The average distance separating Earth and the Moon is 384,000 km. A 2.6x104 kg spaceship located halfway between them. (b) What is the total potential energy of the ship?

To calculate the total potential energy of the spaceship, we need to use the formula for gravitational potential energy:

Potential energy = mgh

Where:
m = mass of the spaceship
g = acceleration due to gravity
h = height or distance

In this case, we have the mass of the spaceship (m = 2.6x10^4 kg) and the average distance between the Earth and Moon (h = 384,000 km).

First, we need to convert the distance from kilometers to meters since the unit of gravitational acceleration is in meters per second squared (m/s^2).

1 km = 1000 m

So, the average distance between the Earth and Moon is 384,000 km = 384,000 x 1000 = 384,000,000 m.

Next, we need to find the acceleration due to gravity. The standard value for this is 9.8 m/s^2 on Earth. Since the spaceship is located halfway between the Earth and Moon, we can assume that the acceleration due to gravity is approximately half of the Earth's value.

g = 9.8 m/s^2 / 2 = 4.9 m/s^2

Now we can substitute the values into the formula:

Potential energy = (2.6x10^4 kg) * (4.9 m/s^2) * (384,000,000 m)

Calculating this expression will give us the total potential energy of the spaceship.