Astrology, that unlikely and vague pseudoscience, makes much of the position of the planets at the moment of one’s birth. The only known force a planet exerts on objects on Earth is gravitational. (a) Calculate the gravitational force exerted on a
4.20 kg baby by the Earth. (b) Calculate the force on the baby due to Jupiter when it is
6.29×1011 m away, its closest approach to Earth. Food for thought: how does the force of Jupiter on the baby compare to the force of the Earth on the baby?
(a) Well, the Earth definitely has a lot of pull when it comes to babies (and pretty much everything else on the planet!). The gravitational force exerted on the baby by the Earth can be calculated using Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the two objects (in this case, the baby and the Earth), and r is the distance between the centers of the two objects.
Now, the mass of the baby is given as 4.20 kg, and the radius of the Earth is around 6,378,000 meters. Plugging in these values, we get:
F = (6.67430 × 10^-11) * (4.20 * 5.97 × 10^24) / (6,378,000)^2
After doing the math, the gravitational force exerted on the baby by the Earth turns out to be approximately 39.23 Newtons.
(b) Now let's calculate the force on the baby due to Jupiter. The mass of Jupiter is approximately 1.898 × 10^27 kg, and the closest approach to Earth is given as 6.29 × 10^11 meters. Plugging in these values into the same formula, we get:
F = (6.67430 × 10^-11) * (4.20 * 1.898 × 10^27) / (6,29 × 10^11)^2
After some calculations, the force on the baby due to Jupiter is roughly 5.95 × 10^-5 Newtons.
Food for thought: The force of Jupiter on the baby is significantly smaller compared to the force of the Earth on the baby. So when it comes to astrological intentions, it seems like Earth has a lot more pull than Jupiter. But hey, at least you won't be blamed on Jupiter when you misbehave!
To calculate the gravitational force exerted on the baby by the Earth, we can use the formula for the gravitational force:
F = G * (m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 = mass of the baby
m2 = mass of the Earth
r = distance between the baby and the center of the Earth
(a) Given that the mass of the baby is 4.20 kg, and the mass of the Earth is approximately 5.972 × 10^24 kg, we can assume that the baby's distance from the center of the Earth is the radius of the Earth, which is approximately 6.371 × 10^6 m.
F = G * (m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2/kg^2) * (4.20 kg * 5.972 × 10^24 kg) / (6.371 × 10^6 m)^2
Calculating this, the gravitational force exerted on the baby by the Earth is approximately 35.06 N.
(b) Now, let's calculate the force on the baby due to Jupiter when it is 6.29 × 10^11 m away, its closest approach to Earth. We'll use the same formula:
F = G * (m1 * m2) / r^2
Where:
m1 = mass of the baby
m2 = mass of Jupiter
r = distance between the baby and Jupiter (6.29 × 10^11 m)
We can approximate the mass of Jupiter as 1.898 × 10^27 kg.
F = G * (m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2/kg^2) * (4.20 kg * 1.898 × 10^27 kg) / (6.29 × 10^11 m)^2
Calculating this, the force on the baby due to Jupiter is approximately 5.37 × 10^-5 N.
Food for thought: Comparing the force of Jupiter on the baby to the force of the Earth on the baby, the force of Jupiter (5.37 × 10^-5 N) is significantly smaller than the force of the Earth (35.06 N).
To calculate the gravitational force exerted on an object, we can use the equation:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (6.67430 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the objects (in this case, the baby and the Earth or Jupiter),
and r is the distance between the objects.
(a) To calculate the gravitational force exerted on the 4.20 kg baby by the Earth, we need to know the mass of the Earth. The mass of the Earth is approximately 5.97 × 10^24 kg. The distance between the baby and the Earth is negligible compared to the radius of the Earth, so we can consider it as the radius of the Earth, which is approximately 6.37 × 10^6 m.
Plugging the values into the equation, we have:
F = (6.67430 × 10^-11 N m^2 / kg^2) * ((4.20 kg) * (5.97 × 10^24 kg)) / (6.37 × 10^6 m)^2
Calculating this, we find that the gravitational force exerted on the baby by the Earth is approximately 39.97 N.
(b) To calculate the force on the baby due to Jupiter when it is 6.29 × 10^11 m away, we need to know the mass of Jupiter. The mass of Jupiter is approximately 1.898 × 10^27 kg.
Plugging the values into the equation, we have:
F = (6.67430 × 10^-11 N m^2 / kg^2) * ((4.20 kg) * (1.898 × 10^27 kg)) / (6.29 × 10^11 m)^2
Calculating this, we find that the force on the baby due to Jupiter is approximately 1.96 × 10^-4 N.
Comparing the force of Jupiter on the baby to the force of the Earth on the baby, we can see that the force of Jupiter is much smaller than the force of the Earth.