Gravitational Force of a rocket

In summary: In this case, the problem asks for the distance above Earth's surface, so you have to subtract Re. This will give you x = Re · [ sqrt(2) - 1 ] .Finally, you are using the radius of Earth in meters. You didn't mention it in your original posting, but what units does the problem ask for?
  • #1
skins266
14
0

Homework Statement



How high does a rocket have to go above Earth's surfae before its weight is half what it would be on earth

Homework Equations



F=GMeMr/r^2, however there are too many variables here to use

The Attempt at a Solution



F/2=GMeMr/((sq root 2)r))^2, but I don;t know if this is right or how to use it without numbers
 
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  • #2
skins266 said:

Homework Statement



How high does a rocket have to go above Earth's surfae before its weight is half what it would be on earth

Homework Equations



F=GMeMr/r^2, however there are too many variables here to use

The Attempt at a Solution



F/2=GMeMr/((sq root 2)r))^2, but I don;t know if this is right or how to use it without numbers

You can deal with this without numbers by using a comparison ratio. The weight of the rocket on the Earth's surface is

W = GMeMr/(Re^2) ,

where Re is the Earth's radius (that's how far the Earth's surface is from its center, which is the r we need in order to apply Newton's gravitation law here.

At the position we're interested in,

(1/2)W = GMeMr/(r^2) ,

where r is the distance from Earth's center that we need to solve for.

What happens when you divide the second equation by the first one? Can you solve the result for r? How do you apply this result to the original question?
 
  • #3
So I will get 1/Re^2 = 2/r^2 and then r = Re - x where x is the distance to the rocket? But then I get lost on applying it to the question.
 
  • #4
skins266 said:
So I will get 1/Re^2 = 2/r^2 and then r = Re - x where x is the distance to the rocket? But then I get lost on applying it to the question.

So this tells you that r^2 = 2 · (Re^2) or r = (Re) · sqrt(2). So the rocket must be about 1.414 times the Earth's radius from the Earth's center. How far does that put it above the Earth's surface? That is the altitude the problem asks for.
 
  • #5
so r = Re(sqrt2) so r = 6.38E6*sqrt2. Which then equals 9022682.528, but when I punch that number into WebAssign it is wrong, so is it not in km, or what
 
  • #6
skins266 said:
so r = Re(sqrt2) so r = 6.38E6*sqrt2. Which then equals 9022682.528, but when I punch that number into WebAssign it is wrong, so is it not in km, or what

First off, this is the distance from the center of Earth; the problem asks for the distance above Earth's surface, so you have to subtract Re. This will give you

x = Re · [ sqrt(2) - 1 ] .

Secondly, you are using the radius of Earth in meters. You didn't mention it in your original posting, but what units does the problem ask for?
 
  • #7
Oh yeah, my bad. It is in km and so my radius would be 6.38E3 and then the answer would be 2642.68 ... which is right. Thanks for your help.
 
  • #8
skins266 said:
Oh yeah, my bad. It is in km and so my radius would be 6.38E3 and then the answer would be 2642.68 ... which is right. Thanks for your help.

Great! Be sure to read these kinds of questions carefully. There is often a homework or exam problem which asks for altitude or gives information in terms of the altitude, rather than the distance to the center of the Earth.
 

What is the gravitational force of a rocket?

The gravitational force of a rocket is the force of attraction between the rocket and the Earth. It is the force that keeps the rocket from floating away into space and allows it to remain in orbit around the Earth.

How is the gravitational force of a rocket calculated?

The gravitational force of a rocket is calculated using Newton's Law of Universal Gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Does the gravitational force of a rocket change during its flight?

Yes, the gravitational force of a rocket changes during its flight. As the rocket moves away from the Earth's surface, the distance between the rocket and the Earth increases, causing the gravitational force to decrease. However, the force remains strong enough to keep the rocket in orbit.

How does the gravitational force of a rocket affect its trajectory?

The gravitational force of a rocket plays a crucial role in determining its trajectory. If the force is too weak, the rocket may not be able to overcome Earth's gravity and will fall back to the surface. If the force is too strong, the rocket may escape Earth's orbit and continue into space.

Can the gravitational force of a rocket be manipulated?

Yes, the gravitational force of a rocket can be manipulated by changing its mass or the distance between it and the Earth. This can be achieved through the use of thrusters or by altering the rocket's trajectory. However, these changes must be carefully calculated to ensure the rocket remains in a stable orbit.

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