In order to calculate the speed at which the space shuttle must be moving when it releases the satellite, we need to determine the orbital velocity of the satellite.
The orbital velocity (v) of an object can be calculated using the following equation:
v = √(GM/R)
where;
G = 6.67 × 10^(-11) N·m²·kg^(-2) (the gravitational constant)
M = 5.97 × 10^(24) kg (the mass of Earth)
R = the distance between the object and the center of Earth
We are given that the satellite is released 700 km above the Earth's surface. Since the radius of the Earth is approximately 6,371 km, the distance between the satellite and the center of the Earth (R) can be calculated as:
R = (6,371 km + 700 km) × 1,000 m/km
R = 7,071,000 m
Now, we can calculate the orbital velocity (v) using the equation:
v = √(6.67 × 10^(-11) N·m²·kg^(-2) × 5.97 × 10^(24) kg / 7,071,000 m)
v ≈ 7,448 m/s
Therefore, the space shuttle must be moving at a speed of approximately 7,448 m/s (relative to Earth) when it releases the satellite.
The space shuttle releases a satellite into a circular orbit 700 km above the Earth. How fast must the shuttle be moving (relative to Earth) when the release occurs?
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