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Gravitational Field Difference on the Human Body while approaching a Black Hole
Newtons Law of Gravitation:
F is the gravitational force
G is the gravitational constant
m1 is the mass of object 1
m2 is the mass of object 2
r is the radius between the two objects
The force (F) is directly proportional to the product of the 2 objects masses, and inversely proportional
to the square of the distance between them.
We will use the super massive black hole at the center of our Milky Way galaxy, which has been
calculated to have a mass of 4.1 million solar masses, or 8.15457x1036 kg. This value will be our m1. For
m2, we will use an average person of 150 lbs, or 68.03886 kg.
m1= 8.15457x1036 kg
m2= 68.03886 kg
G= 6.673x10-11 N∙m2/kg2
Next we will use an average height of human being, say 5 ft 7 inches, which is 1.7018 m. We will take 2
measurements, to show that the gravitational field difference is different at a person’s head, or their
feet. We will first take a standard distance away from black hole, say 1 km. Now if we measure from the
feet up to the head, the feet will be at 0 m, and the head would be at 1.7018. This means that our first
distance would be 1000 m, while or second distance would be 1001.7018 m.
Let’s analyze the first equation which would be the force at the feet.
For the second calculation, we will use the same equation, except use the second distance we found.
This results in the following:
This may not look like a big difference at all, but the gravitational force at your feet is actually
1.25644x1020 N, that’s 125,644,000,000,000,000,000 N bigger than at your head!
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