When calculating weights away from Earth's surface, for example:
At 6.38x10^3 km away from Earth's surface a spacecrafts weight is d=rE+rE
Then F=(1/4)(SpaceCraftWeight)
Why is the distance 2rE?
To understand why the distance is given as 2rE, let's break down the equation and analyze each component.
First, let's clarify some terms:
- rE represents the radius of the Earth.
- d represents the distance of the spacecraft from the Earth's surface.
- SpacecraftWeight refers to the weight of the spacecraft.
In the equation you provided: d = rE + rE, the distance is given as 2rE because it represents the total distance from the center of the Earth to the location of the spacecraft.
To visualize this, imagine a line segment extending from the center of the Earth to the Earth's surface. This length is equal to the radius of the Earth (rE). Now, if the spacecraft is located on the Earth's surface, the distance from the center to the spacecraft would be rE.
However, in this case, the spacecraft is not on the Earth's surface; it is located some distance away from it. That's why we have to consider both the radius of the Earth (rE) and the additional distance (also rE) from the Earth's surface to represent the total distance.
Hence, the formula d = rE + rE simplifies to d = 2rE, which represents the total distance from the center of the Earth to the spacecraft.
By using this distance, the equation F = (1/4)(SpaceCraftWeight) calculates the force (F) experienced by the spacecraft. The factor of 1/4 is included to account for the inverse square law, which states that the force between two objects is inversely proportional to the square of the distance between their centers.
To summarize, the distance being 2rE in the given equation represents the total distance from the center of the Earth to the spacecraft, accounting for both the Earth's radius and the additional distance from the surface.