If a satellite is launched at an orbital radious of twice that of a geostationary satellite ,how much time will the launched satellite take to travel around the earth ?
To find out how much time the launched satellite will take to travel around the Earth, we need to calculate its orbital period. The orbital period of a satellite can be determined using Kepler's Third Law of Planetary Motion, which states that the square of a planet's orbital period is directly proportional to the cube of its average orbital radius.
1. First, let's determine the orbital radius of a geostationary satellite. A geostationary satellite is positioned at a fixed point above the Equator, approximately 35,786 kilometers (22,236 miles) above the Earth's surface.
2. Since the satellite to be launched has an orbital radius twice that of a geostationary satellite, its orbital radius would be 2 * 35,786 kilometers = 71,572 kilometers.
3. Now, we can find the orbital period of the launched satellite. Let's assume T represents the orbital period in hours, and R represents the orbital radius in kilometers.
4. According to Kepler's Third Law, T^2 = k * R^3, where k is a constant value.
5. To solve for the orbital period T, we can rearrange the equation as T = √(k * R^3).
6. Plug in the values for R and solve for T. T = √(k * 71,572^3).
Note: The actual value of the constant k depends on the units used for the orbital radius and period. To keep the units consistent, we can assume the orbital radius is in kilometers, and the resulting orbital period will be in hours.
By following these steps, you should be able to calculate the time it takes for the launched satellite to travel around the Earth.