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)
0.65
0.65
0.57
0.57
0.27
0.27
0.48
The moon's orbital eccentricity can be calculated using the formula:
e = (ra - rp) / (ra + rp)
Given that rp = 0.27ra, we can substitute the values into the formula:
e = (ra - 0.27ra) / (ra + 0.27ra)
Simplifying the equation:
e = (0.73ra) / (1.27ra)
e = 0.73/1.27
Therefore, the moon's orbital eccentricity is approximately 0.57.
To calculate the eccentricity of a moon's orbit, we can use the formula:
Eccentricity (e) = (ra - rp) / (ra + rp)
Given that rp is equal to 0.27ra, we can substitute this value into the formula:
Eccentricity (e) = (ra - 0.27ra) / (ra + 0.27ra)
Simplifying the expression, we get:
Eccentricity (e) = (0.73ra) / (1.27ra)
Canceling out the common factor of "ra", we have:
Eccentricity (e) = 0.73 / 1.27
Therefore, the moon's orbital eccentricity is approximately 0.57. So the correct answer is:
0.57
To find the moon's orbital eccentricity, we can use the formula:
eccentricity (e) = (ra - rp) / (ra + rp)
Given that rp is equal to 0.27ra, we can substitute this value into the formula:
eccentricity (e) = (ra - 0.27ra) / (ra + 0.27ra)
Simplifying further, we get:
eccentricity (e) = 0.73ra / 1.27ra
The 'ra' on both sides of the fraction cancels out:
eccentricity (e) = 0.73 / 1.27
Evaluating the division, we can determine the value of the eccentricity:
eccentricity (e) ≈ 0.57
Therefore, the moon's orbital eccentricity is approximately 0.57.