The asteroid Icarus has a perihelion of 0.19 AU and an orbital eccentricity of 0.83. How do you calculate the asteroid's orbital semimajor axis and aphelion distance from the Sun?
SemiMajor Axis Distance:
Aphelion Distance:
Determine the semimajor axis distance using Equation 2.
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The formula for calculating the semimajor axis of an asteroid's orbit is a = (2 * q) / (1  e), where 'a' is the semimajor axis, 'q' is the perihelion distance, and 'e' is the eccentricity. For example, for Icarus, the formula is a = (2 * 0.19) / (1  0.83). The formula for calculating the aphelion distance is Q = a * (1 + e). Substituting 'a' and 'e' into the formula yields Q = a * (1 + 0.83). Solve for 'a' and 'Q' to determine the semimajor axis and aphelion distance.
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To calculate the asteroid's orbital semimajor axis ((a)) and aphelion distance from the Sun, you can use the following formulas:

Orbital semimajor axis ((a)) can be calculated using the formula: [a = \frac{{\text{{Perihelion}}}}{{1  \text{{Eccentricity}}}}]

Aphelion distance ((Q)) can be calculated using the formula: [Q = a \times (1 + \text{{Eccentricity}})]
Using the given values:
 Perihelion ((r)) = 0.19 AU
 Eccentricity ((e)) = 0.83
Substituting these values into the formulas: [a = \frac{{0.19}}{{1  0.83}}]
[Q = a \times (1 + 0.83)]
Calculating: [a = \frac{{0.19}}{{1  0.83}} = \frac{{0.19}}{{0.17}} ≈ 1.11765 , \text{AU}]
[Q = 1.11765 \times (1 + 0.83) ≈ 2.04758 , \text{AU}]
So, the asteroid's orbital semimajor axis ((a)) is approximately 1.11765 AU, and its aphelion distance from the Sun ((Q)) is approximately 2.04758 AU.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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