Given that the Moon's period about the Earth is 27.32 days and the distance from the Earth to the Moon is 3.84*10^8 m estimate the mass of the Earth. Assume the orbit is circular. Why do you suppose your estimate is high?
The force of attraction= centripetal force
G MeMm/d^2=Mm*V^2/d
but v= 2PId/T
put that in for v in the above, solve for Me.
v= 2PId/T
what does PI mean?
PI is 3.14...
It is a mathematical constant approximately equal to 3.14159, which represents the ratio of a circle's circumference to its diameter. It is commonly used in various mathematical and scientific equations, including those related to circles and trigonometry.
Pi (π) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, meaning it cannot be expressed as a finite fraction or a repeating decimal. The value of pi is approximately 3.14159265358979323846, but for most calculations, we can round it to 3.14 or use the π symbol.
In the given formula, 2πd represents the circumference of the circle, and T represents the period of the Moon's orbit. By dividing the circumference by the period, we can calculate the linear velocity (v) of the Moon in its orbit.
So, whenever you see π in a formula, you can substitute it with the value 3.14 or use the π symbol.