An astronaut in space is in orbit #250# #km# above the surface of Earth. What is the gravitational acceleration on the astronaut at this altitude?

1 Answer
Jun 7, 2016

Answer:

The acceleration due to gravity is given by #a=(GM)/r^2# where G is the gravitational constant and M is the mass of Earth. The value at this altitude is #9.08# #ms^-2#.

Explanation:

Constants:

#G=6.67408xx10^-11# #m^3 kg^-1 s^-2#
#M=5.972xx10^24# #kg#

The radius of Earth is #r=6.371xx10^6# #m#

In this case, we need to add another #2.5xx10^5# #m# (250 km) to the radius, to give #r=6.621xx10^6# #m#

So:

#a=(GM)/r^2=(6.67xx10^-11xx5.97xx10^24)/(6.621xx10^6)^2=9.08# #ms^-2#

This makes sense, since the acceleration due to gravity is #9.81# #ms^-2#. The radius has been increased by only about 4%, but the acceleration due to gravity is inversely proportional to the square of the radius.