An astronaut weighs 720N on earth at sea level. Determine his mass on the moon. Given the moon has a mass of 7.35×10^22kg and average diameter of 3474.2km
trick question?
mass is the same everywhere
mass = 720 / 9.8 = ? kg
weight on the moon is about 1/6 weight on Earth
It's very interesting
To determine the astronaut's mass on the moon, we can use the gravitational force equation:
F = (G * m1 * m2) / r^2
where:
F is the gravitational force
G is the universal gravitational constant (6.67430 × 10^-11 N(m/kg)^2)
m1 is the mass of the astronaut
m2 is the mass of the moon
r is the distance between the center of the astronaut and the center of the moon
Given that the astronaut's weight on Earth is 720N, we can find their mass on Earth using the formula:
Weight = mass * acceleration due to gravity
On Earth, the acceleration due to gravity is approximately 9.8 m/s^2, so:
720N = mass_on_earth * 9.8 m/s^2
Solving for mass_on_earth:
mass_on_earth = 720N / 9.8 m/s^2 = 73.46 kg (approx.)
Now, we can find the gravitational force between the astronaut and the moon using:
F = (G * m1 * m2) / r^2
We can rearrange this equation to solve for the mass of the astronaut on the moon:
m1 = (F * r^2) / (G * m2)
The distance between the center of the moon and the center of the astronaut is equal to the radius of the moon. Given that the moon has an average diameter of 3474.2 km, its radius, r, can be calculated as:
r = diameter / 2 = 3474.2 km / 2 = 1737.1 km = 1.7371 × 10^6 m
Plugging in the values we have:
m1 = (720N * (1.7371 × 10^6 m)^2) / (6.67430 × 10^-11 N(m/kg)^2 * 7.35 × 10^22 kg)
Calculating this expression:
m1 ≈ 71.39 kg
Therefore, the astronaut's mass on the moon is approximately 71.39 kg.
To determine the astronaut's mass on the moon, we need to use the formula relating weight, mass, and gravitational acceleration.
Weight (W) = mass (m) * gravitational acceleration (g)
On Earth, the gravitational acceleration is approximately 9.8 m/s^2. We can rearrange the formula to solve for mass:
m = W / g
Given that the astronaut's weight on Earth is 720N, we can calculate the mass on Earth:
m = 720N / 9.8 m/s^2
m ≈ 73.5 kg
Now, to find the astronaut's weight on the moon, we need to use the formula:
Weight (W) = mass (m) * gravitational acceleration (g)
Since the moon has a different mass and gravitational acceleration than Earth, we need to calculate the gravitational acceleration on the moon.
Using the formula for gravitational acceleration:
g = G * M / r^2
Where G is the universal gravitational constant (approximately 6.6743 × 10^-11 N(m/kg)^2), M is the mass of the moon (7.35×10^22 kg), and r is the radius of the moon (half of the diameter, so 3474.2km/2 = 1737.1km ≈ 1.7371 × 10^6 meters).
Plugging these values into the formula, we can calculate the gravitational acceleration on the moon:
g = (6.6743 × 10^-11 N(m/kg)^2 * 7.35×10^22 kg) / (1.7371 × 10^6 m)^2
g ≈ 1.62 m/s^2
Now we can determine the astronaut's weight on the moon using the formula:
W = m * g
W = 73.5 kg * 1.62 m/s^2
W ≈ 119 N
So, the astronaut would weigh approximately 119N on the moon.