Calculating Mass from Weight and Distance

[majormuss]

Homework Statement

How can I find mass when weight and distance is given.(Note I can't use 9.8m/s^2 as my acceleration of gravity because the question is dealing distances that are extremely high from Earth's surface.And also how can i find the right acceleration at such heights?

Homework Equations

F=ma

The Attempt at a Solution

am stuck cos I know i can't use 9.8m/s^2.

 

[Fightfish]

Have you come across Newton's theory of gravitation?
$$F_{g} = \frac{Gm_{1}m_{2}}{r^2}$$

 

[kerimek]

There are a few factors to consider when calculating mass from weight and distance. First, it is important to understand that weight and mass are not the same thing. Weight is a measure of the force of gravity acting on an object, while mass is a measure of the amount of matter in an object. Therefore, to calculate mass, we need to use the equation F=ma, where F is the force, m is the mass, and a is the acceleration.

In order to find the right acceleration at extremely high distances from Earth's surface, we need to consider the effects of gravity at those distances. The acceleration due to gravity decreases as distance from Earth's surface increases, following the inverse square law. This means that the acceleration at a certain distance from Earth's surface will be less than 9.8m/s^2. To find the exact acceleration at a specific distance, we can use the equation a=(GM)/(r^2), where G is the universal gravitational constant, M is the mass of Earth, and r is the distance from Earth's center.

Once we have calculated the correct acceleration at the given distance, we can use the equation F=ma to find the mass. Remember to convert the weight to Newtons (N) before plugging it into the equation.

Overall, it is important to consider the effects of gravity at different distances from Earth's surface when calculating mass from weight and distance. It may also be helpful to double check your calculations and make sure you are using the correct units.