Question

Law of Universal Gravitation

mass of: radius of:
Earth - 5.98 x 10²⁴ kg Earth - 6.38 x 10⁶ m
Jupiter - 1.91 x 10²⁷ kg Jupiter - 7.14 x 10⁷ m
Mars - 6.43 x 10²³ kg Mars - 3.40 x 10⁶ m
Mercury -3.32 x 10²³ kg Mercury - 2.44 x 10⁶ m
moon - 7.36 x 10²² kg Neptune - 2.43 x 10⁷ m
Neptune - 1.03 x 10²⁶ kg sun - 7.00 x 10⁸ m
Saturn - 5.68 x 10²⁶ kg Uranus - 2.61 x 10⁷ m
sun -1.99 x 10³⁰ kg Venus - 6.05 x 10⁶ m
Uranus -8.74 x 10²⁵ kg
Venus - 4.89 x 10²⁴ kg
distance from Earth to the sun - 1.50 x 10¹¹ m distance from Saturn to the sun -1.43 x 10 ¹² m
distance from Earth to the moon -3.84 x 10⁸ m
1 pound = 4.545 newtons 1 meter = 3.28 feet 1 mile = 1609 meters
How much would a 70.0-kg person weigh on Mercury?

Answer 1

To calculate the weight of a person on Mercury, we can use Newton's Law of Universal Gravitation. First, we need to find the mass of Mercury using the formula g = G * (M / r^2). Once we have the mass of Mercury, we can use the formula F = (G * m1 * m2)/ r^2 to calculate the weight of the person on Mercury.

Step-by-step explanation:

To calculate the weight of a person on Mercury, we can use Newton's Law of Universal Gravitation. The formula is:
F = G * (m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

First, we need to find the mass of Mercury. Given that the mean diameter of Mercury is 4.88 × 10^6 m and the acceleration due to gravity at its surface is 3.78 m/s^2, we can use the formula:
g = G * (M / r^2)
Where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of Mercury, and r is the radius of Mercury.

By rearranging the formula, we can solve for M:
M = g * (r^2) / G
Plugging in the values, we get:
M = (3.78 * (4.88 × 10^6)^2) / (6.67 × 10^-11)

Calculating the above expression will give us the mass of Mercury. Once we have the mass of Mercury, we can use the formula:
F = G * (m1 * m2) / r^2
To calculate the weight of the person on Mercury. Plugging in the values, we can find the weight of the 70.0-kg person on Mercury.