. The space shuttle typically orbits 400 km above the earth's surface. The earth has a mass of 5.98 × 1024 kg and a radius of 6,380 km. A) How much would a 2000 kg part for the space station weigh when it has been lifted to that orbit in the shuttle's cargo bay? B) What is the acceleration due to gravity at that altitude? C) Use your knowledge of gravitation to determine the orbital speed of the shuttle’s cargo.
A) To find the weight of the 2000 kg part when lifted to the orbit, we need to calculate its weight at that altitude. The weight can be calculated using the formula:
Weight = Mass * Acceleration due to gravity
where the mass is given as 2000 kg. The acceleration due to gravity will be different at that altitude compared to the surface of the earth.
B) To calculate the acceleration due to gravity at that altitude, we can use the formula:
g = G * (M / r^2)
where g is the gravitational acceleration, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), M is the mass of the Earth, and r is the distance from the center of the Earth to the altitude.
Given that the radius of the Earth is 6,380 km + 400 km = 6,780 km = 6,780,000 meters, and the mass of the Earth is 5.98 x 10^24 kg, we can calculate the acceleration due to gravity at that altitude.
C) The orbital speed of the shuttle's cargo can be determined using the formula:
v = √(G * M / r)
where v is the velocity, G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the altitude.
By plugging in the known values, we can calculate the orbital speed of the shuttle's cargo.
Let's go through each calculation step by step.
A) Calculating the weight of the part in the shuttle's cargo bay:
Weight = Mass * Acceleration due to gravity
B) Calculating the acceleration due to gravity at that altitude:
g = G * (M / r^2)
C) Calculating the orbital speed of the shuttle's cargo:
v = √(G * M / r)