should be lifespan dovelopment
Newton's first law of motion is an object in motion stays in motion until acted upon by another force. Driving at 30 mph in a car is going to stay constant until you crash the car into a wall, stopping the car.
To find initial velocity, start by multiplying the acceleration by the time. Then, divide that number by 2 and write down the quotient you get. Next, divide the distance by the time and write down that quotient as well. Finally, subtract your first quotient from your second quotient to find the initial velocity.
Kepler's 3rd law of planetary motion is exactly
what we need in order to answer this one:
(orbital period)² / (orbital radius)³ =
the same number for all bodies orbiting the sun
Let's call that number 'K' just for convenience.
So we know that T₀² / R₀³ = K
We're going to be looking for 'T', so let's rearrange the equation now.
Multiply each side by R₀³ .
Now it says
T₀² = K R₀³
Now, take the square root of each side, and we have
T₀ = √ (K R₀³) .
Now the radius is increased to (1.04 R₀).
We want to find the new T .
T = √ K · (1.04 R₀)³
= √ K · 1.124864 R₀³
Pull that decimal out of the radical, by taking its square root:
= 1.0606 √K · R₀³
T = 1.0606 T₀
The orbital time has increased by 6% .
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I suspect we probably could have said that since T varies
as R^1.5 power, we should look for (1.04)^1.5 power.
(1.04)^1.5 = 1.0606 <== bada-bing
