Although astronauts appear weightless, they are not. They only appear weightless because they are in free fall. If a 79 kg astronaut is orbiting Earth with an orbital radius of 5.31×107 m, determine how much the astronaut would weigh. Earth's mass is 5.974 1024 kg.
Your teacher is misleading you greatly. Be careful. I am wondering if you actually have a physics major teacher.
I will solve this question: If a 79 kg astronaut is orbiting Earth with an orbital radius of 5.31×107 m, determine how much the astronaut would weigh ON EARTH. Earth's mass is 5.974 1024 kg.
a) On Earth, the person weights 79*9.8 Newtons.
Now for this question: If a 79 kg astronaut is orbiting Earth with an orbital radius of 5.31×107 m, determine how much the astronaut would weigh in orbit. Earth's mass is 5.974 1024 kg.
Answer: zero, the astronaut is in free fall.
I suspect your teacher has something else in mind, but frankly, I have no idea. If you get many of these, I would drop the class, and get a qualified teacher. Physics is an important subject.
In orbit, there are two forces working: gravity, and centripetal force. To be weightless, those two are equal. Perhaps your teacher wants you to ignore centripetal force, and just figure the gravity force at that orbital radius. I just don't know.
Hmm. I thought gravity provided the centripetal force. The object wants to fly off at a tangent, but gravity keeps bending the trajectory.
Is there another force besides gravity act work?
To determine how much the astronaut would weigh while orbiting Earth, we can use Newton's Law of Universal Gravitation:
F = G * (m1 * m2) / r^2,
where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2), m1 and m2 are the masses of the two objects (in this case, the astronaut and Earth), and r is the distance between their centers of mass (in this case, the orbital radius of the astronaut from Earth's center).
First, we need to find the gravitational force between the astronaut and Earth. Plugging in the values:
F = (6.67430 × 10^-11 N m^2 / kg^2) * (79 kg) * (5.974 × 10^24 kg) / (5.31 × 10^7 m)^2.
Calculating this, we get:
F ≈ 679.21 N.
So, the astronaut would experience a gravitational force of approximately 679.21 Newtons while orbiting Earth.