Question

How much work must an external force do on the satellite to move it from a circular orbit of radius 2 Re to 3 Re, if its mass is 2000 kg? The universal gravitational constant 6.67 × 10−11 N · m2 /kg2 , the mass of the Earth 5.98 × 1024 kg and its radius 6.37 × 106 m. Answer in units of J.

Answer 1

The work done by the external force in moving the satellite is determined as 1.25 x 10¹¹ J.

How to calculate the work done by the external force?

The work done by the external force in moving the satellite is calculated by applying the following formula as shown below.

W = F x R

W = (GmM)/R

where;

• G is universal gravitation constant
• M is the mass of earth
• m is the mass of the satellite
• R is the position of the masses

When the satellite is moved from a circular orbit of radius 2 Re to 3 Re, the distance becomes;

R = 3Re - 2Re

R = Re

W = (GmM)/Re

W = (6.67 x 10⁻¹¹ x 2000 x 5.98 x 10²⁴) / ( 6.37 x 10⁶)

W = 1.25 x 10¹¹ J

Answer 2

20872108843.53741 Joules

Step-by-step explanation:

Re = Radius of Earth = 6.37×10⁶ m

M = Mass of the Earth = 5.98 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m = Mass of satellite = 2000 kg

Potential energy

`U_1=G(Mm)/((2Re))`

`U_2=G(Mm)/((3Re))`

`U_1-U_2=6.67* \:\:\:10^(-11)(5.98* \:\:\:10^(24)* \:\:\:2000)/(2\left(6.37* \:\:\:10^6\right))-6.67* \:\:\:\:10^(-11)(5.98* \:\:\:\:10^(24)* \:\:\:\:2000)/(3\left(6.37* \:\:\:\:10^6\right))\\ =20872108843.53741\ Joules`

Energy required to move the satellite is 20872108843.53741 Joules