What is the magnitude of the apparent weight of a 79 astronaut 5200 from the center of the Earth's Moon in a space vehicle moving at constant velocity?
To calculate the magnitude of the apparent weight of an astronaut on the Moon in a space vehicle moving at a constant velocity, we need to consider the effect of both the gravitational force and the inertial force.
First, we need to determine the gravitational force acting on the astronaut. The gravitational force is given by the formula:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 is the mass of the astronaut, m2 is the mass of the Moon, and r is the distance between the center of the Moon and the astronaut.
The mass of the astronaut is given as 79 kg, and the mass of the Moon is approximately 7.342 × 10^22 kg. The distance from the center of the Moon to the astronaut is not provided, but assuming the space vehicle is on the surface of the Moon, we can use the radius of the Moon which is approximately 1,737 km or 1.737 × 10^6 m.
Second, the apparent weight also includes the effect of the inertial force due to the constant velocity of the vehicle. When an object is moving at a constant velocity, the inertial force is equal in magnitude and opposite in direction to the gravitational force. This means that the apparent weight of the astronaut is equal to the gravitational force.
To get the final answer, we can substitute the given values into the formula for the gravitational force and calculate the magnitude.
Let's calculate it step by step:
1. Convert the mass of the Moon and the radius of the Moon to SI units:
- The mass of the Moon remains the same: 7.342 × 10^22 kg
- Convert the radius of the Moon to meters: 1,737 km * 1000 = 1.737 × 10^6 m
2. Plug the values into the formula for the gravitational force:
F = G * (m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2 / kg^2) * (79 kg * 7.342 × 10^22 kg) / (1.737 × 10^6 m)^2
3. Calculate the magnitude of the gravitational force.
Now let me do the calculations.