Question

The mass of the Hubble Space Telescope is 11,600 kg. Determine the weight of the telescope as it is in its orbit 598 km above the earth's surface. Mearth =5.98×1024 kg, Rearth =6.37×106 m

Answer 1

The weight of the Hubble Space Telescope in its orbit can be calculated using Newton's law of universal gravitation. By substituting the given values into the gravitational force formula, we find that the telescope's weight is approximately 9.82 x 10^4 Newtons at an altitude of 598 km above the Earth's surface.

Step-by-step explanation:

To calculate the weight of the Hubble Space Telescope when it is in its orbit above Earth's surface, we will use Newton's law of universal gravitation. The weight of an object in orbit is essentially the gravitational force acting on it. This force can be calculated using the formula:

F = G * (m1 * m2) / r^2

Where:

F is the gravitational force (weight of the telescope in orbit)

G is the gravitational constant (6.674x10^-11 N(m^2)/(kg^2))

m1 is the mass of the Earth (5.98×10^24 kg)

m2 is the mass of the Hubble Space Telescope (11,600 kg)

r is the distance from the center of the Earth to the telescope, which includes Earth's radius plus the altitude of the telescope in orbit (6.37×10^6 m + 598×10^3 m)

Calculating the distance r:

r = Earth's radius + telescope's altitude above Earth's surface

r = 6.37×10^6 m + 598×10^3 m

r = 6.968×10^6 m

Now, we can substitute all the values into the formula:

F = (6.674×10^-11 N(m^2)/(kg^2)) * ((5.98×10^24 kg) * (11,600 kg)) / (6.968×10^6 m)^2

After calculating, we find:

F ≈ 9.82 x 10^4 N

This is the weight of the Hubble Space Telescope at the given altitude above Earth's surface. It is important to remember that while the telescope has weight due to the gravitational pull, it is in freefall around the Earth, which is why it does not crash into the Earth's surface, thereby giving the experience of weightlessness.

Answer 2

To determine the weight of the Hubble Space Telescope in its orbit, we need to use Newton's Law of Universal Gravitation.

Step-by-step explanation:

To determine the weight of the Hubble Space Telescope in its orbit, we need to use Newton's Law of Universal Gravitation. The weight of an object in orbit can be calculated using the formula w = mg, where weight (w) equals mass (m) multiplied by the acceleration due to gravity (g).

In this case, the mass of the telescope is given as 11,600 kg. The acceleration due to gravity in orbit is calculated using the formula g = G * (Mearth / R²), where G is the gravitational constant, Mearth is the mass of the Earth, and R is the distance from the center of the Earth to the orbit of the telescope.

Plugging in the given values for Mearth and R, we can calculate g. Then, multiplying the mass of the telescope by g will give us the weight of the telescope in its orbit.