Gravitational Field Strength & Satellites

Gravitational Field Strength

Gravitational force per unit mass on an object

g = Fg / m

(units = N/Kg) g = gravitational field strength Fg = Force of gravity (also weight) m = mass

Gravitational Field Strength

Example Problem:

While in orbit in the space shuttle, the gravitational field strength on an astronaut is 7.83 N/Kg.

1. How much does an 80 kg astronaut weigh on the shuttle?

2. How much does the astronaut weigh on Earth?

Gravitational Field Strength ProblemHow much does an 80 kg astronaut weigh on

the shuttle?g = Fg / m (solve for Fg)

Fg= (7.83 N/Kg) x (80 Kg)= 626.4 N (we don’t express in N)= 626.4 N x .22 lbs/N= 137.8 lbs

Gravitational Field Strength Problem

How much does the astronaut weigh on Earth?

Fg = (9.8 N/Kg) x (80 Kg)

= 784 N

= (784 N) x (.22 lbs/N)

= 172.5 lbs

Satellite Speed & Period

Remember, to solve for altitude you must include the radius of the Earth

To solve for altitude, use the equation a = v2 (solve for “r”)

rspeed / velocity: v = sqrt Gxm / rperiod: T = 2π x sqrt R3

GM

Satellite Speed & Period

When solving these problems, you use the “M” – the large mass that the satellite is revolving around

“R” – the radius / altitude of the satellite above the object it is orbiting