Calculate the acceleration due to gravity

In summary, the conversation is about calculating the acceleration due to gravity (g) for an object orbiting 200 kilometers above the Earth's surface. The equation for the force of gravity between two objects separated by a distance is F = (GMm)/R^2, and the equation for acceleration is F = ma. By combining these equations, one can find an expression for a and determine what percentage it is of 9.8m/s2. The hint suggests that objects of different mass fall at the same rate, ignoring air resistance.
  • #1
Linco
10
0
Many people mistakenly believe that austronauts that orbit the Earth are "above gravity." Calculate the acceleration due to gravity (g) for space shuttle territory, 200 kilometeres above the Earth's surface. Earth's mass is 6x1024 kilograms and its radius is 6.38 x 106 meters (6380 kilometers). Your answer is what percentage of 9.8m/s2?

Can anyone point me in the right direct to figure this out? I am not really sure what formula to use.
 
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  • #2
Which equation describes the force of gravity between any two point objects separated by some distance? The equation can also be used when the objects are both spherical, or when one of the two is very large and spherical.
 
  • #3
Your physics textbook probably gives the formula for acceleration. If not, it surely gives these two formulas:

[tex]F=\frac {GMm}{R^2}[/tex]

and

[tex]F=ma[/tex]

Use Algegra to combine these formulas to write an expression for [tex]a[/tex].
Hint: If you do it right, your little m's will cancel (illustrating that objects of different mass fall at the same rate ignoring air resistance).
 

Related to Calculate the acceleration due to gravity

1. What is the formula for calculating the acceleration due to gravity?

The formula for calculating the acceleration due to gravity is a = g, where a is the acceleration and g is the gravitational acceleration constant which is approximately 9.8 m/s2.

2. How is the acceleration due to gravity related to mass and distance?

The acceleration due to gravity is directly proportional to the mass of the object and inversely proportional to the square of the distance between the objects. This means that the greater the mass, the greater the gravitational force, and the farther the distance, the weaker the gravitational force.

3. What factors affect the acceleration due to gravity?

The acceleration due to gravity is affected by the mass and distance of the objects, as well as the gravitational constant. It also varies depending on the location, as the strength of gravity is slightly different on different planets and at different altitudes.

4. How can the acceleration due to gravity be measured?

The acceleration due to gravity can be measured using a variety of methods, such as dropping objects and measuring the time it takes to fall, using a pendulum and measuring its period, or using sophisticated tools such as gravimeters.

5. Can the acceleration due to gravity ever be 0?

No, the acceleration due to gravity cannot be 0. Even if there are no objects present, there is still a gravitational force between the objects and the Earth, and therefore there will always be some acceleration due to gravity present.

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