Use table to answer the question
\Planet Estimated Mass of Planet (10^24 kg)
Venus 4.87
Mars 0.642
Jupiter 1,898.0
Neptune 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 exerted by each planet on the spacecraft. The gravitational force can be calculated using the formula:
F = G * (M1 * M2) / r^2
Where:
F is the gravitational force (in newtons)
G is the gravitational constant, approximately 6.67430 * 10^-11 N(m/kg)^2
M1 is the mass of the planet (in kilograms)
M2 is the mass of the spacecraft (which we can assume as negligible compared to the planet's mass)
r is the distance between the spacecraft and the planet (in meters)
Given that the spacecraft flies within 500,000 km (or 500,000,000 meters) of each planet, we can calculate the gravitational force exerted by each planet using the formula above.
For Venus:
F = G * (Mass of Venus * Mass of spacecraft) / (Distance^2)
= (6.67430 * 10^-11) * (4.87 * 10^24) * (Mass of spacecraft) / (500,000,000)^2
For Mars:
F = G * (Mass of Mars * Mass of spacecraft) / (Distance^2)
= (6.67430 * 10^-11) * (0.642 * 10^24) * (Mass of spacecraft) / (500,000,000)^2
For Jupiter:
F = G * (Mass of Jupiter * Mass of spacecraft) / (Distance^2)
= (6.67430 * 10^-11) * (1,898.0 * 10^24) * (Mass of spacecraft) / (500,000,000)^2
For Neptune:
F = G * (Mass of Neptune * Mass of spacecraft) / (Distance^2)
= (6.67430 * 10^-11) * (102.0 * 10^24) * (Mass of spacecraft) / (500,000,000)^2
By calculating the gravitational force using the above equations, we can determine which planet would gravitationally attract the spacecraft the most.