A SpaceX Falcon 9 rocket carrying two astronauts launched from the Kennedy Space Centre in Florida on 30th May 2020 - Leaving Cert Physics - Question a - 2021

The ISS orbits the Earth every 93 minutes. To find the number of full orbits in a day:

1 day = 24 hours = 1440 minutes

Now, calculate the number of orbits:

This means the ISS completes approximately 15 full orbits each day.

Newton’s law of universal gravitation states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers:

where:

• $F$ is the force of attraction,
• $G$ is the gravitational constant,
• $m_1$ and $m_2$ are the masses of the objects,
• $r$ is the distance between the centers of the two masses.

Weight is calculated using the formula:

where:

• $W$ is weight,
• $m$ is mass ($85$ kg),
• $g$ is acceleration due to gravity on Earth ($9.8 ext{ m/s}^2$).

Substituting the values:

Thus, the astronaut’s weight on Earth is $833$ N.

The mass of an object does not change regardless of location. Therefore, the astronaut’s mass at the altitude of the ISS remains $85$ kg.

At an altitude of 400 km, the acceleration due to gravity is 90% of that at Earth's surface:

W_{ISS} = m \cdot g_{ISS} = 85 ext{ kg} \cdot 8.82 ext{ m/s}^2 = 749.7 ext{ N}