What is the weight and altitude?

Question

an object weighs 600N on Earth and it is placed 100km above the surface of the Earth.

a. what is its weight?

b. what is its altitude?

please give the steps/solution..

Answer 1

a) what is its weight? well it is 600N

b) Let's look at the old gravity equation

F= G Mm/R^2

G- universal gravitational constant

R- radius of the Earth

M - mass of the Earth

m - mass of the object

At 100km or 10^5m

R2= R+ 10^5

weight at 100km = G Mm/(R2)^2  or

W2= G Mm/(R +10^5)^2

Let's find out what is the ratio of W1/W2

W1/W2=  G Mm/R^2 / G Mm/(R +10^5)^2  or

W1/W2= (R +10^5)^2  / R^2  finally

W1/W2= (1 +10^5/R)^2

Let the Earth radius be  6,360 km or 6.36 x 10^6 m

we have

W1/W2= (1 +10^5/6.36 x 10^6 )^2

W1/W2= 1.032 that means that the object on the surface of the Earth will be 1.032 heavier than 100 km above the surface.

then W2= W1/ 1.032= 582N

Answer 2

The radius of the earth can be taken as 6,378,100m At this distance from the centre of the earth, the object has a force of 600N.

The distance from the centre of the earth is increased to 6,478,100m.

The force of the object(its weight) will change to:

600* (6378100)²/(6478100)²

New force(weight) will be: 581.62N

The altitude of the object is 100km or 100,000 m (altitude is the height of an object above the earth's surface, which you have given as 100km)