Question

Gravitational Force of Objects at Different Distances From Earth(round to nearest 100ths place)Object in SpaceAltitudeabove SeaLevel(meters)Distance fromCenter ofEarth (meters)Mass ofObject/Person(kilogram)Mass of Earth(kilogram)GravitationalForceExperienced(Newton)Orbit or Fall toEarth?Person at SeaLevel06,377,500755.97 x 1024N/APerson at Peakof MountEverest8,8486,386,348755.97 x 1024N/ATiangong-1Satellite208,0006,585,5008,5065.97 x 1024Fall to EarthSpaceX StarlinkSatellite538,7006,916,200260,0005.97 x 1024OrbitGPS Satellites20,189,00026,566,5001,6305.97 x 1024OrbitGOES WeatherSatellite35,786,20042,163,7002,8575.97 x 1024OrbitDirecTV35.793.50042.171.00035735.97 x 1024Orbit

Answer 1

Given the formula:

$F_g=\frac{Gm_1m_2}{d^2}$

Where:

G = 6.67 x 10^-11

m1 = Mass of object per person

m2 - mass of earth

d = distance between objects

Let's solve for the gravitational forces.

We have:

1) Person at sea level:

$F_g=\frac{(6.67\ast10^{-11})\ast75\ast5.97\ast10^{24}}{6377500^2}=734.28N$

2) Person at peak of mount everest:

$F_g=\frac{(6.67\ast10^{-11})\ast75\ast5.97\ast10^{24}}{(6386348-8848)^2}=734.28N$

3) Tiangong-1 satellite:

$F_g=\frac{(6.67\ast10^{-11})\ast8506\ast5.97\ast10^{24}}{(6585500-208000)^2}=83276.91N$

4) Space-X starlink satellite:

$F_g=\frac{(6.67\ast10^{-11})\ast260000\ast5.97\ast10^{24}}{(6916200-538700)^2}=2545496.94N$

5) GPS satellites:

$F_g=\frac{(6.67\ast10^{-11})\ast1630\ast5.97\ast10^{24}}{(26566500-20189000)^2}=15958.31N$

6) GOES weather satellite:

$F_g=\frac{(6.67\ast10^{-11})\ast2857\ast5.97\ast10^{24}}{(42163700-35786200)^2}=27971.10N$

7) DirecTV satellite:

$F_g=\frac{(6.67\ast10^{-11})\ast3573\ast5.97\ast10^{24}}{(42171000-35793500)^2}=34981.00N$

8) SiriusXM:

$F_g=\frac{(6.67\ast10^{-11})\ast7000\ast5.97\ast10^{24}}{(30784500-24407000)^2}=68532.61N$

9) Moon:

$F_g=\frac{(6.67\ast10^{-11})\ast7.35\cdot10^{22}\ast5.97\ast10^{24}}{(384399000-378021500)^2}=7.20\ast10^{23}$

Part 2:

A satellite stay in orbit due to force of gravity and the statellites momentum from its launch into space.

A statellite may fall back to earth due to a drag that causes the staellites orbit go decay. This drag happens when the staellite run into traces of the earth's atmosphere.