Variable Speed Orbital
With the given data, how do you prove that a lunar month is about 28 days long?
With the given data, how do you prove that a lunar month is about 28 days long?
Me (mass of earth) = 5.98 E 24 kg
Mm (mass of moon) = 7.4 E 22 kg
Rm (radius of moon) = 1.74 E 6 m
Re (radius of earth) = 6.38 E 6 m
e*m (distance between SURFACES of earth and moon) = 3.84 E 8 m
*All of the variables used are supposed to have a subscript (for instance, Mm = M subscript m).
*I’m not sure about the variable “e*m” because that’s how it appears on the sheet, but I assume it’s one variable altogether.
*A hint on the paper says that you have to calculate the following: moon’s orbital radius, force of gravity between earth and moon, moon’s centripetal acceleration, linear speed, and its period. I don’t know how to find the last three. With acceleration I could find velocity, or find acceleration with velocity.
I did delete a similar question and add some information, but I didn’t I’d be able to get any answers again by simply adding “additional details.”
So the main things you need are the acceleration, linear speed, and period.
In circular motion (moon isn’t strictly circular, but close enough for this problem), there is always a centripetal acceleration. In this case that acceleration is caused by gravity (the force of which you’ve already calculated).
a = v^2 / r
But since F=ma, and you know the moon’s mass, you can calculate the moon’s acceleration. You now have the linear velocity of the moon when you solve for “v”.
With “v”, you know the distance the moon travels (2 * pi * radius of orbit), so you can calculate the time it takes or the period:
T = 2 * pi * orbit radius / v
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