On April 25 1990, the Hubble Space Telescope (HST) was...

On April 25 $1990,$ the Hubble Space Telescope (HST) was deployed into a circular orbit 625 kilometers above the surface of the earth. The HST completes an earth orbit every 1.61 hours. (IMAGE CAN'T COPY). a. Find the angular velocity, with respect to the center of the earth, of the HST. Round your answer to the nearest 0.1 radian per hour. 3.9 radians per hour b. Find the linear velocity of the HST. (Hint: The radius of the earth is about 6370 kilometers.) Round your answer to the nearest 100 kilometers per hour. $27,300 \mathrm{km} / \mathrm{h}$

On April 25 $1990,$ the Hubble Space Telescope (HST) was deployed into a circular orbit 625 kilometers above the surface of the earth. The HST completes an earth orbit every 1.61 hours.
(IMAGE CAN'T COPY).
a. Find the angular velocity, with respect to the center of the earth, of the HST. Round your answer to the nearest 0.1 radian per hour. 3.9 radians per hour
b. Find the linear velocity of the HST. (Hint: The radius of the earth is about 6370 kilometers.) Round your answer to the nearest 100 kilometers per hour. $27,300 \mathrm{km} / \mathrm{h}$

Key Concepts

Circular Motion

Circular motion refers to the movement of an object along the circumference of a circle. In the context of orbital dynamics, it describes how satellites or celestial bodies travel in a path around a central body, such as the Earth. Understanding this concept is fundamental for analyzing the behavior of objects in orbit, including their velocities and accelerations.

Angular Velocity

Angular velocity is the rate at which an object rotates around a central point and is typically measured in radians per unit time. In orbital mechanics, it can be calculated as 2? divided by the orbital period, providing a measure of how quickly the satellite sweeps through its circular orbit.

Linear Velocity

Linear velocity is the speed at which an object travels along its circular path, measured in units of distance per time. In circular motion, it is directly related to the angular velocity and the radius of the orbit, as given by the formula v = r × ?, where r is the orbital radius and ? is the angular velocity.

Orbital Radius

The orbital radius is the distance from the center of the central body (like Earth) to the orbiting object. This is determined by adding the object’s altitude above the surface to the radius of the central body. The orbital radius is a key factor in calculating both the linear and angular velocities in orbital mechanics.

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