Question

Newton's Law of Gravitation states that two bodies with masses M and N attract each other with a force F=G

r
2

MN
​
, where r is the distance between the bodies and G is the gravitational constant. Use Newton's Law of Gravitation to compute the work (in J) required to launch a 1000-kg satellite vertically to an orbit 1000 km high. You may assume that Earth's mass is 5.98×10
24
kg and is concentrated at its center. Take the radius of the Earth to be 6.37×10
6
m and G=6.67×10
−11
N⋅m
2
/kg
2
. Work done =J

Answer 1

To compute the work required to launch a 1000-kg satellite vertically to an orbit 1000 km high, we can use Newton's Law of Gravitation by calculating the initial potential energy and the final potential energy of the satellite.

Step-by-step explanation:

To compute the work required to launch a 1000-kg satellite vertically to an orbit 1000 km high using Newton's Law of Gravitation, we need to find the initial potential energy and the final potential energy of the satellite. The change in potential energy will give us the work done.

First, we can calculate the initial potential energy using the formula U = -GMm/R, where U is the potential energy, G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and R is the radius of the Earth plus the height of the orbit.

Next, we can calculate the final potential energy using the same formula, but with R being the radius of the Earth. Finally, we can subtract the initial potential energy from the final potential energy to find the work done.

Answer 2

The wok required to launch the satellite is determined as 5.41 x 10¹⁰ J.

How to calculate the work done?

The wok required to launch the satellite is calculated by applying the following formula as shown below;

work required, W = F x r

F = GMm/r²

W = GMm/r² x r

W = GMm/r

where;

• M is the mass of the earth
• m is the mass of the satellite
• r is the distance
• G is universal gravitation constant

W = (6.67 x 10⁻¹¹ x 5.98 x 10²⁴ x 1000 ) / ( 1 x 10⁶ + 6.37 x 10⁶)

W = 5.41 x 10¹⁰ J