Question

Two satellites are in circular orbits around a planet with a radius of 9.00x10⁶m.One satellite has a mass of 68.0kg,an orbital radius of 5.00x10⁷m, and an orbital speed of 4800 m/s The second satellite has a mass of 84.0kgand an orbital radius of 3.00kgx10⁷m.

1. What is the gravitational force acting on the first satellite?
A) 2.26 x10⁷N
B) 4.51 x10⁷N
C) 6.78 x10⁷N
D) 9.02x10⁷N
2. What is the gravitational force acting on the second satellite?
A) 1.13x10⁷N
B) 2.26x10⁷N
C) 3.39x10⁷N
D) 4.51x10⁷N

Answer 1

The gravitational force acting on the first satellite is 9.02 x 10^7 N, while the gravitational force acting on the second satellite is 4.51 x 10^7 N.

Step-by-step explanation:

To calculate the gravitational force acting on each satellite, we can use the formula F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant (6.67 x 10^-11 N(m/kg)^2), m1 and m2 are the masses of the two satellites, and r is the distance between the centers of the two satellites.

1. Gravitational force acting on the first satellite:

Using the given data:

• Mass of the first satellite (m1) = 68.0 kg
• Distance between the first satellite and the planet (r) = 5.00 x 10^7 m

Plugging in these values into the formula:

F = (6.67 x 10^-11 N(m/kg)^2 * 68.0 kg * 5.00 x 10^7 m) / (5.00 x 10^7 m)^2

Simplifying the equation:

F = 9.02 x 10^7 N

Therefore, the gravitational force acting on the first satellite is 9.02 x 10^7 N.

2. Gravitational force acting on the second satellite:

Using the given data:

• Mass of the second satellite (m2) = 84.0 kg
• Distance between the second satellite and the planet (r) = 3.00 x 10^7 m

Plugging in these values into the formula:

F = (6.67 x 10^-11 N(m/kg)^2 * 68.0 kg * 3.00 x 10^7 m) / (3.00 x 10^7 m)^2

Simplifying the equation:

F = 4.51 x 10^7 N

Therefore, the gravitational force acting on the second satellite is 4.51 x 10^7 N