For a moon orbiting its planet, rp is the shortest distance between the moon and its planet and ra is the longest distance between the moon and its planet. What is a moon's orbital eccentricity if rp is equal to 0.27ra ?(1 point) Responses 0.27 0.27 0.57 0.57 0.65 0.65 0.48
The eccentricity of a moon's orbit can be calculated using the formula:
eccentricity = (ra - rp) / (ra + rp)
Given that rp = 0.27ra, we can substitute this value into the formula:
eccentricity = (ra - 0.27ra) / (ra + 0.27ra)
= 0.73ra / 1.27ra
≈ 0.57
Therefore, the moon's orbital eccentricity is approximately 0.57.
The mass of an object doubles. What happens to the gravitational force between it and another object whose mass stays the same, assuming they remain the same distance apart?(1 point) Responses The amount of the gravitational force remains the same. The amount of the gravitational force remains the same. The amount of the gravitational force decreases by one-half. The amount of the gravitational force decreases by one-half. The amount of the gravitational force doubles. The amount of the gravitational force doubles. The amount of the gravitational force quadruples.
The amount of the gravitational force doubles.
Based on Kepler's observations about planetary motion, what is the relationship between a planet's orbital velocity and its distance from the sun?(1 point) Responses The greater the distance, the slower the orbital velocity. The greater the distance, the slower the orbital velocity. As distance is cut in half, orbital velocity decreases. As distance is cut in half, orbital velocity decreases. The greater the distance, the greater the orbital velocity. The greater the distance, the greater the orbital velocity. Distance has no effect on orbital velocity.
The greater the distance, the slower the orbital velocity.
What shape is the moon's orbit around Earth?(1 point) Responses a circle a circle an ellipse that is almost circular an ellipse that is almost circular an ellipse that is elongated an ellipse that is elongated a spiral
The shape of the moon's orbit around Earth is an ellipse that is almost circular.
Which are features of Copernicus's model of the solar system? Select the three correct answers.(2 points) Responses Earth is fixed to a crystalline sphere. Earth is fixed to a crystalline sphere. The planets move in perfect circles. The planets move in perfect circles. The outer planets move in epicycles. The outer planets move in epicycles. All planets orbit the Sun at the same speed. All planets orbit the Sun at the same speed. The stars are fixed to an outer sphere. The stars are fixed to an outer sphere. The Sun is at the center.
The three correct features of Copernicus's model of the solar system are:
1. The planets move in perfect circles.
2. All planets orbit the Sun at the same speed.
3. The Sun is at the center.
To find the moon's orbital eccentricity, we need to understand the definition of eccentricity and how it relates to the shortest and longest distances between the moon and its planet.
The orbital eccentricity of a celestial object is a measure of how non-circular its orbit is. It is calculated using the equation:
Eccentricity (e) = (ra - rp) / (ra + rp)
where ra is the longest distance between the moon and its planet (apoapsis) and rp is the shortest distance between the moon and its planet (periapsis).
Given that rp is equal to 0.27ra, we can substitute these values into the formula:
Eccentricity (e) = (0.27ra - ra) / (0.27ra + ra)
Simplifying the equation:
Eccentricity (e) = (-0.73ra) / (1.27ra)
Now we can cancel out the "ra" terms in the numerator and denominator:
Eccentricity (e) = -0.73 / 1.27
Calculating this expression:
Eccentricity (e) ≈ -0.5748
Since eccentricity is always positive, we take the absolute value of the calculated value:
Eccentricity (e) ≈ 0.5748
Therefore, the correct answer is 0.57.