Use table to answer the question
\Planet
Venus
Mars
Jupiter
Neptune
Estimated Mass of Planet (10^24 kg)
4.87
0.642
1,898.0
102.0
A spacecraft flies within 500,000 km of each of these planets. Which one would gravitationally attract the spacecraft the most?
a. Neptune
b. Venus
c. Mars
d. Jupiter
To determine which planet would gravitationally attract the spacecraft the most, we need to calculate the gravitational force experienced by the spacecraft from each planet. The formula to calculate gravitational force is:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
m1 is the mass of the spacecraft (assumed to be very small compared to the planet)
m2 is the mass of the planet
r is the distance between the spacecraft and the planet
We can calculate the gravitational force for each planet and compare them to determine the one that exerts the most force. Since the mass of the spacecraft is not given, we can assume it to be 1 kg for simplicity.
Gravitational force exerted by Venus:
F_v = G * (m1 * m2) / r^2
F_v = (6.67430 × 10^-11) * (1 * 4.87 * 10^24) / (500,000)^2
Gravitational force exerted by Mars:
F_m = G * (m1 * m2) / r^2
F_m = (6.67430 × 10^-11) * (1 * 0.642 * 10^24) / (500,000)^2
Gravitational force exerted by Jupiter:
F_j = G * (m1 * m2) / r^2
F_j = (6.67430 × 10^-11) * (1 * 1,898.0 * 10^24) / (500,000)^2
Gravitational force exerted by Neptune:
F_n = G * (m1 * m2) / r^2
F_n = (6.67430 × 10^-11) * (1 * 102.0 * 10^24) / (500,000)^2
Now we can calculate these forces:
F_v = 0.0535 N
F_m = 8.39 x 10^-3 N
F_j = 5.163 N
F_n = 9.89 x 10^-4 N
From the calculated values, we can see that Jupiter exerts the most gravitational force on the spacecraft. Therefore, the answer is d. Jupiter.