Question

A 2170 kg space station orbits Earth at an altitude of 5.27 x 10^5 m. Find the magnitude of the force with which the space station attracts Earth. The mass and mean radius of Earth are 5.98 x 10^24 kg and 6.37 x 10^6 m, respectively.

Answer 1

Answer:

F = 18195.59 N or F = 18196 rounded up

Explanation:

force = GMm/d^2

G = 6.67x10^-11

M = 5.98x10^24 kg

m = 2170kg

d = 6370000 + 527000 = 6897000m

putting all values   (6.67x10^-11)(5.98x10^24)(2170)/(6897000^2) = 18195.59....

Answer 2

The magnitude of the force with which the space station attracts Earth is about 1.82 × 10⁴ Newton

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Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows:

$\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }$

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem !

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Given:

mass of space station = m = 2170 kg

radius of the orbit = R = 5.27 × 10⁵ + 6.37 × 10⁶ = 6.897 × 10⁶ m/s

mass of Earth = M = 5.98 × 10²⁴ kg

Asked:

Gravitational Force = F = ?

Solution:

$F = G \frac{M.m}{R^2}$

$F = 6.67 \times 10^{-11} \times \frac{5.98 \times 10^{24} \times 2170}{(6.897 \times 10^6)^2}$

$F \approx 1.82 \times 10^4 \texttt{ Newton}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields

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Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant