Calculate Perihelion Distance of Mars Using Solar System Parameters

In summary, the conversation discusses calculating the distance of Mars from the Sun at perihelion using the equation r = a(1 - e^2) / (1 +e cos θ), with given values of a = 1.5237 AU and e = 0.0934. The correct solution is 1.38 AU. The conversation also mentions a previous error in obtaining the solution due to a calculator mistake.
  • #1
ZedCar
354
1

Homework Statement


Assuming that the sun lies at the principal focus of the solar system, and given that the semi-major axis and eccentricity of Mars is 1.5237 AU and 0.0934 respectively, calculate:

The distance (in AU) when Mars is closest to the Sun (known as perihelion). The angle θ=0°


Homework Equations



r = a(1 - e^2) / (1 +e cos θ)



The Attempt at a Solution



The correct solution is 1.38 AU

Though if I use the above eqn putting a=1.5237 and e=0.0934 I get an answer of 16.17.

Thanks for any help!
 
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  • #2
Must be finger problems with the calculator :smile:

What values do you calculate for the numerator and denominator of the expression?
 
  • #3
Sorry about that! I'm getting the correct answer now...!
 

1. What is a perihelion distance?

A perihelion distance is the closest distance between a planet or object in our solar system and the sun. It is typically measured in astronomical units (AU), with 1 AU being the average distance between Earth and the sun.

2. How do you calculate the perihelion distance of Mars?

To calculate the perihelion distance of Mars, you need to know the semi-major axis of Mars' orbit (1.524 AU) and the eccentricity of its orbit (0.0934). Then, you can use the formula: Perihelion Distance = Semi-Major Axis * (1 - Eccentricity).

3. What are the solar system parameters needed for this calculation?

The solar system parameters needed for this calculation are the semi-major axis and eccentricity of Mars' orbit. These can be found in many astronomy textbooks or on reputable websites such as NASA's Solar System Exploration page.

4. Why is it important to calculate the perihelion distance of Mars?

Calculating the perihelion distance of Mars can help us better understand the planet's orbit and its relationship to the sun. It can also provide insights into the planet's climate and any potential changes in its orbit over time.

5. How does the perihelion distance of Mars compare to that of Earth?

The perihelion distance of Mars is about 1.38 AU, while the perihelion distance of Earth is about 0.98 AU. This means that Mars is, on average, about 0.4 AU farther away from the sun at its closest point compared to Earth's closest point.

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