the space shuttle typically orbits 400 km above the earth's surface.the earth hass a mass of 5.98*10 to the 24 squared kg and a raduis of 6,380 km.A)how much would a 2000 kg part form the space station weight 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 spedd of the shuttle's cargo.
A) To calculate the weight of the part when it is lifted to the orbit, we need to determine the force of gravity acting on it. The weight of an object is given by the equation:
Weight = mass * acceleration due to gravity
In this case, the mass of the part is given as 2000 kg, and we need to find the acceleration due to gravity at the given altitude.
B) To calculate the acceleration due to gravity at the given altitude, we can use the formula for gravitational acceleration:
acceleration due to gravity = (gravitational constant * mass of the Earth) / (radius of the Earth + altitude)^2
In this case, the mass of the Earth is given as 5.98 * 10^24 kg, and the radius of the Earth is given as 6,380 km. We can convert the altitude to meters by multiplying it by 1000.
C) To determine the orbital speed of the shuttle's cargo, we can use some knowledge of gravitation and orbital mechanics. The formula for the orbital speed of an object in circular orbit is:
orbital speed = square root((gravitational constant * mass of the Earth) / (radius of the Earth + altitude))
Again, we can substitute the given values to obtain the final answer.
Now, let's calculate the answers step by step.
A) Weight of the part when lifted to the orbit:
Weight = mass * acceleration due to gravity
B) Acceleration due to gravity at that altitude:
acceleration due to gravity = (gravitational constant * mass of the Earth) / (radius of the Earth + altitude)^2
C) Orbital speed of the shuttle's cargo:
orbital speed = square root((gravitational constant * mass of the Earth) / (radius of the Earth + altitude))
By substituting the given values into the above formulas, we can calculate the desired answers.
A) To find the weight of the 2000 kg part at the given orbit, we can use the equation:
Weight = Mass * Acceleration due to gravity
The mass of the part is given as 2000 kg. To calculate the acceleration due to gravity at that altitude, we need to consider the gravitational force. The formula for gravitational force is:
F = (G * m1 * m2) / r^2
Where:
G is the gravitational constant = 6.67430 x 10^-11 N*m^2/kg^2
m1 is the mass of the Earth = 5.98 x 10^24 kg
m2 is the mass of the part = 2000 kg
r is the distance between the center of the Earth and the orbit of the part, which is the sum of the Earth's radius and the orbit height.
r = 6380 km + 400 km
Converting both the Earth's radius and the orbit height to meters:
r = (6380 km + 400 km) * 1000 = 6780000 meters
Now we can plug the values into the formula to find the acceleration due to gravity:
F = (G * m1 * m2) / r^2
F = (6.67430 x 10^-11 N*m^2/kg^2 * 5.98 x 10^24 kg * 2000 kg) / (6780000 meters)^2
Calculating this will give us the gravitational force at the given orbit altitude.
B) To find the acceleration due to gravity at that altitude, we can use the formula:
Acceleration due to gravity = Gravitational force / mass of the part
C) To find the orbital speed of the shuttle's cargo, we can use the formula:
Orbital speed = square root of (Gravitational constant * mass of the Earth / radius of the orbit)