A Titan IV rocket has put your spacecraft in a circular orbit around Earth at an altitude of 230 km. Calculate the force due to gravitational attraction between the Earth and the spacecraft in N if the mass of the spacecraft is 2300 kg.

G Me m /r^2

dds

2300kg

To calculate the force due to gravitational attraction between the Earth and the spacecraft, we can use Newton's Law of Universal Gravitation.

The formula for gravitational force is:

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

Where:
F is the force of gravitational attraction between two objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 N * (m/kg)^2),
m1 is the mass of the first object (Earth in this case),
m2 is the mass of the second object (spacecraft in this case),
and r is the distance between the centers of the two objects.

In this case, we have the mass of the spacecraft (m2 = 2300 kg) and the altitude of the orbit above Earth's surface (230 km).

To calculate the distance between the centers of the two objects (r), we need to know Earth's radius and add the altitude above the surface to it.

The radius of Earth (R) is approximately 6371 km, but in order to use the same unit for distance, we need to convert it to meters:
R = 6371 km * 1000 m/km = 6,371,000 m

Now, we can calculate the total distance between the centers of the Earth and the spacecraft:
r = R + altitude
= 6,371,000 m + 230,000 m
= 6,601,000 m

Substituting the values into the formula:

F = (G * m1 * m2) / r^2
Plugging in the values:
F = (6.67430 x 10^-11 N * (m/kg)^2) * (5.972 x 10^24 kg) * (2300 kg) / (6,601,000 m)^2

Solving this equation will give you the force due to gravitational attraction between the Earth and the spacecraft in Newtons (N).