A spacecraft flies within 500,000 km of each of these planets. Based on its mass, which planet would gravitationally attract the spacecraft the most?
Planet
Venus
Mars
Jupiter
Neptune
Estimated Mass of Planet (10^24 kg)
4.87
0.642
1,898.0
102.0
To determine which planet would gravitationally attract the spacecraft the most based on its mass, we need to calculate the gravitational force of each planet on the spacecraft.
The gravitational force between two objects can be calculated using the formula:
F = (G * m1 * m2) / d^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.674 * 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects
d is the distance between the centers of the two objects
Let's calculate the gravitational force for each planet:
Venus:
Mass of Venus (m1) = 4.87 * 10^24 kg
Mass of spacecraft (m2) = assume some constant value
Distance (d) = 500,000 km = 500,000,000 meters
F_venus = (6.674 * 10^-11 N m^2 / kg^2 * 4.87 * 10^24 kg * m2) / (500,000,000 m)^2
Mars:
Mass of Mars (m1) = 0.642 * 10^24 kg
Distance (d) = 500,000,000 meters
F_mars = (6.674 * 10^-11 N m^2 / kg^2 * 0.642 * 10^24 kg * m2) / (500,000,000 m)^2
Jupiter:
Mass of Jupiter (m1) = 1,898.0 * 10^24 kg
Distance (d) = 500,000,000 meters
F_jupiter = (6.674 * 10^-11 N m^2 / kg^2 * 1,898.0 * 10^24 kg * m2) / (500,000,000 m)^2
Neptune:
Mass of Neptune (m1) = 102.0 * 10^24 kg
Distance (d) = 500,000,000 meters
F_neptune = (6.674 * 10^-11 N m^2 / kg^2 * 102.0 * 10^24 kg * m2) / (500,000,000 m)^2
To determine which planet gravitationally attracts the spacecraft the most, we need to compare the values of F for each planet. The planet with the highest value of F will attract the spacecraft the most.