles, or ~35,788 kilometers. An orbit with this period and altitude can exist at any inclination to the equator but clearly, a satellite in any such orbit with an inclination to the equator, cannot remain over a fixed point on the Earth's surface. On the other hand, a satellite in an orbit in the plane of the earth's equator and with the required altitude and period, does remain fixed over a point on the equator. This equatorial geosynchronous orbit is what is referred to as a geostationary orbit. The orbital velocity of satellites in this orbit is ~10,088 feet per second or ~6,877 MPH. The point on the orbit where the circular velocity of the launching rocket reaches 10,088 fps, and shuts down, is the point where the separated satellite will remain.
The mean velocity of the earth in its orbit derives from
2(3.14(92,960,242/365.25(24)= 66,630MPH.
To calculate the speed of a satellite in a geosynchronous orbit about Earth, we need to consider the radius of the orbit and the period of the satellite's orbit. The geosynchronous orbit is an orbit where a satellite orbits around the Earth at the same rotational speed as the Earth itself.
The radius of a geosynchronous orbit is the distance from the center of the Earth to the satellite. This radius is approximately 42,164 kilometers.
The period of a geosynchronous orbit is the time it takes for the satellite to complete one full orbit around the Earth. The period is equal to the rotational period of the Earth, which is approximately 24 hours.
To calculate the speed of the satellite, we can use the formula:
Speed = (circumference of the orbit) / (period of the orbit)
The circumference of the orbit can be calculated using the formula:
Circumference = 2 * π * radius
Thus, the speed of the satellite in a geosynchronous orbit around Earth is:
Speed = (2 * π * 42164 km) / (24 hours)
To convert the units to meters per second, we need to convert kilometers to meters and hours to seconds:
Speed = (2 * π * 42164000 meters) / (24 hours * 3600 seconds)
Now, let's calculate the speed:
Speed = 3073.7 m/s (approximately)
The speed of a satellite in a geosynchronous orbit around Earth is approximately 3073.7 meters per second.
To compare this with the speed of the Earth as it orbits the Sun, we need to know the radius of Earth's orbit around the Sun and the period of Earth's orbit.
The radius of Earth's orbit, also known as the astronomical unit (AU), is approximately 149.6 million kilometers.
The period of Earth's orbit around the Sun is approximately 365.25 days.
Using the same formula as before:
Speed = (2 * π * radius) / (period)
Speed = (2 * π * 149.6 million km) / (365.25 days * 24 hours * 3600 seconds)
After converting the units, we get the speed:
Speed = 29785.8 m/s (approximately)
The speed of Earth as it orbits the Sun is approximately 29785.8 meters per second.
Therefore, the speed of the satellite in a geosynchronous orbit around Earth is much smaller compared to the speed of the Earth as it orbits the Sun.