"two planets have the same mass, but planet a has 3 times the radius of planet
1 answer:
The gravitational acceleration on the surface of planet A is:
where G is the gravitational constant,
is the mass of planet A and 
its radius.
Similarly, the gravitational acceleration on the surface of planet B is:
The ratio between the gravitational acceleration on planet A and B becomes:
The problem says that the two masses are equal:
while planet A has 3 times the radius of planet B: 
. Substituting into the ratio, we get:
so, gravity on planet B is 9 times stronger than planet A.
where G is the gravitational constant,
Similarly, the gravitational acceleration on the surface of planet B is:
The ratio between the gravitational acceleration on planet A and B becomes:
The problem says that the two masses are equal:
so, gravity on planet B is 9 times stronger than planet A.
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Answer:
g(h) = g ( 1 - 2(h/R) )
<em>*At first order on h/R*</em>
Explanation:
Hi!
We can derive this expression for distances h small compared to the earth's radius R.
In order to do this, we must expand the newton's law of universal gravitation around r=R
Remember that this law is:
In the present case m1 will be the mass of the earth.
Additionally, if we remember Newton's second law for the mass m2 (with m2 constant):
Therefore, we can see that
With a the acceleration due to the earth's mass.
Now, the taylor series is going to be (at first order in h/R):
a(R) is actually the constant acceleration at sea level
and
Therefore:
Consider that the error in this expresion is quadratic in (h/R), and to consider quadratic correctiosn you must expand the taylor series to the next power: