Question

If a satellite is placed in a circular orbit of 270 kilometers above the Earth, what is the equation of 3) the path of the satellite if the origin is placed at the center of the Earth (the diameter of the Earth is approximately 30,000 kilometers)?

Answer 1

The equation for the path of a satellite in a circular orbit can be expressed as r = R + h, where r is the distance from the center of the Earth to the satellite, R is the radius of the Earth, and h is the altitude of the satellite above the Earth's surface. The radius of the Earth is approximately 30,000 kilometers and the altitude of the satellite is 270 kilometers. Plugging in these values, the distance from the center of the Earth to the satellite is calculated to be 30,270 kilometers.

Step-by-step explanation:

The equation for the path of a satellite in a circular orbit can be derived using the concept of centripetal force. For an object in circular motion, the centripetal force is provided by the gravitational force between the satellite and the Earth. The equation for the path of the satellite can be expressed as:

r = R + h

Where:

• r is the distance from the center of the Earth to the satellite
• R is the radius of the Earth
• h is the altitude of the satellite above the Earth's surface

In this case, the radius of the Earth (R) is approximately 30,000 kilometers and the altitude of the satellite (h) is 270 kilometers. Plugging in these values, we can calculate the distance from the center of the Earth to the satellite (r) using the equation:

r = 30000 + 270 = 30270 kilometers