Calculate the force of Earth's gravity on a spacecraft 3.00 Earth radii above the Earth's surface if its mass is 1450 kg?

Answer 1

note: distance needs to be in meters, mass in kg

g = (G*Mass Earth)/(Radius earth + distance above earth surface)^2

g = (6.673e-11 * 5.98e24)/(6.38e6 + 12800e3)^2

g = 1.08 m/s^2

force = mass * acceleration

force = 1200 kg * 1.08 m/s^2

force = 1296 N

Also, there is an easier formula.

Earth's gravitational force decreases with the square of the distance from earth's center. So, The force of gravity = (1/r^2)mg

Force of gravity = (1/3^2)(1200)(9.80m/s/s)

r = 3 because the craft is 2 Earth radii away from the surface and we need to calculate to Earth's center

F = (1200 * 9.8m/s/s)/9 = 1300N rounded to 2 sig figs

Answer 2

1580 n

actually this answer is wrong, here's the right one with workings.

when the surface acceleration and radius are known, the equation for acceleration at another point is:

a = ( sa / ( ( d/r )^2 ) )

key:

sa = surface acceleration (earth = 9.81 ( m/s )/s )

d = distance from earths centre to craft

r = distance from earths centre to surface

so:

a = ( 9.81 / ( ( 4/1 )^2 ) )

a = 9.81 / 16

a = 0.613 ( m/s )/s

so if mass =1450 kg

f = m * a

f = 1450 * 0.613 = 889 newtons

Answer 3

You haven't told us the astronaut's mass, so we can't give you a number for his weight.

All we can say is that since he is (12,800/6,378) = 2 earth radii from the center

of the Earth, his weight is (1/2)2 = 1/4 of whatever it is on the surface.