How long would it take for an apple to fall to the earth

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    apple Earth Fall
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Discussion Overview

The discussion revolves around the hypothetical scenario of an apple falling to Earth from the distance of the Moon. Participants explore the calculations involved in determining the time it would take for the apple to reach Earth, as well as the implications of its initial position and velocity relative to the Sun and Earth.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant inquires about the time it would take for an apple to fall to Earth from the distance of the Moon and how to calculate it.
  • Another participant suggests that the gravitational force varies as the apple approaches Earth, indicating that calculus would be necessary for accurate calculations.
  • It is noted that if the apple were stationary relative to the Sun at the Moon's distance, it would have an initial speed equal to Earth's orbital speed, which exceeds escape velocity, leading to the conclusion that the apple would fall into the Sun rather than Earth.
  • A participant mentions the possibility of using Kepler's third law to obtain results related to the fall time.
  • Further discussion highlights that the angle of the apple's position relative to Earth could affect its trajectory, with some suggesting it might not fall directly into the Sun but would still be subjected to extreme heat if it approached closely.
  • One participant elaborates on the conditions under which the apple would enter a heliocentric orbit after passing close to Earth, referencing specific distances and calculations related to gravitational influences.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the trajectory and fate of the apple, particularly concerning its initial conditions and the effects of gravitational forces. The discussion remains unresolved, with no consensus reached on the implications of the apple's fall.

Contextual Notes

There are limitations regarding the assumptions made about the apple's initial state, the effects of Earth's atmosphere, and the calculations involved in determining its trajectory and fall time. The discussion does not resolve these complexities.

Yazz
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How long would it take for an apple to fall to the Earth if it were as far away as the Moon and how do you calculate that?

And, say the apple appeared out of nowhere stationary (relative to the Sun) at that distance, would the movement of the Earth leave the apple behind or would the apple follow?
 
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Yazz said:
How long would it take for an apple to fall to the Earth if it were as far away as the Moon and how do you calculate that?

The force of gravity on an object is $$F=\frac{Gm_1m_2}{r^2}$$
The force will vary as it comes near the Earth, so you would need Calculus.
If you know the force, you know the acceleration,then you can use the SUVAT equations
 
Yazz said:
And, say the apple appeared out of nowhere stationary (relative to the Sun) at that distance, would the movement of the Earth leave the apple behind or would the apple follow?

An apple stationary with respect to the sun at the distance of the moon would have a speed relative to the Earth equal to Earth's orbital speed (30 km/s) which is in far excess of escape velocity. Therefore the apple would fall into the sun and not the earth.
 
QuantumPion said:
An apple stationary with respect to the sun at the distance of the moon would have a speed relative to the Earth equal to Earth's orbital speed (30 km/s) which is in far excess of escape velocity. Therefore the apple would fall into the sun and not the earth.

Depends on the angle relative to the Earth of where the apple is.
 
Buckleymanor said:
Depends on the angle relative to the Earth of where the apple is.
Yes and no. While the apple might not fall "into" the Sun, it will fall so close to the Sun that it will still be burnt to a crisp.

Assuming that the apple's perigee is at least 100 km above the surface of the Earth (any closer and it will be burnt to a crisp by the Earth's atmosphere) means that after grazing the atmosphere and escaping the Earth's gravitational clutches, the apple will be in a heliocentric orbit with a perihelion distance of 0.8 solar radii above the surface of the Sun.

http://www.wolframalpha.com/input/?...ntial+of+the+sun))+-+1+au)/(solar+radius)+-+1
 

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