A moon is orbiting the planet Jupiter, 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 0.48 0.48 0.27 0.27 0.57 0.57 0.65
The eccentricity of an orbit can be calculated using the formula:
eccentricity = (ra - rp) / (ra + rp)
Given that rp = 0.27ra, we can substitute this value in the formula:
eccentricity = (ra - 0.27ra) / (ra + 0.27ra)
eccentricity = (0.73ra) / (1.27ra)
eccentricity ≈ 0.57
Therefore, the correct answer is 0.57.
To find the moon's orbital eccentricity, we can use 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)
Simplifying the equation:
eccentricity = (0.73ra) / (1.27ra)
The 'ra' cancels out:
eccentricity = 0.73 / 1.27
Calculating the division:
eccentricity ≈ 0.5748
Therefore, the moon's orbital eccentricity is approximately 0.575.
To calculate the eccentricity of a moon's orbit, we need to use the ratio of the shortest distance (rp) to the longest distance (ra). The formula for eccentricity (e) is given by:
e = (ra - rp) / (ra + rp)
In this case, we are given that rp is equal to 0.27ra. Substituting this value into the formula, we get:
e = (ra - 0.27ra) / (ra + 0.27ra)
Simplifying this expression, we have:
e = (0.73ra) / (1.27ra)
Now, we can cancel out the factor of "ra":
e = 0.73 / 1.27
Evaluating this expression, we find:
e ≈ 0.57
Therefore, the moon's orbital eccentricity is approximately 0.57.