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 in ceres in pounds?

 To calculate the weight of a 72 kg astronaut on Ceres, we'll first need to determine the astronaut's weight using the formula:

Weight = Mass × Surface Gravity

The surface gravity on any celestial body can be calculated with the formula:

Surface Gravity = (G * Mass of the body) / (Radius of the body)^2

where G is the universal gravitational constant (G = 6.67430 × 10^-11 N m^2/kg^2).

However, we can simplify the comparison between the surface gravity of Earth and Ceres by taking ratios, since the gravitational constant G and the mass of the astronaut will cancel out in the ratio.

On Earth, the average surface gravity (g_Earth) is 9.81 m/s^2. The mass of Ceres is 0.0002 times the mass of Earth, and the radius of Ceres is 0.073 times the radius of Earth. The surface gravity on Ceres (g_Ceres) compared to Earth would be:

g_Ceres = g_Earth * (Mass of Ceres / Mass of Earth) / (Radius of Ceres / Radius of Earth)^2 g_Ceres = 9.81 m/s^2 * 0.0002 / 0.073^2

Let's calculate it:

g_Ceres = 9.81 * 0.0002 / (0.073 * 0.073) g_Ceres ≈ 9.81 * 0.0002 / 0.005329 g_Ceres ≈ 0.3684 N/kg

Now, to find the weight of the astronaut on Ceres, we'll multiply their mass by Ceres' surface gravity:

Weight on Ceres = Mass of astronaut * g_Ceres Weight on Ceres = 72 kg * 0.3684 N/kg Weight on Ceres ≈ 26.525 N

The weight is in Newtons, but we want to convert it to pounds. The conversion factor is 1 N = 0.224809 lb.

Weight on Ceres in pounds = 26.525 N * 0.224809 lb/N Weight on Ceres in pounds ≈ 5.964 lb

So, a 72 kg astronaut would weigh approximately 5.96 pounds on Ceres.

To calculate an astronaut's weight on Ceres, we'll start by using Newton's law of universal gravitation to establish the force of gravity (weight) on Ceres compared to that on Earth.

The force of gravity experienced by an object is given by the formula: F = G * (m1 * m2) / r^2

where F is the force of gravity, G is the gravitational constant (G = 6.674 × 10^-11 N * (m/kg)^2), m1 is the mass of the first object (in this case, Ceres), m2 is the mass of the second object (the astronaut), and r is the distance between the centers of the two objects (the radius of Ceres).

Since we're interested in the change of weight (which is the force due to gravity) from Earth to Ceres and not the actual force values, we can ignore the gravitational constant and compare the ratios of weight from Earth to Ceres because the gravitational constant and the astronaut's mass (as long as it is constant) will cancel out.

Let m_e be the mass of the Earth and r_e the radius of the Earth, then the weight of the astronaut on Earth (W_e) is given by: W_e = G * (m_e * m_astro) / r_e^2

The weight of the astronaut on Ceres (W_c) is given by: W_c = G * (m_c * m_astro) / r_c^2

where m_c is the mass of Ceres, and r_c is the radius of Ceres.

Now we have been given m_c as 0.0002 times Earth's mass (m_e) and r_c as 0.073 times Earth's radius (r_e).

W_c / W_e = (m_c * m_astro) / r_c^2 * r_e^2 / (m_e * m_astro) = (0.0002 * m_e * m_astro / (0.073 * r_e)^2) * (r_e^2 / (m_e * m_astro)) = 0.0002 / 0.073^2

Now, we calculate the value: W_c / W_e = 0.0002 / (0.073 * 0.073)

W_c / W_e ≈ 0.0002 / 0.005329

W_c / W_e ≈ 0.037536

So the astronaut's weight on Ceres is approximately 0.037536 times their weight on Earth.

The astronaut's weight on Earth is 72 kg multiplied by the acceleration due to gravity on Earth, which is approximately 9.8 m/s^2: W_e = 72 kg * 9.8 m/s^2 W_e ≈ 705.6 N

Now, to find the weight on Ceres, we'll multiply the weight on Earth by the ratio we have calculated: W_c = 705.6 N * 0.037536 W_c ≈ 26.49 N

To convert Newtons to pounds, we use the conversion factor 1 N ≈ 0.224809 lb: Weight in pounds = 26.49 N * 0.224809 lb/N Weight in pounds ≈ 5.955 lb

So, a 72 kg astronaut would weigh approximately 5.955 pounds on Ceres.