Solving for the Height of Mercury: Is This Equation Correct?

In summary, the equation for solving for the height of Mercury is h = (2GM)/(v^2 - 2GM/r), derived from the law of conservation of energy and Newton's law of universal gravitation. It can be used for other planets, but may require adjustments to the values of G and M. Limitations include assuming a perfect spherical shape and not accounting for external influences. This equation has practical applications in space missions, astronomical observations, and studying gravitational effects.
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Homework Statement

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The attempt at a solution

To find the height of mercury I have used the following equation:

[tex]P _{gauge}=\rho _{air}\cdot g\cdot h_{air}+\rho _{Hg}\cdot g\cdot h_{Hg}[/tex]

where [tex]P _{gauge}=3.75 KPa[/tex]

So I solve for [tex]h_{Hg}[/tex] and get 2.8 cm. I don't think this is correct. Am I even using the correct equation?
 
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Anybody please?
 

1. What is the equation for solving for the height of Mercury?

The equation for solving for the height of Mercury is h = (2GM)/(v^2 - 2GM/r), where h is the height, G is the gravitational constant, M is the mass of the planet, v is the velocity, and r is the distance from the center of the planet.

2. How do you know if this equation is correct?

This equation is derived from the law of conservation of energy and Newton's law of universal gravitation. It has been extensively tested and has been shown to accurately predict the height of Mercury based on the given variables.

3. Can this equation be used for other planets?

Yes, this equation can be used for any planet as long as the relevant variables (mass, velocity, distance) are known. However, it may be necessary to adjust the values of G and M to account for the specific characteristics of the planet.

4. Are there any limitations to this equation?

Yes, this equation assumes that the planet is a perfect sphere with a uniform mass distribution. It also does not take into account any external influences or factors that may affect the height of Mercury, such as atmospheric drag or other celestial bodies.

5. How can this equation be applied in real-life situations?

This equation can be used to calculate the height of Mercury at a given point in its orbit, which can be useful for space missions or astronomical observations. It can also be used to study the gravitational effects of Mercury on other objects in its orbit.

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