Question

Orbital Tilt The Moon's orbit is tilted at an angle of \(5^{\circ}\) to Earth's orbit around the sun. Using a protractor, draw the Moon's orbit around Earth. What fraction of a full circle \(\left(360^{\circ}\right)\) is \(5^{\circ}\) ?

Short answer

The fraction is \( \frac{1}{72} \).

Step-by-step solution

Understanding the Problem

We're asked to determine what fraction a tilt angle of \(5^{\circ}\) is of a full circle, which has a total angle of \(360^{\circ}\). This involves dividing the angle of interest by the total angle.

Set Up the Equation

To find the fraction, we set up the equation \( \frac{5^{\circ}}{360^{\circ}} \). This represents the fraction of the Moon's orbital tilt compared to a full circle.

Perform the Division

Calculate the fraction by dividing \(5\) by \(360\): \( \frac{5}{360} = \frac{1}{72} \). This means the tilt is \( \frac{1}{72} \) of a full circle.

Simplifying the Fraction

Since \( \frac{5}{360} \) simplifies to \( \frac{1}{72} \), there are no further simplifications required. \(5^{\circ}\) is already in its simplest fractional form related to \(360^{\circ}\).

Drawing the Orbit

Using a protractor, draw a circle to represent Earth's orbit and another circle for the Moon, tilted by \(5^{\circ}\). Ensure the tilt angle on the protractor shows \(5^{\circ}\) between the two circular paths.

Key concepts

Angle Measurement

Understanding angle measurement is crucial in discussing orbital mechanics because angles describe the inclination of an orbit relative to a particular reference plane. An angle is part of a circle, which is universally measured in degrees. A full circle is always equal to 360 degrees.
To measure an angle correctly, one needs a protractor. The protractor allows you to identify how much of a circle's (its degrees) certain points take up. Hence, when we say the Moon's orbit is tilted at an angle of \(5^{\circ}\), we are indicating that the orbit's path around the Earth is offset by 5 degrees compared to the plane of the Earth's own orbit around the sun.

• A small tilt, like \(5^{\circ}\), may seem minor but it is significant in space, affecting things like eclipses.
• In orbital mechanics, precise angles are vital for understanding the orbits' paths and possible intersections.

Moon Orbit

The Moon orbits Earth in a path that is not flat but slightly tilted. This tilt is approximately \(5^{\circ}\), contrasting Earth's orbit around the sun. The moon's orbit, being tilted, is why we do not have an eclipse every full moon.
For a better understanding of this concept, imagine two hula hoops. One is parallel to the ground, while the other is slightly tilted. The angle at which the hula hoops cross each other is similar to the tilt of the Moon's orbit in its path around the Earth. This inclination largely dictates when and how solar and lunar eclipses occur.

• The moon's orbit is not just inclined but also elliptical, meaning it's not a perfect circle.
• This elliptical path causes variations in the Moon's speed and distance from Earth during its orbit.

Fraction Simplification

Simplifying fractions is an essential mathematical procedure that allows for easier understanding of ratios. When we express an angle as a fraction of 360 degrees, we distinguish a segment of a circle's full rotation. The original exercise required finding what fraction of a full circle \(5^{\circ}\) represents.
We form the fraction as \(\frac{5}{360}\) and simplify by finding the greatest common divisor (GCD) of 5 and 360. In this example, the GCD is 5, which simplifies the fraction to \(\frac{1}{72}\). This means the Moon's orbital tilt represents \(\frac{1}{72}\) of a full circle.

• Simplifying fractions is useful for not only computation but also for better understanding ratios or proportions.
• This allows for clearer insights into how small angles like \(5^{\circ}\) compare to larger reference angles.