A satellite is in geostationary orbit 22,500 miles above the earth. IF the radius of the earth is 3,960 miles, how fast is the satellite moving in miles per day? How fast is the satellite moving in miles per hour?
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 ~22,238.64 miles, or ~35,787.875 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 ~10,088.25 feet per second or ~6,877 MPH. The point on the orbit where the circular velocity of the launching rocket reaches 10,088.25 fps, and shuts down, is the point where the separated satellite will remain. The point on the Earth's surface immediately below the satellite is moving with a velocity of 1525.85 ft./sec.
The distance traveled during the 24 hour clock day is 6877(24)MPD
To determine the speed of the satellite, we need to calculate the circumference of its orbit.
The radius of the geostationary orbit is the distance from the center of the Earth to the satellite, which is 3,960 miles + 22,500 miles = 26,460 miles.
The circumference of a circle is calculated using the formula: C = 2πr, where C is the circumference and r is the radius.
In this case, the circumference of the orbit is 2π(26,460 miles) = 166,617.96 miles.
Now, let's calculate the speed of the satellite in miles per day and miles per hour.
To find the speed in miles per day, we need to know how long it takes for the satellite to complete one orbit. Since the satellite is in geostationary orbit, it takes exactly 24 hours for it to complete one orbit (as it stays fixed above the same point on Earth). Therefore, the speed in miles per day is equal to the circumference of the orbit: 166,617.96 miles per day.
To find the speed in miles per hour, we divide the speed in miles per day by the number of hours in a day. There are 24 hours in a day, so the speed in miles per hour is: 166,617.96 miles / 24 hours = 6,942.41 miles per hour.
Therefore, the satellite is moving at a speed of approximately 166,617.96 miles per day and 6,942.41 miles per hour.