Question

When the united states was running its space shuttle program, the space shuttle usually orbited earth at an altitude of 310 km. the radius of the earth is 6.38x10⁶ m, the mass of the earth is 5.98x10²⁴ kg, the mass of the space shuttle is 80,000 kg, and the mass of the sun is 1.98x10³⁰ kg.

Answer 1

When a space shuttle orbits Earth once at an altitude of 310 km, it travels a distance of approximately 42,000 km but has a displacement of 0 m as it returns to its original position.

Step-by-step explanation:

The question asks about the distance a space shuttle would travel and its displacement after orbiting the Earth once. To answer this question, we first consider the altitude at which the shuttle orbits, which is given as 310 km above the Earth's surface. The radius of the Earth is 6.38×10⁶ m, so the total radius of the shuttle's orbit is the sum of the Earth's radius and the shuttle's altitude in meters.

Orbit Radius = Earth's Radius + Shuttle's Altitude
= 6.38×10⁶ m + 310×103 m
= 6.38×10⁶ m + 310,000 m
= 6.69×10⁶ m

The distance traveled by the shuttle while completing one orbit is the circumference of the orbit, which can be calculated using the formula for the circumference of a circle (C = 2πr).

Distance Traveled = 2π(6.69×10⁶ m) ≈ 42×10⁶ m

The displacement of the shuttle, after completing one orbit, is actually zero as it returns to the starting point, which means it does not have a net change in position.

Displacement = 0 m

To summarize, when a space shuttle orbits Earth once, the shuttle travels approximately 42,000 km but has a displacement of 0 since it completes a loop and comes back to the starting position. Such calculations are important in understanding basic kinematics involved in spaceflight and orbital mechanics.