Question

The largest asteroid, ceres, has a radius 0.073 times the radius of earth and a mass of 0.0002 earth masses. how much would a 72 kg astronaut weigh on ceres in pounds?

Answer 1

To find the weight of a 72 kg astronaut on Ceres, you need to calculate the gravitational force and then convert it to pounds.

Step-by-step explanation:

To calculate the weight of a 72 kg astronaut on Ceres, we need to find the gravitational force acting on the astronaut. The gravitational force is given by the equation F = mg, where F is the gravitational force, m is the mass of the object (72 kg), and g is the acceleration due to gravity on Ceres.

The acceleration due to gravity on Ceres can be calculated using the formula g = G (M/r^2), where G is the gravitational constant (6.674 * 10^-11 N m^2/kg^2), M is the mass of Ceres in kilograms (0.0002 times the mass of Earth), and r is the radius of Ceres in meters (0.073 times the radius of Earth).

Now we can substitute the values into the equation:

g = (6.674 * 10^-11 N m^2/kg^2) * (0.0002 * (5.972 * 10^24 kg)) / ((0.073 * (6.378 * 10^6 m))^2)

After calculating g, we can find the weight of the astronaut by multiplying the mass by the acceleration due to gravity:

Weight = m * g

Finally, we can convert the weight from kilograms to pounds by multiplying by 2.20462 (1 kg = 2.20462 lbs).

Answer 2

By definition, the weight of a human being on earth is given by the following expression:
f = m * g
Where,
m = mass
g = gravity.
On the other hand, gravity is also defined as:
g = G * M / R ^ 2
Where,
M: Mass of the earth.
G: gravitational constant.
R: Earth radio.
Taking these definitions into account then:
For Ceres:
gc = G * Mc / (Rc) ^ 2
Where,
Mc = 0.0002 M
Rc = 0.073R
Rewriting:
gc = G * (0.0002 M) / (0.073R ^ 2)
gc = (0.0002 / 0.073 ^ 2) * (G * M / R ^ 2)
gc = 0.0375g
Then, the weight will be
fc = m * gc.
fc = m * (0.0375) * g.
(0.0375) * m * g
(0.0375) * (72) * (2.2) = 5.94lb
answer:
a 72 kg astronaut weigh on ceres in pounds is 5.94lb