Satellite orbiting Earth problem involving weight?

In summary, the conversation discusses the weight and velocity of a satellite in orbit around the Earth. It is determined that at a certain distance above the Earth's surface, the weight would be half of what it is on the surface. To maintain this orbit, the velocity of the satellite would need to be calculated. Additionally, if a weighing machine is brought on the satellite, the weight would still be determined by the force equation F=Gm1m2/r^2.
  • #1
kalisious
13
0

Homework Statement


Imagine you are sent in a satellite.
a) How far above the surface of the Earth would you lose 1/2 of your weight?
b) To maintain the satellite orbiting around the Earth at that distance, what will be the velocity of the satellite?
c) Imagine you have taken a weighing machine with you. If you try to measure your weight what will it be? (Satellite is still orbiting Earth as in b)


Homework Equations


F=Gm1m2/r^2
PE=-GMEm/r

G=6.673*10^-11


The Attempt at a Solution


No idea.
 
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  • #2
F=Gm1m2/r^2 is the weight. Weight is a force in units of Newtons.
I suggest you put in some reasonable number for your mass and figure out your weight at the surface of the Earth. Then see if you can find the radius that results in half that weight.
 
  • #3


I can provide a response to this content. Firstly, let's address the concept of weight in space. Weight is a measure of the gravitational force exerted on an object by a celestial body. In space, there is no gravity, so objects do not have weight in the traditional sense. However, they do have mass, which is a measure of the amount of matter an object contains.

Now, let's address the problem at hand. To answer part a), we need to understand that the gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as you move farther away from the Earth, the force of gravity decreases. At a certain distance, the force of gravity will be half of what it is on the surface of the Earth, and this is where you will lose half of your weight. This distance can be calculated using the equation F=Gm1m2/r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, you and the Earth), and r is the distance between them.

For part b), we need to understand that an object in orbit is constantly falling towards the Earth but also moving sideways fast enough to avoid crashing into it. This sideways motion is called velocity. The velocity required to maintain an orbit at a certain distance can be calculated using the equation v=√(GM/r), where v is the velocity, G is the gravitational constant, M is the mass of the Earth, and r is the distance between the satellite and the Earth.

Lastly, for part c), it's important to note that in orbit, objects experience weightlessness because they are in a state of freefall. This means that the weighing machine would not be able to measure your weight as there is no force acting on you. It would simply read zero. However, your mass would remain the same.

I hope this explanation helps you understand the problem better. Keep exploring and asking questions, that's what being a scientist is all about!
 

1. How does the weight of a satellite in orbit around Earth compare to its weight on the ground?

The weight of a satellite in orbit around Earth is significantly less than its weight on the ground. This is due to the fact that in orbit, the satellite is experiencing weightlessness or microgravity, which is caused by the balance between the gravitational pull of Earth and the centrifugal force of the satellite's orbit.

2. Why does the weight of a satellite in orbit around Earth change?

The weight of a satellite in orbit around Earth can change due to a few factors. One factor is the altitude of the satellite's orbit, as the gravitational pull of Earth decreases with distance. Another factor is the mass of the Earth, as a heavier Earth would have a stronger gravitational pull on the satellite.

3. How does the weight of a satellite in orbit around Earth affect its speed?

The weight of a satellite in orbit around Earth does not directly affect its speed. However, the speed of the satellite is dependent on its distance from Earth and the force of gravity, both of which are affected by the satellite's weight.

4. What is the difference between weight and mass in the context of a satellite in orbit around Earth?

Weight and mass are often used interchangeably, but they have different meanings in the context of a satellite in orbit around Earth. Mass refers to the amount of matter an object contains, while weight is a measure of the force of gravity on that object. In microgravity, the weight of an object is essentially zero, but its mass remains the same.

5. How does the weight of a satellite in orbit around Earth impact its trajectory?

The weight of a satellite in orbit around Earth does not significantly impact its trajectory. The trajectory of a satellite is primarily determined by its initial launch velocity and the gravitational pull of Earth. However, weight can affect the altitude and speed of the satellite's orbit, which can indirectly impact its trajectory.

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