Calculate the percentage of Earth’s gravitational force on the ISS astronauts while orbiting at an altitude of 248 miles above Earth’s surface.
The wording of this question puzzles me because if they are in orbit they feel no gravitational force since the centripetal acceleration (v^2/R) exactly balances earth gravity.
However if you wish to separate out those two factors then use
Forbit = G m Me / Rorbit^2
Fground = G m Me Rearth^2
so 100*Forbit/Fearth
= 100 *Rearth^2/Rorbit^2
To calculate the percentage of Earth's gravitational force on the International Space Station (ISS) astronauts while orbiting at an altitude of 248 miles above Earth's surface, we can use the formula for the acceleration due to gravity at a certain distance from the center of the Earth.
The acceleration due to gravity at a particular distance from the center of the Earth can be calculated using the following formula:
g = (G * M) / r^2
Where:
g = acceleration due to gravity
G = gravitational constant (approximately 6.67430 x 10^-11 N(m/kg)^2)
M = mass of the Earth (approximately 5.972 x 10^24 kg)
r = distance from the center of the Earth to the object (248 miles converted to meters)
First, let's convert the altitude of 248 miles to meters:
1 mile = 1609.34 meters
248 miles = 248 * 1609.34 meters
Now we can calculate the acceleration due to gravity at this altitude:
g = (6.67430 x 10^-11 N(m/kg)^2 * 5.972 x 10^24 kg) / (248 * 1609.34 meters)^2
Using the given values, we can evaluate the expression:
g = (6.67430 x 10^-11 * 5.972 x 10^24) / (248 * 1609.34)^2 (Note: The units cancel out)
g ≈ 8.79 m/s^2
Now, to calculate the percentage of Earth's gravitational force on the ISS astronauts, we need to compare it to the acceleration due to gravity on Earth's surface:
g_surface = 9.8 m/s^2 (approximate value)
To find the percentage, we divide the calculated value for g in orbit by the value on Earth's surface and multiply by 100:
percentage = (8.79 m/s^2 / 9.8 m/s^2) * 100
percentage ≈ 89.7%
Therefore, the percentage of Earth's gravitational force acting on the ISS astronauts while orbiting at an altitude of 248 miles above Earth's surface is approximately 89.7%.
To calculate the percentage of Earth's gravitational force on the International Space Station (ISS) at an altitude of 248 miles above Earth's surface, you need to compare the gravitational force on the ISS to the gravitational force at the Earth's surface. Here's how you can do it:
Step 1: Find the gravitational force on the ISS at an altitude of 248 miles.
The formula to calculate gravitational force is given by: F = (G * m1 * m2) / r^2
where:
F = gravitational force
G = gravitational constant (approximately 6.67430 x 10^-11 N m^2 / kg^2)
m1 = mass of Earth
m2 = mass of the object (in this case ISS)
r = distance between the center of Earth and the center of the object (in this case altitude of 248 miles above Earth's surface)
Step 2: Find the gravitational force on Earth's surface.
At the Earth's surface, the equation simplifies to: F = m * g
where:
F = gravitational force
m = mass of the object (in this case the mass of an object is typically its weight)
g = acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
Step 3: Calculate the percentage.
Once you have the gravitational forces from Step 1 and Step 2, divide the force on the ISS by the force on Earth's surface, and then multiply by 100 to get the percentage.
Note: The ISS is constantly moving in orbit, so the altitude can vary slightly. In this case, we assume a specific altitude of 248 miles for calculation purposes.
Now, let's plug in the numbers and calculate the percentage:
Step 1: Gravitational force on the ISS at an altitude of 248 miles above Earth's surface.
F = (G * m1 * m2) / r^2
= (6.67430 x 10^-11 N m^2 / kg^2) * (5.972 x 10^24 kg) * (419,725 kg) / (6371 + 248)^2
Step 2: Gravitational force on Earth's surface.
F = m * g
= (419,725 kg) * (9.8 m/s^2)
Step 3: Calculate the percentage.
Percentage = (Gravitational force on the ISS / Gravitational force on Earth's surface) * 100
Plug in the values obtained from Step 1 and Step 2 into Step 3 to get the desired percentage.