Using Newton's Law of Universal Gravitation, compare the weight of a 68.1 kg astronaut on the surface of the earth to the gravitational pull of the Earth on the same astronaut when she is on the International Space Station.

Constants: Average altitude of the ISS above the surface of the Earth = 387 km. You can find the other constants you will need on the Astronomy Formula Chart.

(In Moodle, enter large numbers with scientific E notation. Example: 100 = 1.00*102 in scientific notation, or 1.00E2 in scientific E notation. Don't forget measurement units! If there are two blanks, enter the numerical value in the first blank, and the measurement unit in the second blank. Example: 1.0 m + 1.0 m = .)

The weight of the astronaut near the surface of the earth:
Fg = mg = (68.1 kg)(strength of gravitational field, g m/s2) =

The pull of the Earth on the astronaut near the surface of the earth:
(G (Nm2)/kg2)(mass of earth, M♁ )(mass of astronaut, 68.1 kg) / (radius of earth, R♁ m)2 =

The pull of the Earth on the astronaut when she is on the ISS:
(G (Nm2)/kg2)(mass of earth, M♁ )(mass of astronaut, 68.1 kg) / (radius of earth, R♁ m + altitude of ISS: )2 =

So, why is the astronaut 'weightless' when she is on the space station?

To compare the weight of the astronaut on the surface of the Earth to the gravitational pull of the Earth on the astronaut when she is on the International Space Station (ISS), we need to use Newton's Law of Universal Gravitation.

First, let's calculate the weight of the astronaut near the surface of the Earth. The weight (W) is given by the formula W = mg, where m is the mass of the astronaut and g is the strength of the gravitational field near the surface of the Earth.

Weight of the astronaut near the surface of the Earth:
W = (68.1 kg) * (g m/s^2)

Next, we need to calculate the pull of the Earth on the astronaut near the surface of the Earth using Newton's Law of Universal Gravitation. The formula is given by F = (G * M * m) / R^2, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the astronaut, and R is the radius of the Earth.

Pull of the Earth on the astronaut near the surface of the Earth:
F = (G * M♁ * m) / R♁^2

To calculate the pull of the Earth on the astronaut when she is on the ISS, we need to consider the altitude of the ISS above the surface of the Earth. We will add the altitude (in this case, 387 km) to the radius of the Earth in the formula.

Pull of the Earth on the astronaut when she is on the ISS:
F = (G * M♁ * m) / (R♁ + altitude of ISS)^2

Now, let's address why the astronaut is 'weightless' when she is on the space station. The concept of weightlessness in space is due to the phenomenon of freefall. In space, both the astronaut and the space station are in constant freefall towards the Earth. Because both are falling towards the Earth with the same acceleration, the astronaut experiences a feeling of weightlessness. The gravitational pull of the Earth on the astronaut and the space station is balanced by their inertia, resulting in a perception of weightlessness.