Freefall of an object in Space (towards earth)

In summary, the conversation discusses a problem involving finding the final velocity of an object as it hits the atmosphere of Earth. The student believes their professor made a mistake in their calculation and presents their own solution. They also mention the values used for G, M, and m. The conversation ends with a discussion about the starting point of the object and the relevance of the difference in altitude.
  • #1
LiorSh
24
0
Hi guys,

My professor showed us in class how to find the final velocity of an object as it hits the the atmosphere of earth(Rf=6.37e6) and I think he might have made a mistake. I have been trying to solve the same problem but I get different answer than the one my professor showed in class.
The Ri=6.37e6 + 10^5. Vi=0.

The way I solved it - 1/2mvf^2 −GmM/Rf=−GmM/Ri (I canceled out the m)
My answer is 695 m/s.

It seems like my professor didn't cancel out the first m and he got 435 or something around that number.
I wonder if there is a reason why he didn't cancel the first m, or rather he just forgot to do so.

Thank you so much!
 
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  • #2
You might want to check your values for "G" and for "M." If your prof came up with 435, you've both missed something.
 
  • #3
My answer is 695, not 435. I think my professor canceled out the m from the right side but didn't from the left side of the equation.
the G = 6.67e-11
M = 5.98e24
m= 10 kg - but we canceled it out anyway so it doesn't matter.
 
  • #4
LiorSh said:
the final velocity of an object as it hits the the atmosphere of earth

Hits the atmosphere of the Earth starting from where? "Free-fall" makes it sound like the object is falling in from infinity, but your calculation doesn't make sense for that problem. The formula you're using looks like you're trying to calculate the speed of an object dropped from the top of the atmosphere to the surface of the Earth (if there were no air resistance), and in that case Bystander is right - neither your 695 m/sec nor the professor's 435 m/sec is close.

As an aside: The difference between ##(6.37\times{10}^6)^2## and ##(6.37\times{10}^6+1\times{10}^5)^2## is so small as to be irrelevant (especially with only one significant digit in the atmospheric thickness) that you can save yourself some work and take the gravitational force to be the same at both altitudes.
 
  • #5
I see what you did there, I have no idea why the professor solved it this way then. that's how he showed in class. the the object is moving towards Earth from that distance and we need to figure out what would be the speed when Rf= 6.37e6 meters. (starting from the Ri=6.37e6+10^5).
 

1. What is freefall in space?

Freefall in space refers to the movement of an object towards a celestial body, such as the Earth, under the influence of gravity. In this scenario, the object is only affected by the gravitational force of the celestial body and is not subject to any other external forces.

2. How is freefall different in space compared to on Earth?

In space, freefall is essentially the same as falling on Earth, except that there is no air resistance to slow down the object's descent. This means that objects in freefall in space will continue to accelerate towards the celestial body until they reach its surface, whereas on Earth, air resistance would eventually cause the object to reach a constant speed.

3. What factors influence the speed of freefall in space?

The speed of freefall in space is primarily influenced by the mass of the celestial body and the distance between the object and the celestial body. Objects will experience a greater acceleration and faster freefall towards a more massive celestial body, and the closer an object is to the celestial body, the faster it will freefall.

4. Can an object in freefall in space ever stop?

No, an object in freefall in space will continue to accelerate towards the celestial body until it reaches its surface. The only way for an object to stop in space would be if it were to encounter another force, such as the thrust from a spacecraft's engines.

5. How does freefall in space impact astronauts?

Astronauts in space experience freefall constantly, as they are in orbit around the Earth and are essentially falling towards it. This can cause the sensation of weightlessness, as there is no force acting against their bodies. However, this constant freefall can also have physical effects on the body, such as reduced bone and muscle density due to the lack of gravity's resistance.

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