At what altitude above the Earth's surface is the acceleration due to gravity equal to g/128?
i did
g/128=(G*Earth's mass)/r^2
then solved for r and got 72080960. its within 10% of the correct answer but not correct. what am i doing wrong? (ive already rounding differently,etc)
you need to subtract earth radius from r, the question asked for altitude.
There was a easier way to do this.
g/128=g*(re/(re+alt))^2 notice the g's divide out, or
(re+alt)^2/re^2=128
or (1+alt/re )^2=128
take the sqrt of each side...
alt= re * (sqrt128 -1)
Now you see why your answer was within ten percent, as the sqrt 128 is about 11.
To find the altitude above Earth's surface where the acceleration due to gravity is equal to g/128, we can use the equation:
g/128 = (G * Earth's mass) / r^2
where:
g is the acceleration due to gravity on Earth's surface,
G is the gravitational constant, and
r is the distance between the center of Earth and the point at altitude.
Let's go through the steps to solve for r.
1. Rearrange the equation to solve for r:
r^2 = (G * Earth's mass) / (g/128)
2. Simplify the right-hand side:
r^2 = (G * Earth's mass) * (128 / g)
3. Take the square root of both sides to solve for r:
r = √[(G * Earth's mass) * (128 / g)]
Now, it seems like you have already performed these steps and obtained r ≈ 72080960. However, the result is not correct. The reason for this discrepancy might be related to the values used for the gravitational constant (G) and the acceleration due to gravity (g).
Ensure that you are using the correct values:
- The gravitational constant (G) is approximately 6.674 × 10^(-11) m^3/(kg s^2).
- The acceleration due to gravity (g) is approximately 9.8 m/s^2.
Double-checking these values and redoing the calculation should yield the correct result.
To find the altitude above the Earth's surface where the acceleration due to gravity is equal to g/128, you made a correct first step by equating the gravitational force formula with the acceleration formula:
g/128 = (G * Earth's mass) / r^2
Where:
g is the acceleration due to gravity on the surface of the Earth,
G is the gravitational constant,
r is the distance from the center of the Earth to the object, and
Earth's mass refers to the mass of the Earth.
Now, let's go through the steps to solve for r correctly:
1. Rearrange the equation to solve for r:
r^2 = (G * Earth's mass * 128) / g
2. Take the square root of both sides:
r = √[(G * Earth's mass * 128) / g]
3. Substitute the necessary values:
- Gravitational constant, G = 6.67 x 10^-11 N(m/kg)^2
- Mass of the Earth, Earth's mass = 5.972 x 10^24 kg
- Acceleration due to gravity on the surface of the Earth, g = 9.8 m/s^2
r = √[(6.67 x 10^-11 N(m/kg)^2 * 5.972 x 10^24 kg * 128) / 9.8 m/s^2]
Evaluating this equation correctly should give you the correct answer.